center of gravity vs center of mass
TRANSCRIPT
-
7/30/2019 Center of Gravity vs Center of Mass
1/25
1
Center of Gravity vs Center of Mass
The center of mass and center of gravity are two concepts frequently encounters in the study of physic
These are also concepts that are most confused between, and often people use them interchangeably, whic
is erroneous. This article will explain the difference between center of mass and center of gravity and l
readers have a clearer understanding.
Center of mass of a rigid body is also called its center of gravity. However, this is true only in circumstance
where gravitational forces are uniform. Since gravitational force of earth is taken to be uniform at all place
the center of mass and the center of gravity are effectively same. Center of gravity is defined as the averag
location of the weight of an object. In the case of earth, since gravitational pull is same at all places, each maelement would weigh the same so the center of gravity is identical to the center of mass. However, in a no
uniform gravitational field, the center of gravity is not the same as the center of mass. Center of mass is
fixed property which is the average location of the mass of the body. It has nothing to do with gravity.
In the case of artificial satellites, gravitational pull is not uniform and in such conditions, center of gravi
refers to the mean location of the gravitational pull acting on the body of the satellite. This obviously resul
in slight difference between its center of mass and the center of gravity.
The center of mass of a body does not coincide with its center of gravity and this is a property that
exploited by sport car makers to keep the center of mass as low as possible to make the car have a bett
balance. The concept of difference between center of mass and center of gravity is also exploited by hig
jumpers when they perform Fosbury Flop and bend their bodies in such a way so as to clear the high ba
without touching it. They bend their bodies in such a way that they clear the bar despite their center of manot clearing the bar.
Center of Mass vs Center of Gravity
Center of mass and center of gravity are often taken as one in the study of physicsbecause of the uniform gravitational pull of earth.
However, in non uniform gravitational fields, center of mass is away from the centerof gravity
This fact is used by designers to make cars with a very low center of mass so as togive better balance.
OR
The center of mass is a geometrical measurement considering only mass distribution and not weightdistribution. Centre of mass is a mathematically defined point for an object, which is unaffected by external
field/force unless it is deformed by the external field/ force.
However, centre of gravity is a point from where net weight is assumed to act. Clearly it depends on gravity
which is an external force.
Normally, centre of mass and gravity are same, this is because Earths gravitational field is uniform.
Now, consider a situation in which gravitational field is non-uniform. Also, imagine a very long uniform rod
If you consider two parts of rod with same mass, the force of gravitation (weight) will be different on both
instead of same mass. Due to which, its centre of gravity and center of mass will be different.
Because of this, the position of centre of mass of this rod will be different from that of centre of weight.
Normally, on Earth gravity is uniform so center of mass and gravity are same for most of the objects. But
again be cautious!
APPLICATIONS
Finding the center of mass of a system is very useful in observing and recording many physical phenomena
Mathematically, the center of mass of a system is merely the result of a summation or integral where the
masses of differing points times their distance from the 'center' squared, and then an infinite amount of the
-
7/30/2019 Center of Gravity vs Center of Mass
2/25
2
values are taken, the integral, and added together. Everyday activities can be explained better with the
concept of the center of mass.Gravity
The acceleration due to the gravitational force between an object and the earth is considered to be 9.8m/s^
or 32ft/s^2. Many people go under the assumption that everything in the earth's atmosphere is thought to
accelerate at this speed downwards, but it's untrue. This constant of gravity is the acceleration that the
center of mass of a system moves with, and not everything within that system has to move with that
acceleration. For instance, if a meter stick is raised about 40 degrees to the horizontal and a penny is atop th
highest point of the meter stick, the two objects will not fall at the same speed. The meter stick will fall fastein a vacuum, because the penny is part of the meter stick to begin with and then when the meter stick is
dropped, the center of mass travels faster than the penny, making it very evident as the penny just falls shor
of the same speed of the meter stick.
The Human Body
When jumping in the air, one would assume that the entire weight of the body has to lifted uniformly, but it
not true. The body has a center of mass just like anything else, and with the ability of the body to stretch, th
total height of someones jump is not necessarily the same height as the weight of their body. Usually when
someone jumps up they squat down to gain force through their legs and the ground, and while jumping,
stretch their arm up to it's highest point. The center of mass is usually around the waist(depends upon the
individual), thereby letting the jumper travel a larger distance upward without doing as much work. A grea
representation of the center of mass is the high jumper and how, through proper technique, they can elevattheir center of mass over the bar while letting the rest of their body just flex around the bar, creating a
technique that enables less work, and thereby a greater vertical distance to be achieved. When lifting a heav
object, one has the tendency to lean in the opposite direction of side where the object is being held. This is
because the body wants to achieve a balance that can enable it to move more uniformly. The center of mass
originally symmetrical with the body, but when, say a suitcase, is lifted with one arm, the body tends to lean
in the opposite direction, as to reform the center of mass with this new object introduced into the system.
Center of mass
Inphysics, the center of mass, or barycenter, of a distribution of mass in space is the unique point where
the weighted relative position of the distributed mass sums to zero. The distribution of mass is balancedaround the center of mass and the average of the weighted position coordinates of the distributed mass
defines its coordinates. Calculations inmechanicsare simplified when formulated with respect to the cente
of mass.
In the case of a singlerigid body, the center of mass is fixed in relation to the body, and if the body has
uniform density, it will be located at thecentroid. The center of mass may be located outside the physical
body, as is sometimes the case forhollowor open-shaped objects, such as ahorseshoe. In the case of a
distribution of separate bodies, such as theplanetsof theSolar System, the center of mass may not
correspond to the position of any individual member of the system.
The center of mass is a useful reference point for calculations inmechanicsthat involve masses distributed
space, such as thelinearandangular momentumof planetary bodies andrigid body dynamics. Inorbital
mechanics, the equations of motion of planets are formulated aspoint masseslocated at the centers of massThecenter of mass frameis aninertial framein which the center of mass of a system is at rest at with respe
the origin of the coordinate system.
History
The concept of "center of mass" in the form of the "center of gravity" was first introduced by the ancient
Greek physicist, mathematician, and engineerArchimedes of Syracuse. He worked with simplified
assumptions about gravity that amount to a uniform field, thus arriving at the mathematical properties of
what we now call the center of mass. Archimedes showed that thetorqueexerted on aleverby weights
resting at various points along the lever is the same as what it would be if all of the weights were moved to
single point their center of mass. In work on floating bodies he demonstrated that the orientation of a
http://en.wikipedia.org/wiki/Physicshttp://en.wikipedia.org/wiki/Physicshttp://en.wikipedia.org/wiki/Physicshttp://en.wikipedia.org/wiki/Mechanicshttp://en.wikipedia.org/wiki/Mechanicshttp://en.wikipedia.org/wiki/Mechanicshttp://en.wikipedia.org/wiki/Rigid_bodyhttp://en.wikipedia.org/wiki/Rigid_bodyhttp://en.wikipedia.org/wiki/Rigid_bodyhttp://en.wikipedia.org/wiki/Centroidhttp://en.wikipedia.org/wiki/Centroidhttp://en.wikipedia.org/wiki/Centroidhttp://en.wikipedia.org/wiki/Hollowhttp://en.wikipedia.org/wiki/Hollowhttp://en.wikipedia.org/wiki/Hollowhttp://en.wikipedia.org/wiki/Horseshoehttp://en.wikipedia.org/wiki/Horseshoehttp://en.wikipedia.org/wiki/Horseshoehttp://en.wikipedia.org/wiki/Planetshttp://en.wikipedia.org/wiki/Planetshttp://en.wikipedia.org/wiki/Planetshttp://en.wikipedia.org/wiki/Solar_Systemhttp://en.wikipedia.org/wiki/Solar_Systemhttp://en.wikipedia.org/wiki/Solar_Systemhttp://en.wikipedia.org/wiki/Mechanicshttp://en.wikipedia.org/wiki/Mechanicshttp://en.wikipedia.org/wiki/Mechanicshttp://en.wikipedia.org/wiki/Momentumhttp://en.wikipedia.org/wiki/Momentumhttp://en.wikipedia.org/wiki/Momentumhttp://en.wikipedia.org/wiki/Angular_momentumhttp://en.wikipedia.org/wiki/Angular_momentumhttp://en.wikipedia.org/wiki/Angular_momentumhttp://en.wikipedia.org/wiki/Rigid_body_dynamicshttp://en.wikipedia.org/wiki/Rigid_body_dynamicshttp://en.wikipedia.org/wiki/Rigid_body_dynamicshttp://en.wikipedia.org/wiki/Orbital_mechanicshttp://en.wikipedia.org/wiki/Orbital_mechanicshttp://en.wikipedia.org/wiki/Orbital_mechanicshttp://en.wikipedia.org/wiki/Orbital_mechanicshttp://en.wikipedia.org/wiki/Point_masshttp://en.wikipedia.org/wiki/Point_masshttp://en.wikipedia.org/wiki/Point_masshttp://en.wikipedia.org/wiki/Center_of_mass_framehttp://en.wikipedia.org/wiki/Center_of_mass_framehttp://en.wikipedia.org/wiki/Center_of_mass_framehttp://en.wikipedia.org/wiki/Inertial_framehttp://en.wikipedia.org/wiki/Inertial_framehttp://en.wikipedia.org/wiki/Inertial_framehttp://en.wikipedia.org/wiki/Archimedeshttp://en.wikipedia.org/wiki/Archimedeshttp://en.wikipedia.org/wiki/Archimedeshttp://en.wikipedia.org/wiki/Torquehttp://en.wikipedia.org/wiki/Torquehttp://en.wikipedia.org/wiki/Torquehttp://en.wikipedia.org/wiki/Leverhttp://en.wikipedia.org/wiki/Leverhttp://en.wikipedia.org/wiki/Leverhttp://en.wikipedia.org/wiki/Leverhttp://en.wikipedia.org/wiki/Torquehttp://en.wikipedia.org/wiki/Archimedeshttp://en.wikipedia.org/wiki/Inertial_framehttp://en.wikipedia.org/wiki/Center_of_mass_framehttp://en.wikipedia.org/wiki/Point_masshttp://en.wikipedia.org/wiki/Orbital_mechanicshttp://en.wikipedia.org/wiki/Orbital_mechanicshttp://en.wikipedia.org/wiki/Rigid_body_dynamicshttp://en.wikipedia.org/wiki/Angular_momentumhttp://en.wikipedia.org/wiki/Momentumhttp://en.wikipedia.org/wiki/Mechanicshttp://en.wikipedia.org/wiki/Solar_Systemhttp://en.wikipedia.org/wiki/Planetshttp://en.wikipedia.org/wiki/Horseshoehttp://en.wikipedia.org/wiki/Hollowhttp://en.wikipedia.org/wiki/Centroidhttp://en.wikipedia.org/wiki/Rigid_bodyhttp://en.wikipedia.org/wiki/Mechanicshttp://en.wikipedia.org/wiki/Physics -
7/30/2019 Center of Gravity vs Center of Mass
3/25
3
floating object is the one that makes its center of mass as low as possible. He developed mathematical
techniques for finding the centers of mass of objects of uniform density of various well-defined shapes.[1]
Later mathematicians who developed the theory of the center of mass includePappus of Alexandria,Guido
Ubaldi,Francesco Maurolico,[2]Federico Commandino,[3]Simon Stevin,[4]Luca Valerio,[5]Jean-Charles de la
Faille,Paul Guldin,[6]John Wallis,Louis Carr,Pierre Varignon, andAlexis Clairaut.[7]
Newton's second lawis reformulated with respect to the center of mass inEuler's first law.[8]
Diagram of an educational toy that balances on a point: the CM (C) settles below its support (P)[edit]Definition of center of mass
The center of mass is the unique point at the center of a distribution of mass in space that has the property
that the weighted position vectors relative to this point sum to zero.
[edit]A system of particles
In the case of a system of particles Pi, i=1, ..., n, each with mass mi that are located in space with
coordinates ri, i=1,...,n,, the coordinates R of the center of mass satisfy the condition,
Solve this equation for R to obtain the formula,
where M is the sum of the masses of all of the particles.
[edit]A continuous volume
If the mass distribution is continuous with the density (r) within a volume V, then the integral of theweighted position coordinates of the points in this volume relative to the center of mass R is zero, that is
Solve this equation for the coordinates R to obtain
where M is the total mass in the volume.
If a continuous mass distribution has uniformdensity, which means is constant, then the center of mass isthe same as thecentroidof the volume.[9]
[edit]Barycentric coordinates
The coordinates R of the center of mass of a two-particle system, P1 and P2, with masses m1 and m2 is given
by
http://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEShore20089.E2.80.9311-1http://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEShore20089.E2.80.9311-1http://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEShore20089.E2.80.9311-1http://en.wikipedia.org/wiki/Pappus_of_Alexandriahttp://en.wikipedia.org/wiki/Pappus_of_Alexandriahttp://en.wikipedia.org/wiki/Pappus_of_Alexandriahttp://en.wikipedia.org/wiki/Guido_Ubaldihttp://en.wikipedia.org/wiki/Guido_Ubaldihttp://en.wikipedia.org/wiki/Guido_Ubaldihttp://en.wikipedia.org/wiki/Guido_Ubaldihttp://en.wikipedia.org/wiki/Francesco_Maurolicohttp://en.wikipedia.org/wiki/Francesco_Maurolicohttp://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEBaron200491.E2.80.9394-2http://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEBaron200491.E2.80.9394-2http://en.wikipedia.org/wiki/Federico_Commandinohttp://en.wikipedia.org/wiki/Federico_Commandinohttp://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEBaron200494.E2.80.9396-3http://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEBaron200494.E2.80.9396-3http://en.wikipedia.org/wiki/Simon_Stevinhttp://en.wikipedia.org/wiki/Simon_Stevinhttp://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEBaron200496.E2.80.93101-4http://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEBaron200496.E2.80.93101-4http://en.wikipedia.org/wiki/Luca_Valeriohttp://en.wikipedia.org/wiki/Luca_Valeriohttp://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEBaron2004101.E2.80.93106-5http://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEBaron2004101.E2.80.93106-5http://en.wikipedia.org/wiki/Jean-Charles_de_la_Faillehttp://en.wikipedia.org/wiki/Jean-Charles_de_la_Faillehttp://en.wikipedia.org/wiki/Jean-Charles_de_la_Faillehttp://en.wikipedia.org/wiki/Jean-Charles_de_la_Faillehttp://en.wikipedia.org/wiki/Paul_Guldinhttp://en.wikipedia.org/wiki/Paul_Guldinhttp://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEMancosu199956.E2.80.9361-6http://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEMancosu199956.E2.80.9361-6http://en.wikipedia.org/wiki/John_Wallishttp://en.wikipedia.org/wiki/John_Wallishttp://en.wikipedia.org/wiki/John_Wallishttp://en.wikipedia.org/wiki/Louis_Carr%C3%A9_(mathematician)http://en.wikipedia.org/wiki/Louis_Carr%C3%A9_(mathematician)http://en.wikipedia.org/wiki/Louis_Carr%C3%A9_(mathematician)http://en.wikipedia.org/wiki/Pierre_Varignonhttp://en.wikipedia.org/wiki/Pierre_Varignonhttp://en.wikipedia.org/wiki/Pierre_Varignonhttp://en.wikipedia.org/wiki/Alexis_Clairauthttp://en.wikipedia.org/wiki/Alexis_Clairauthttp://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEWalton18552-7http://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEWalton18552-7http://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEWalton18552-7http://en.wikipedia.org/wiki/Newton%27s_second_lawhttp://en.wikipedia.org/wiki/Newton%27s_second_lawhttp://en.wikipedia.org/wiki/Euler%27s_laws#Euler.27s_first_lawhttp://en.wikipedia.org/wiki/Euler%27s_laws#Euler.27s_first_lawhttp://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEBeatty200629-8http://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEBeatty200629-8http://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEBeatty200629-8http://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit§ion=2http://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit§ion=2http://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit§ion=2http://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit§ion=3http://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit§ion=3http://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit§ion=3http://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit§ion=4http://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit§ion=4http://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit§ion=4http://en.wikipedia.org/wiki/Densityhttp://en.wikipedia.org/wiki/Densityhttp://en.wikipedia.org/wiki/Densityhttp://en.wikipedia.org/wiki/Centroidhttp://en.wikipedia.org/wiki/Centroidhttp://en.wikipedia.org/wiki/Centroidhttp://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTELevi200985-9http://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTELevi200985-9http://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTELevi200985-9http://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit§ion=5http://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit§ion=5http://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit§ion=5http://en.wikipedia.org/wiki/File:CoG_stable.svghttp://en.wikipedia.org/wiki/File:CoG_stable.svghttp://en.wikipedia.org/wiki/File:CoG_stable.svghttp://en.wikipedia.org/wiki/File:CoG_stable.svghttp://en.wikipedia.org/wiki/File:CoG_stable.svghttp://en.wikipedia.org/wiki/File:CoG_stable.svghttp://en.wikipedia.org/wiki/File:CoG_stable.svghttp://en.wikipedia.org/wiki/File:CoG_stable.svghttp://en.wikipedia.org/wiki/File:CoG_stable.svghttp://en.wikipedia.org/wiki/File:CoG_stable.svghttp://en.wikipedia.org/wiki/File:CoG_stable.svghttp://en.wikipedia.org/wiki/File:CoG_stable.svghttp://en.wikipedia.org/wiki/File:CoG_stable.svghttp://en.wikipedia.org/wiki/File:CoG_stable.svghttp://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit§ion=5http://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTELevi200985-9http://en.wikipedia.org/wiki/Centroidhttp://en.wikipedia.org/wiki/Densityhttp://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit§ion=4http://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit§ion=3http://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit§ion=2http://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEBeatty200629-8http://en.wikipedia.org/wiki/Euler%27s_laws#Euler.27s_first_lawhttp://en.wikipedia.org/wiki/Newton%27s_second_lawhttp://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEWalton18552-7http://en.wikipedia.org/wiki/Alexis_Clairauthttp://en.wikipedia.org/wiki/Pierre_Varignonhttp://en.wikipedia.org/wiki/Louis_Carr%C3%A9_(mathematician)http://en.wikipedia.org/wiki/John_Wallishttp://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEMancosu199956.E2.80.9361-6http://en.wikipedia.org/wiki/Paul_Guldinhttp://en.wikipedia.org/wiki/Jean-Charles_de_la_Faillehttp://en.wikipedia.org/wiki/Jean-Charles_de_la_Faillehttp://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEBaron2004101.E2.80.93106-5http://en.wikipedia.org/wiki/Luca_Valeriohttp://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEBaron200496.E2.80.93101-4http://en.wikipedia.org/wiki/Simon_Stevinhttp://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEBaron200494.E2.80.9396-3http://en.wikipedia.org/wiki/Federico_Commandinohttp://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEBaron200491.E2.80.9394-2http://en.wikipedia.org/wiki/Francesco_Maurolicohttp://en.wikipedia.org/wiki/Guido_Ubaldihttp://en.wikipedia.org/wiki/Guido_Ubaldihttp://en.wikipedia.org/wiki/Pappus_of_Alexandriahttp://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEShore20089.E2.80.9311-1 -
7/30/2019 Center of Gravity vs Center of Mass
4/25
4
Let the percentage of the total mass divided between these two particles vary from 100% P1 and 0%
P2 through 50% P1 and 50% P2 to 0% P1 and 100% P2, then the center of mass R moves along the line from
P1 to P2. The percentages of mass at each point can be viewed as projective coordinates of the pointR on th
line, and are termed barycentric coordinates. This can be generalized to three points and four points to
define projective coordinates in the plane, and in space, respectively.
[edit]Systems with periodic boundary conditions
For particles in a system withperiodic boundary conditionstwo particles can be neighbors even though the
are on opposite sides of the system. This occurs often inmolecular dynamicssimulations, for example, in
which clusters form at random locations and sometimes neighboring atoms cross the periodic boundary.When a cluster straddles the periodic boundary, a naive calculation of the center of mass will be incorrect. A
generalized method for calculating the center of mass for periodic systems is to treat each
coordinate,xandyand/orz, as if it were on a circle instead of a line.[10]The calculation takes every
particle'sxcoordinate and maps it to an angle,
wherexmax is the system size in thexdirection. From this angle, two new points can be generated:
In the plane, these coordinates lie on a circle of radiusxmax. From the collection of and valuesfrom all the particles, the averages and are calculated. These values are mapped back into a new
angle, , from which thexcoordinate of the center of mass can be obtained:
The process can be repeated for all dimensions of the system to determine the complete center of mass. The
utility of the algorithm is that it allows the mathematics to determine where the "best" center of mass is,
instead of guessing or usingcluster analysisto "unfold" a cluster straddling the periodic boundaries. It must
be noted that if both average values are zero, , then is undefined. This is a correct result,
because it only occurs when all particles are exactly evenly spaced. In that condition, theirxcoordinates aremathematically identical in aperiodic system.
[edit]Center of gravity
Center of gravity is the point in a body around which theresultant torquedue to gravity forces vanish. Near
the surface of the earth, where the gravity acts downward as a parallel force field, the center of gravity and
the center of mass are the same.
The study of the dynamics of aircraft, vehicles and vessels assumes that the system moves in near-earth
gravity, and therefore the terms center of gravity and center of mass are used interchangeably.
In physics the benefits of using the center of mass to model a mass distribution can be seen by considering
theresultantof the gravity forces on a continuous body. Consider a body of volume V with density (r) at
each pointr in the volume. In a parallel gravity field the force fat each pointr is given by,
where dm is the mass at the pointr, g is the acceleration of gravity, and kis a unit vector defining the vertic
direction. Choose a reference pointR in the volume and compute theresultant forceand torque at this point
and
If the reference pointR is chosen so that it is the center of mass, then
http://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit§ion=6http://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit§ion=6http://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit§ion=6http://en.wikipedia.org/wiki/Periodic_boundary_conditionshttp://en.wikipedia.org/wiki/Periodic_boundary_conditionshttp://en.wikipedia.org/wiki/Periodic_boundary_conditionshttp://en.wikipedia.org/wiki/Molecular_dynamicshttp://en.wikipedia.org/wiki/Molecular_dynamicshttp://en.wikipedia.org/wiki/Molecular_dynamicshttp://en.wikipedia.org/wiki/Center_of_mass#cite_note-10http://en.wikipedia.org/wiki/Center_of_mass#cite_note-10http://en.wikipedia.org/wiki/Center_of_mass#cite_note-10http://en.wikipedia.org/wiki/Cluster_analysishttp://en.wikipedia.org/wiki/Cluster_analysishttp://en.wikipedia.org/wiki/Cluster_analysishttp://en.wikipedia.org/wiki/Periodic_boundary_conditions#Practical_implementation:_continuity_and_the_minimum_image_conventionhttp://en.wikipedia.org/wiki/Periodic_boundary_conditions#Practical_implementation:_continuity_and_the_minimum_image_conventionhttp://en.wikipedia.org/wiki/Periodic_boundary_conditions#Practical_implementation:_continuity_and_the_minimum_image_conventionhttp://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit§ion=7http://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit§ion=7http://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit§ion=7http://en.wikipedia.org/wiki/Resultant_forcehttp://en.wikipedia.org/wiki/Resultant_forcehttp://en.wikipedia.org/wiki/Resultant_forcehttp://en.wikipedia.org/wiki/Resultant_forcehttp://en.wikipedia.org/wiki/Resultant_forcehttp://en.wikipedia.org/wiki/Resultant_forcehttp://en.wikipedia.org/wiki/Resultant_forcehttp://en.wikipedia.org/wiki/Resultant_forcehttp://en.wikipedia.org/wiki/Resultant_forcehttp://en.wikipedia.org/wiki/Resultant_forcehttp://en.wikipedia.org/wiki/Resultant_forcehttp://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit§ion=7http://en.wikipedia.org/wiki/Periodic_boundary_conditions#Practical_implementation:_continuity_and_the_minimum_image_conventionhttp://en.wikipedia.org/wiki/Cluster_analysishttp://en.wikipedia.org/wiki/Center_of_mass#cite_note-10http://en.wikipedia.org/wiki/Molecular_dynamicshttp://en.wikipedia.org/wiki/Periodic_boundary_conditionshttp://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit§ion=6 -
7/30/2019 Center of Gravity vs Center of Mass
5/25
5
which means the resultant torque T=0. Because the resultant torque is zero the body will move as though it
is a particle with its mass concentrated at the center of mass.
By selecting the center of gravity as the reference point for a rigid body, the gravity forces will not cause the
body to rotate, which means weight of the body can be considered to be concentrated at the center of mass.
[edit]Linear and angular momentum
The linear and angular momentum of a collection of particles can be simplified by measuring the position
and velocity of the particles relative to the center of mass. Let the system of particles Pi, i=1,...,n be located athe coordinates ri and velocities vi. Select a reference pointR and compute the relative position and velocity
vectors,
The total linear and angular momentum vectors relative to the reference pointR are
and
IfR is chosen as the center of mass these equations simplify to
Newton's laws of motion require that for any system with no external forces the momentum of the system i
constant, which means the center of mass moves with constant velocity. This applies for all systems with
classical internal forces, including magnetic fields, electric fields, chemical reactions, and so on. More
formally, this is true for any internal forces that satisfyNewton's Third Law.[11]
[edit]Locating the center of mass
Main article:Locating the center of mass
Plumb line method
The experimental determination of the center of mass of a body uses gravity forces on the body and relies o
the fact that in the parallel gravity field near the surface of the earth the center of mass is the same as the
center of gravity.
http://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit§ion=8http://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit§ion=8http://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit§ion=8http://en.wikipedia.org/wiki/Newton%27s_Third_Lawhttp://en.wikipedia.org/wiki/Newton%27s_Third_Lawhttp://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEKleppnerKolenkow1973117-11http://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEKleppnerKolenkow1973117-11http://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEKleppnerKolenkow1973117-11http://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit§ion=9http://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit§ion=9http://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit§ion=9http://en.wikipedia.org/wiki/Locating_the_center_of_masshttp://en.wikipedia.org/wiki/Locating_the_center_of_masshttp://en.wikipedia.org/wiki/Locating_the_center_of_masshttp://en.wikipedia.org/wiki/File:Center_gravity_2.svghttp://en.wikipedia.org/wiki/File:Center_gravity_2.svghttp://en.wikipedia.org/wiki/File:Center_gravity_2.svghttp://en.wikipedia.org/wiki/File:Center_gravity_2.svghttp://en.wikipedia.org/wiki/File:Center_gravity_2.svghttp://en.wikipedia.org/wiki/File:Center_gravity_2.svghttp://en.wikipedia.org/wiki/File:Center_gravity_2.svghttp://en.wikipedia.org/wiki/File:Center_gravity_2.svghttp://en.wikipedia.org/wiki/File:Center_gravity_2.svghttp://en.wikipedia.org/wiki/File:Center_gravity_2.svghttp://en.wikipedia.org/wiki/File:Center_gravity_2.svghttp://en.wikipedia.org/wiki/File:Center_gravity_2.svghttp://en.wikipedia.org/wiki/File:Center_gravity_2.svghttp://en.wikipedia.org/wiki/File:Center_gravity_2.svghttp://en.wikipedia.org/wiki/Locating_the_center_of_masshttp://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit§ion=9http://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEKleppnerKolenkow1973117-11http://en.wikipedia.org/wiki/Newton%27s_Third_Lawhttp://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit§ion=8 -
7/30/2019 Center of Gravity vs Center of Mass
6/25
6
The center of mass of a body with an axis of symmetry and constant density must lie on this axis. Thus, the
center of mass of a circular cylinder of constant density has its center of mass on the axis of the cylinder. In
the same way, the center of mass of a spherically symmetric body of constant density is at the center of the
sphere. In general, for any symmetry of a body, its center of mass will be a fixed point of that symmetry.[12]
[edit]In two dimensions
An experimental method for locating the center of mass is to suspend the object from two locations and to
dropplumb linesfrom the suspension points. The intersection of the two lines is the center of mass.[13]
The shape of an object might already be mathematically determined, but it may be too complex to use a
known formula. In this case, one can subdivide the complex shape into simpler, more elementary shapes,whose centers of mass are easy to find. If the total mass and center of mass can be determined for each area
then the center of mass of the whole is the weighted average of the centers.[14]This method can even work
for objects with holes, which can be accounted for as negative masses.[15]
A direct development of theplanimeterknown as an integraph, or integerometer, can be used to establish
the position of thecentroidor center of mass of an irregular two-dimensional shape. This method can be
applied to a shape with an irregular, smooth or complex boundary where other methods are too difficult. It
was regularly used by ship builders to compare with the requireddisplacementandcentre of buoyancyof a
ship, and ensure it would not capsize.[16][17]
[edit]In three dimensions
An experimental method to locate the three dimensional coordinates of the center of mass begins by
supporting the object at three points and measuring the forces, F1, F2, and F3that resist the weight of theobject, W= -Wk(kis the unit vector in the vertical direction). Letr1, r2, and r3 be the position coordinates of
the support points, then the coordinates Rof the center of mass satisfy the condition that the resultant torqu
is zero,
or
This equation yields the coordinates of the center of mass R* in the horizontal plane as,
The center of mass lies on the vertical line L, given by
The three dimensional coordinates of the center of mass are determined by performing this experiment
twice with the object positioned so that these forces are measured for two different horizontal planes
through the object. The center of mass will be the intersection of the two lines L1 and L2 obtained from the
two experiments.
[edit]Applications
Estimated center of mass/gravity (blue sphere) of a gymnast at the end of performing a cartwheel. Notice
center is outside the body in this position.
http://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEFeynmanLeightonSands196319.3-12http://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEFeynmanLeightonSands196319.3-12http://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEFeynmanLeightonSands196319.3-12http://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit§ion=10http://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit§ion=10http://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit§ion=10http://en.wikipedia.org/wiki/Plumb_linehttp://en.wikipedia.org/wiki/Plumb_linehttp://en.wikipedia.org/wiki/Plumb_linehttp://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEKleppnerKolenkow1973119.E2.80.93120-13http://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEKleppnerKolenkow1973119.E2.80.93120-13http://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEKleppnerKolenkow1973119.E2.80.93120-13http://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEFeynmanLeightonSands196319.1.E2.80.9319.2-14http://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEFeynmanLeightonSands196319.1.E2.80.9319.2-14http://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEFeynmanLeightonSands196319.1.E2.80.9319.2-14http://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEHamill200920.E2.80.9321-15http://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEHamill200920.E2.80.9321-15http://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEHamill200920.E2.80.9321-15http://en.wikipedia.org/wiki/Planimeterhttp://en.wikipedia.org/wiki/Planimeterhttp://en.wikipedia.org/wiki/Planimeterhttp://en.wikipedia.org/wiki/Centroidhttp://en.wikipedia.org/wiki/Centroidhttp://en.wikipedia.org/wiki/Centroidhttp://en.wikipedia.org/wiki/Displacement_(ship)http://en.wikipedia.org/wiki/Displacement_(ship)http://en.wikipedia.org/wiki/Displacement_(ship)http://en.wikipedia.org/wiki/Centre_of_buoyancyhttp://en.wikipedia.org/wiki/Centre_of_buoyancyhttp://en.wikipedia.org/wiki/Centre_of_buoyancyhttp://en.wikipedia.org/wiki/Center_of_mass#cite_note-16http://en.wikipedia.org/wiki/Center_of_mass#cite_note-16http://en.wikipedia.org/wiki/Center_of_mass#cite_note-16http://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit§ion=11http://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit§ion=11http://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit§ion=11http://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit§ion=12http://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit§ion=12http://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit§ion=12http://en.wikipedia.org/wiki/File:CofM.jpghttp://en.wikipedia.org/wiki/File:CofM.jpghttp://en.wikipedia.org/wiki/File:CofM.jpghttp://en.wikipedia.org/wiki/File:CofM.jpghttp://en.wikipedia.org/wiki/File:CofM.jpghttp://en.wikipedia.org/wiki/File:CofM.jpghttp://en.wikipedia.org/wiki/File:CofM.jpghttp://en.wikipedia.org/wiki/File:CofM.jpghttp://en.wikipedia.org/wiki/File:CofM.jpghttp://en.wikipedia.org/wiki/File:CofM.jpghttp://en.wikipedia.org/wiki/File:CofM.jpghttp://en.wikipedia.org/wiki/File:CofM.jpghttp://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit§ion=12http://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit§ion=11http://en.wikipedia.org/wiki/Center_of_mass#cite_note-16http://en.wikipedia.org/wiki/Center_of_mass#cite_note-16http://en.wikipedia.org/wiki/Centre_of_buoyancyhttp://en.wikipedia.org/wiki/Displacement_(ship)http://en.wikipedia.org/wiki/Centroidhttp://en.wikipedia.org/wiki/Planimeterhttp://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEHamill200920.E2.80.9321-15http://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEFeynmanLeightonSands196319.1.E2.80.9319.2-14http://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEKleppnerKolenkow1973119.E2.80.93120-13http://en.wikipedia.org/wiki/Plumb_linehttp://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit§ion=10http://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEFeynmanLeightonSands196319.3-12 -
7/30/2019 Center of Gravity vs Center of Mass
7/25
7
Engineers try to design asports car's center of mass as low as possible to make the carhandlebetter.
Whenhigh jumpersperform a "Fosbury Flop", they bend their body in such a way that it clears the bar whil
its center of mass does not.[18]
[edit]Aeronautics
Main article:Center of gravity of an aircraft
The center of mass is an important point on anaircraft, which significantly affects the stability of the aircraf
To ensure the aircraft is stable enough to be safe to fly, the center of mass must fall within specified limits. I
the center of mass is ahead of the forward limit, the aircraft will be less maneuverable, possibly to the point
of being unable to rotate for takeoff or flare for landing.[19]
If the center of mass is behind the aft limit, theaircraft will be more maneuverable, but also less stable, and possibly so unstable that it is impossible to fly.
The moment arm of theelevatorwill also be reduced, which makes it more difficult to recover from
astalledcondition.[20]
Forhelicoptersinhover, the center of mass is always directly below therotorhead. In forward flight, the
center of mass will move aft to balance the negative pitch torque produced by applyingcycliccontrol to
propel the helicopter forward; consequently a cruising helicopter flies "nose-down" in level flight.
[edit]Astronomy
Two bodies orbiting a barycenter inside one body
Main article:Barycentric coordinates (astronomy)
The center of mass plays an important role in astronomy and astrophysics, where it is commonly referred tas the barycenter. The barycenter is the point between two objects where they balance each other; it is the
center of mass where two or more celestial bodiesorbiteach other. When amoonorbits aplanet, or a plane
orbits astar, both bodies are actually orbiting around a point that lies away from the center of the primary
(larger) body.[21]For example, the Moon does not orbit the exact center of theEarth, but a point on a line
between the center of the Earth and the Moon, approximately 1,710 km (1062 miles) below the surface of
the Earth, where their respective masses balance. This is the point about which the Earth and Moon orbit as
they travel around theSun. If the masses are more similar, e.g.,Pluto and Charon, the barycenter will fall
outside both bodies.[edit]
Question: Center of Gravity DefinitionThe term "center of gravity" has implications for all things related to posture, including postural issues such
asswaybackand designingposture exerciseprograms and more.
The center of gravity is a theoretical place in your body where your mass is considered to concentrate.Answer:
What do I mean by that? Well, here on earth, weight and mass are pretty much the same thing.
You can think ofmassas how much resistance your body has when moving - or the force of inertia as it
applies to your weight. (In outer space, you become weightless, but your mass stays the same. This is
because in outer space the force of gravity does not act on your body.)
http://en.wikipedia.org/wiki/Sports_carhttp://en.wikipedia.org/wiki/Sports_carhttp://en.wikipedia.org/wiki/Sports_carhttp://en.wikipedia.org/wiki/Car_handlinghttp://en.wikipedia.org/wiki/Car_handlinghttp://en.wikipedia.org/wiki/Car_handlinghttp://en.wikipedia.org/wiki/High_jumphttp://en.wikipedia.org/wiki/High_jumphttp://en.wikipedia.org/wiki/High_jumphttp://en.wikipedia.org/wiki/Fosbury_Flophttp://en.wikipedia.org/wiki/Fosbury_Flophttp://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEVan_Pelt2005185-18http://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEVan_Pelt2005185-18http://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEVan_Pelt2005185-18http://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit§ion=13http://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit§ion=13http://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit§ion=13http://en.wikipedia.org/wiki/Center_of_gravity_of_an_aircrafthttp://en.wikipedia.org/wiki/Center_of_gravity_of_an_aircrafthttp://en.wikipedia.org/wiki/Center_of_gravity_of_an_aircrafthttp://en.wikipedia.org/wiki/Aircrafthttp://en.wikipedia.org/wiki/Aircrafthttp://en.wikipedia.org/wiki/Aircrafthttp://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEFederal_Aviation_Administration20071.4-19http://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEFederal_Aviation_Administration20071.4-19http://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEFederal_Aviation_Administration20071.4-19http://en.wikipedia.org/wiki/Elevator_(aircraft)http://en.wikipedia.org/wiki/Elevator_(aircraft)http://en.wikipedia.org/wiki/Elevator_(aircraft)http://en.wikipedia.org/wiki/Stall_(flight)http://en.wikipedia.org/wiki/Stall_(flight)http://en.wikipedia.org/wiki/Stall_(flight)http://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEFederal_Aviation_Administration20071.3-20http://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEFederal_Aviation_Administration20071.3-20http://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEFederal_Aviation_Administration20071.3-20http://en.wikipedia.org/wiki/Helicopterhttp://en.wikipedia.org/wiki/Helicopterhttp://en.wikipedia.org/wiki/Helicopterhttp://en.wikipedia.org/wiki/Hover_(helicopter)http://en.wikipedia.org/wiki/Hover_(helicopter)http://en.wikipedia.org/wiki/Hover_(helicopter)http://en.wikipedia.org/wiki/Rotorheadhttp://en.wikipedia.org/wiki/Rotorheadhttp://en.wikipedia.org/wiki/Rotorheadhttp://en.wikipedia.org/wiki/Helicopter_flight_controls#Cyclichttp://en.wikipedia.org/wiki/Helicopter_flight_controls#Cyclichttp://en.wikipedia.org/wiki/Helicopter_flight_controls#Cyclichttp://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit§ion=14http://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit§ion=14http://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit§ion=14http://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)http://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)http://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)http://en.wikipedia.org/wiki/Orbithttp://en.wikipedia.org/wiki/Orbithttp://en.wikipedia.org/wiki/Natural_satellitehttp://en.wikipedia.org/wiki/Natural_satellitehttp://en.wikipedia.org/wiki/Natural_satellitehttp://en.wikipedia.org/wiki/Planethttp://en.wikipedia.org/wiki/Planethttp://en.wikipedia.org/wiki/Planethttp://en.wikipedia.org/wiki/Starhttp://en.wikipedia.org/wiki/Starhttp://en.wikipedia.org/wiki/Starhttp://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEMurrayDermott199945.E2.80.9347-21http://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEMurrayDermott199945.E2.80.9347-21http://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEMurrayDermott199945.E2.80.9347-21http://en.wikipedia.org/wiki/Earthhttp://en.wikipedia.org/wiki/Earthhttp://en.wikipedia.org/wiki/Earthhttp://en.wikipedia.org/wiki/Sunhttp://en.wikipedia.org/wiki/Sunhttp://en.wikipedia.org/wiki/Sunhttp://en.wikipedia.org/wiki/Pluto#Charonhttp://en.wikipedia.org/wiki/Pluto#Charonhttp://en.wikipedia.org/wiki/Pluto#Charonhttp://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit§ion=15http://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit§ion=15http://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit§ion=15http://backandneck.about.com/od/posture/f/sway-back.htmhttp://backandneck.about.com/od/posture/f/sway-back.htmhttp://backandneck.about.com/od/posture/f/sway-back.htmhttp://backandneck.about.com/od/exerciseandsport/tp/Posture-Exercise.htmhttp://backandneck.about.com/od/exerciseandsport/tp/Posture-Exercise.htmhttp://backandneck.about.com/od/exerciseandsport/tp/Posture-Exercise.htmhttp://physics.about.com/od/glossary/g/mass.htmhttp://physics.about.com/od/glossary/g/mass.htmhttp://physics.about.com/od/glossary/g/mass.htmhttp://en.wikipedia.org/wiki/File:Orbit3.gifhttp://en.wikipedia.org/wiki/File:Orbit3.gifhttp://en.wikipedia.org/wiki/File:Orbit3.gifhttp://en.wikipedia.org/wiki/File:Orbit3.gifhttp://physics.about.com/od/glossary/g/mass.htmhttp://backandneck.about.com/od/exerciseandsport/tp/Posture-Exercise.htmhttp://backandneck.about.com/od/posture/f/sway-back.htmhttp://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit§ion=15http://en.wikipedia.org/wiki/Pluto#Charonhttp://en.wikipedia.org/wiki/Sunhttp://en.wikipedia.org/wiki/Earthhttp://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEMurrayDermott199945.E2.80.9347-21http://en.wikipedia.org/wiki/Starhttp://en.wikipedia.org/wiki/Planethttp://en.wikipedia.org/wiki/Natural_satellitehttp://en.wikipedia.org/wiki/Orbithttp://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)http://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit§ion=14http://en.wikipedia.org/wiki/Helicopter_flight_controls#Cyclichttp://en.wikipedia.org/wiki/Rotorheadhttp://en.wikipedia.org/wiki/Hover_(helicopter)http://en.wikipedia.org/wiki/Helicopterhttp://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEFederal_Aviation_Administration20071.3-20http://en.wikipedia.org/wiki/Stall_(flight)http://en.wikipedia.org/wiki/Elevator_(aircraft)http://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEFederal_Aviation_Administration20071.4-19http://en.wikipedia.org/wiki/Aircrafthttp://en.wikipedia.org/wiki/Center_of_gravity_of_an_aircrafthttp://en.wikipedia.org/w/index.php?title=Center_of_mass&action=edit§ion=13http://en.wikipedia.org/wiki/Center_of_mass#cite_note-FOOTNOTEVan_Pelt2005185-18http://en.wikipedia.org/wiki/Fosbury_Flophttp://en.wikipedia.org/wiki/High_jumphttp://en.wikipedia.org/wiki/Car_handlinghttp://en.wikipedia.org/wiki/Sports_car -
7/30/2019 Center of Gravity vs Center of Mass
8/25
8
Center of Mass - Theory and Application
Another way of looking at this is that the center of gravity (mass) is the point at which the body's mass is
equally balanced. This changes depending on one's position (arms up/down, leaning, etc). Dancers, gymnas
and tight-rope walkers are examples of how the human body compensates for changes in the center of
gravity to maintain balance.
Usually the center of gravity is located in front of your sacrum bone, at about the second sacral level. (The
sacrum is made up of five bones fused together vertically.) So when you are on planet earth your weight, or
mass, is thought to be concentrated at this point in front of yoursacrum. The downward pull of gravity (line
of gravity) passes through this point, as well.To understand the difference between theory and practical application of this concept, lets compare thehuman body to a baseball for a minute. From a point in the exact center, the baseball is of equal weight and
shape all the way around, is it not? So, with any movement of the ball, this center point moves right along
with it. Easy.
But when we consider center of gravity in the human body, things get more complicated. As we mentioned
before, because the body has moving parts (arms, legs, head, various areas of the trunk), every time you do,
well, anything, the shape of your overall form changes. And if you carry something like a suitcase or grocery
bag or if you wear abackpack, this adds weight, which changes the center of gravity, too.
So, we can say that the center of gravity is a constantly changing point in the body that represents where th
weight (mass) of the rest of your body is equally balanced in every direction. This point can and does chang
based on what youre carrying and how youre carrying it, as well as the position you take and themovements you make.My personal take on it this: In an ideal situation I like to think of the center of gravity as the place from whic
you can operate your whole body as a unit, while gracefully coordinating the movement of appendages as
you go.
When calculating in single particle systems such as an atom or a defined point, the physical shape and
geometry of its mass is insignificant. However in real life, no object is simply a particle and possess a great
complications in its physical geometry. When dealing with such problems, we calculate the kinematics
relative to its center of mass. But not only is the center of mass used for physical objects, also for multi-
particle systems which can be treated as a single entity and the dynamics of each particle is calculated
relative to the system's center of mass.COM IN ASTRONOMY
Inastronomy,barycentric coordinates are non-rotating coordinates with origin at thecenter of massof
two or more bodies.
The barycenter (or barycentre; from the Greek -heavy+ -centre + -ic[1]) is the point betweetwo objects where they balance each other. For example, it is the center of mass where two or more celestia
bodiesorbiteach other. When amoonorbits aplanet, or a planet orbits astar, both bodies are actually
orbiting around a point that is not at the center of the primary (the larger body). For example, the moon doe
not orbit the exact center of theEarth, but a point on a line between the center of the Earth and the Moon,
approximately 1,710 km below the surface of the Earth, where their respective masses balance. This is the
point about which the Earth and Moon orbit as they travel around theSun.
http://backandneck.about.com/od/s/g/sacrumsacral.htmhttp://backandneck.about.com/od/s/g/sacrumsacral.htmhttp://backandneck.about.com/od/s/g/sacrumsacral.htmhttp://backandneck.about.com/od/childrensissues/tp/Backpacks-Back-Packs-Back-Pain.htmhttp://backandneck.about.com/od/childrensissues/tp/Backpacks-Back-Packs-Back-Pain.htmhttp://backandneck.about.com/od/childrensissues/tp/Backpacks-Back-Packs-Back-Pain.htmhttp://en.wikipedia.org/wiki/Astronomyhttp://en.wikipedia.org/wiki/Astronomyhttp://en.wikipedia.org/wiki/Astronomyhttp://en.wikipedia.org/wiki/Center_of_masshttp://en.wikipedia.org/wiki/Center_of_masshttp://en.wikipedia.org/wiki/Center_of_masshttp://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)#cite_note-1http://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)#cite_note-1http://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)#cite_note-1http://en.wikipedia.org/wiki/Orbithttp://en.wikipedia.org/wiki/Orbithttp://en.wikipedia.org/wiki/Orbithttp://en.wikipedia.org/wiki/Natural_satellitehttp://en.wikipedia.org/wiki/Natural_satellitehttp://en.wikipedia.org/wiki/Planethttp://en.wikipedia.org/wiki/Planethttp://en.wikipedia.org/wiki/Planethttp://en.wikipedia.org/wiki/Starhttp://en.wikipedia.org/wiki/Starhttp://en.wikipedia.org/wiki/Starhttp://en.wikipedia.org/wiki/Earthhttp://en.wikipedia.org/wiki/Earthhttp://en.wikipedia.org/wiki/Earthhttp://en.wikipedia.org/wiki/Sunhttp://en.wikipedia.org/wiki/Sunhttp://en.wikipedia.org/wiki/Sunhttp://en.wikipedia.org/wiki/Sunhttp://en.wikipedia.org/wiki/Earthhttp://en.wikipedia.org/wiki/Starhttp://en.wikipedia.org/wiki/Planethttp://en.wikipedia.org/wiki/Natural_satellitehttp://en.wikipedia.org/wiki/Orbithttp://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)#cite_note-1http://en.wikipedia.org/wiki/Center_of_masshttp://en.wikipedia.org/wiki/Astronomyhttp://backandneck.about.com/od/childrensissues/tp/Backpacks-Back-Packs-Back-Pain.htmhttp://backandneck.about.com/od/s/g/sacrumsacral.htm -
7/30/2019 Center of Gravity vs Center of Mass
9/25
9
Contents
[hide]
1 Two-body problem
1.1 Examples
1.2 Inside or outside the Sun?
1.3 Animations
2 Relativistic corrections
3 Selected barycentric orbital elements
4 References
[edit]Two-body problem
The barycenter is one of thefociof theelliptical orbitof each body. This is an important concept in the field
ofastronomy,astrophysics, and the like (seetwo-body problem). In a simple two-body case, r1, the distance
from the center of the primary to the barycenter is given by:
Ifa is the semi-major axis of the system, r1 is thesemi-major axisof the primary's orbit around the
barycenter, and r2 = ar1 is the semi-major axis of the secondary's orbit. When the barycenter islocated within the more massive body, that body will appear to "wobble" rather than following a discernible
orbit.[edit]Examples
The following table sets out some examples from theSolar System. Figures are given rounded to
threesignificant figures. The last two columns show R1, the radius of the first (more massive) body,
and r1/R1, the ratio of the distance to the barycenter and that radius: a value less than one shows that the
barycenter lies inside the first body.
Examples
Larger
body
m1
(mE=1)
Smaller
body
m2
(mE=1)
a
(km)
r1
(km)
R1
(km)r1/R1
Remarks
Earth 1 Moon 0.0123 384,000 4,670 6,380 0.732
The Earth has a perceptible "wobble"; seetides.
Pluto 0.0021 Charon0.000254
(0.121 mPluto)19,600 2,110 1,150 1.83
Both bodies have distinct orbits around the barycenter, and as such Pluto and Charon were considered
adouble planetby many before the redefinition ofplanetin August 2006.
Sun 333,000 Earth 1150,000,000
(1AU)449 696,000 0.00064
The Sun's wobble is barely perceptible.
Sun 333,000 Jupiter318
(0.000955 mSun)
778,000,000
(5.20 AU)742,000 696,000 1.07
The Sun orbits a barycenter just above its surface.[2]
[edit]Inside or outside the Sun?
Ifm1m2 which is true for the Sun and any planet then the ratio r1/R1 approximates to:
Hence, the barycenter of the Sun-planet system will lie outside the Sun only if:
http://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)http://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)http://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)http://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)#Two-body_problemhttp://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)#Two-body_problemhttp://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)#Exampleshttp://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)#Exampleshttp://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)#Inside_or_outside_the_Sun.3Fhttp://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)#Inside_or_outside_the_Sun.3Fhttp://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)#Animationshttp://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)#Animationshttp://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)#Relativistic_correctionshttp://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)#Relativistic_correctionshttp://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)#Selected_barycentric_orbital_elementshttp://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)#Selected_barycentric_orbital_elementshttp://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)#Referenceshttp://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)#Referenceshttp://en.wikipedia.org/w/index.php?title=Barycentric_coordinates_(astronomy)&action=edit§ion=1http://en.wikipedia.org/w/index.php?title=Barycentric_coordinates_(astronomy)&action=edit§ion=1http://en.wikipedia.org/w/index.php?title=Barycentric_coordinates_(astronomy)&action=edit§ion=1http://en.wikipedia.org/wiki/Focus_(geometry)http://en.wikipedia.org/wiki/Focus_(geometry)http://en.wikipedia.org/wiki/Focus_(geometry)http://en.wikipedia.org/wiki/Elliptic_orbithttp://en.wikipedia.org/wiki/Elliptic_orbithttp://en.wikipedia.org/wiki/Elliptic_orbithttp://en.wikipedia.org/wiki/Astronomyhttp://en.wikipedia.org/wiki/Astronomyhttp://en.wikipedia.org/wiki/Astronomyhttp://en.wikipedia.org/wiki/Astrophysicshttp://en.wikipedia.org/wiki/Astrophysicshttp://en.wikipedia.org/wiki/Astrophysicshttp://en.wikipedia.org/wiki/Two-body_problemhttp://en.wikipedia.org/wiki/Two-body_problemhttp://en.wikipedia.org/wiki/Two-body_problemhttp://en.wikipedia.org/wiki/Semi-major_axishttp://en.wikipedia.org/wiki/Semi-major_axishttp://en.wikipedia.org/wiki/Semi-major_axishttp://en.wikipedia.org/w/index.php?title=Barycentric_coordinates_(astronomy)&action=edit§ion=2http://en.wikipedia.org/w/index.php?title=Barycentric_coordinates_(astronomy)&action=edit§ion=2http://en.wikipedia.org/w/index.php?title=Barycentric_coordinates_(astronomy)&action=edit§ion=2http://en.wikipedia.org/wiki/Solar_Systemhttp://en.wikipedia.org/wiki/Solar_Systemhttp://en.wikipedia.org/wiki/Solar_Systemhttp://en.wikipedia.org/wiki/Significant_figureshttp://en.wikipedia.org/wiki/Significant_figureshttp://en.wikipedia.org/wiki/Significant_figureshttp://en.wikipedia.org/wiki/Kilometrehttp://en.wikipedia.org/wiki/Kilometrehttp://en.wikipedia.org/wiki/Kilometrehttp://en.wikipedia.org/wiki/Earthhttp://en.wikipedia.org/wiki/Earthhttp://en.wikipedia.org/wiki/Moonhttp://en.wikipedia.org/wiki/Moonhttp://en.wikipedia.org/wiki/Tidehttp://en.wikipedia.org/wiki/Tidehttp://en.wikipedia.org/wiki/Tidehttp://en.wikipedia.org/wiki/Plutohttp://en.wikipedia.org/wiki/Plutohttp://en.wikipedia.org/wiki/Charon_(moon)http://en.wikipedia.org/wiki/Charon_(moon)http://en.wikipedia.org/wiki/Double_planethttp://en.wikipedia.org/wiki/Double_planethttp://en.wikipedia.org/wiki/Double_planethttp://en.wikipedia.org/wiki/Planethttp://en.wikipedia.org/wiki/Planethttp://en.wikipedia.org/wiki/Planethttp://en.wikipedia.org/wiki/Sunhttp://en.wikipedia.org/wiki/Sunhttp://en.wikipedia.org/wiki/Astronomical_unithttp://en.wikipedia.org/wiki/Astronomical_unithttp://en.wikipedia.org/wiki/Jupiterhttp://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)#cite_note-NASA2005-2http://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)#cite_note-NASA2005-2http://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)#cite_note-NASA2005-2http://en.wikipedia.org/w/index.php?title=Barycentric_coordinates_(astronomy)&action=edit§ion=3http://en.wikipedia.org/w/index.php?title=Barycentric_coordinates_(astronomy)&action=edit§ion=3http://en.wikipedia.org/w/index.php?title=Barycentric_coordinates_(astronomy)&action=edit§ion=3http://en.wikipedia.org/w/index.php?title=Barycentric_coordinates_(astronomy)&action=edit§ion=3http://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)#cite_note-NASA2005-2http://en.wikipedia.org/wiki/Jupiterhttp://en.wikipedia.org/wiki/Astronomical_unithttp://en.wikipedia.org/wiki/Sunhttp://en.wikipedia.org/wiki/Planethttp://en.wikipedia.org/wiki/Double_planethttp://en.wikipedia.org/wiki/Charon_(moon)http://en.wikipedia.org/wiki/Plutohttp://en.wikipedia.org/wiki/Tidehttp://en.wikipedia.org/wiki/Moonhttp://en.wikipedia.org/wiki/Earthhttp://en.wikipedia.org/wiki/Kilometrehttp://en.wikipedia.org/wiki/Significant_figureshttp://en.wikipedia.org/wiki/Solar_Systemhttp://en.wikipedia.org/w/index.php?title=Barycentric_coordinates_(astronomy)&action=edit§ion=2http://en.wikipedia.org/wiki/Semi-major_axishttp://en.wikipedia.org/wiki/Two-body_problemhttp://en.wikipedia.org/wiki/Astrophysicshttp://en.wikipedia.org/wiki/Astronomyhttp://en.wikipedia.org/wiki/Elliptic_orbithttp://en.wikipedia.org/wiki/Focus_(geometry)http://en.wikipedia.org/w/index.php?title=Barycentric_coordinates_(astronomy)&action=edit§ion=1http://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)#Referenceshttp://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)#Selected_barycentric_orbital_elementshttp://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)#Relativistic_correctionshttp://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)#Animationshttp://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)#Inside_or_outside_the_Sun.3Fhttp://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)#Exampleshttp://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)#Two-body_problemhttp://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy) -
7/30/2019 Center of Gravity vs Center of Mass
10/25
10
That is, where the planet is heavy andfar from the Sun.
If Jupiter hadMercury's orbit (57,900,000 km, 0.387 AU), the Sun-Jupiter barycenter would be only 5,500 k
from the center of the Sun (r1/R1 ~ 0.08). But even if the Earth hadEris'orbit (68 AU), the Sun-Earth
barycenter would still be within the Sun (just over 30,000 km from the center).
To calculate the actual motion of the Sun, you would need to sum all the influences from all
theplanets,comets,asteroids, etc. of theSolar System(seen-body problem). If all the planets were aligned
on the same side of the Sun, the combined center of mass would lie about 500,000 km above the Sun's
surface.
The calculations above are based on the mean distance between the bodies and yield the mean value r1. But
all celestial orbits are elliptical, and the distance between the bodies varies between theapses, depending otheeccentricity,e. Hence, the position of the barycenter varies too, and it is possible in some systems for the
barycenter to be sometimes inside and sometimes outside the more massive body. This occurs where:
Note that the Sun-Jupiter system, with eJupiter = 0.0484, just fails to qualify: 1.05 1.07 > 0.954.[edit]Animations
Images are representative (made by hand), not simulated.
wo bodies of similar mass
biting a common
arycenter (similar to the90
ntiopesystem)
Two bodies with a difference
in mass orbiting a common
barycenter external to both
bodies, as in thePlutoCharonsystem
Two bodies with a major difference in
mass orbiting a common barycenter
internal to one body (similar to
theEarthMoonsystem)
http://en.wikipedia.org/wiki/Mercury_(planet)http://en.wikipedia.org/wiki/Mercury_(planet)http://en.wikipedia.org/wiki/Mercury_(planet)http://en.wikipedia.org/wiki/Eris_(dwarf_planet)http://en.wikipedia.org/wiki/Eris_(dwarf_planet)http://en.wikipedia.org/wiki/Planethttp://en.wikipedia.org/wiki/Planethttp://en.wikipedia.org/wiki/Planethttp://en.wikipedia.org/wiki/Comethttp://en.wikipedia.org/wiki/Comethttp://en.wikipedia.org/wiki/Comethttp://en.wikipedia.org/wiki/Asteroidhttp://en.wikipedia.org/wiki/Asteroidhttp://en.wikipedia.org/wiki/Asteroidhttp://en.wikipedia.org/wiki/Solar_Systemhttp://en.wikipedia.org/wiki/Solar_Systemhttp://en.wikipedia.org/wiki/Solar_Systemhttp://en.wikipedia.org/wiki/N-body_problemhttp://en.wikipedia.org/wiki/N-body_problemhttp://en.wikipedia.org/wiki/N-body_problemhttp://en.wikipedia.org/wiki/Apsishttp://en.wikipedia.org/wiki/Apsishttp://en.wikipedia.org/wiki/Apsishttp://en.wikipedia.org/wiki/Eccentricity_(orbit)http://en.wikipedia.org/wiki/Eccentricity_(orbit)http://en.wikipedia.org/wiki/Eccentricity_(orbit)http://en.wikipedia.org/w/index.php?title=Barycentric_coordinates_(astronomy)&action=edit§ion=4http://en.wikipedia.org/w/index.php?title=Barycentric_coordinates_(astronomy)&action=edit§ion=4http://en.wikipedia.org/w/index.php?title=Barycentric_coordinates_(astronomy)&action=edit§ion=4http://en.wikipedia.org/wiki/90_Antiopehttp://en.wikipedia.org/wiki/90_Antiopehttp://en.wikipedia.org/wiki/90_Antiopehttp://en.wikipedia.org/wiki/90_Antiopehttp://en.wikipedia.org/wiki/Plutohttp://en.wikipedia.org/wiki/Plutohttp://en.wikipedia.org/wiki/Charon_(moon)http://en.wikipedia.org/wiki/Charon_(moon)http://en.wikipedia.org/wiki/Earthhttp://en.wikipedia.org/wiki/Earthhttp://en.wikipedia.org/wiki/Moonhttp://en.wikipedia.org/wiki/Moonhttp://en.wikipedia.org/wiki/File:Orbit3.gifhttp://en.wikipedia.org/wiki/File:Orbit2.gifhttp://en.wikipedia.org/wiki/File:Orbit1.gifhttp://en.wikipedia.org/wiki/File:Orbit3.gifhttp://en.wikipedia.org/wiki/File:Orbit2.gifhttp://en.wikipedia.org/wiki/File:Orbit1.gifhttp://en.wikipedia.org/wiki/File:Orbit3.gifhttp://en.wikipedia.org/wiki/File:Orbit2.gifhttp://en.wikipedia.org/wiki/File:Orbit1.gifhttp://en.wikipedia.org/wiki/Moonhttp://en.wikipedia.org/wiki/Earthhttp://en.wikipedia.org/wiki/Charon_(moon)http://en.wikipedia.org/wiki/Plutohttp://en.wikipedia.org/wiki/90_Antiopehttp://en.wikipedia.org/wiki/90_Antiopehttp://en.wikipedia.org/wiki/File:Orbit3.gifhttp://en.wikipedia.org/wiki/File:Orbit2.gifhttp://en.wikipedia.org/wiki/File:Orbit1.gifhttp://en.wikipedia.org/wiki/File:Orbit3.gifhttp://en.wikipedia.org/wiki/File:Orbit2.gifhttp://en.wikipedia.org/wiki/File:Orbit1.gifhttp://en.wikipedia.org/w/index.php?title=Barycentric_coordinates_(astronomy)&action=edit§ion=4http://en.wikipedia.org/wiki/Eccentricity_(orbit)http://en.wikipedia.org/wiki/Apsishttp://en.wikipedia.org/wiki/N-body_problemhttp://en.wikipedia.org/wiki/Solar_Systemhttp://en.wikipedia.org/wiki/Asteroidhttp://en.wikipedia.org/wiki/Comethttp://en.wikipedia.org/wiki/Planethttp://en.wikipedia.org/wiki/Eris_(dwarf_planet)http://en.wikipedia.org/wiki/Mercury_(planet) -
7/30/2019 Center of Gravity vs Center of Mass
11/25
11
[edit]Relativistic corrections
Inclassical mechanics, this definition simplifies calculations and introduces no known problems. Ingeneral
relativity, problems arise because, while it is possible, within reasonable approximations, to define the
barycenter, the associated coordinate system does not fully reflect the inequality of clock rates at different
locations. Brumberg explains how to set up barycentric coordinates in general relativity.[3]
The coordinate systems involve a world-time, i.e., a global time coordinate that could be set up bytelemetry
Individual clocks of similar construction will not agree with this standard, because they are subject to
differinggravitational potentialsor move at various velocities, so the world-time must be slaved to some
ideal clock; that one is assumed to be very far from the whole self-gravitating system. This time standard is
calledBarycentric Coordinate Time, "TCB".
[edit]Selected barycentric orbital elements
Barycentric osculating orbital elements for some objects in the Solar System:[4]
ObjectSemi-major axis
(inAU)
Apoapsis
(in AU)Orbital period in years
C/2006 P1 (McNaught) 2050 4100 92600
Comet Hyakutake 1700 3410 70000
C/2006 M4 (SWAN) 1300 2600 47000
(308933) 2006 SQ372 799 1570 22600
(87269) 2000 OO67 549 1078 12800
90377 Sedna 506 937 11400
2007 TG422 501 967 11200
For objects at such high eccentricity, the Sun's barycentric coordinates are more stable than heliocentric
coordinates.[5]
Top Research InstitutesIndian Institute of Technology (IIT), BombayIndian Institute of Science (IISc)(www.iisc.ernet.in)
Bhabha Atomic Research Centre (BARC)
Defence Research and Development Organization (DRDO)
Indian Space Research Organization (ISRO)
Tata Institute of Fundamental Research
Indian Institute of Astrophysics
Saha Institute of Nuclear Physics
All India Institute of Medical Sciences
wo bodies with similar mass orbiting a common barycenter,
ternal to both bodies, with eccentricelliptic orbits(a
mmon situation forbinary stars)
Two bo
with an
extrem
differen
in mass
orbitin
commo
barycen
internaone bod
(simila
theSun
Earthsy
m)
http://en.wikipedia.org/w/index.php?title=Barycentric_coordinates_(astronomy)&action=edit§ion=5http://en.wikipedia.org/w/index.php?title=Barycentric_coordinates_(astronomy)&action=edit§ion=5http://en.wikipedia.org/w/index.php?title=Barycentric_coordinates_(astronomy)&action=edit§ion=5http://en.wikipedia.org/wiki/Classical_mechanicshttp://en.wikipedia.org/wiki/Classical_mechanicshttp://en.wikipedia.org/wiki/Classical_mechanicshttp://en.wikipedia.org/wiki/General_relativityhttp://en.wikipedia.org/wiki/General_relativityhttp://en.wikipedia.org/wiki/General_relativityhttp://en.wikipedia.org/wiki/General_relativityhttp://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)#cite_note-3http://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)#cite_note-3http://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)#cite_note-3http://en.wikipedia.org/wiki/Telemetryhttp://en.wikipedia.org/wiki/Telemetryhttp://en.wikipedia.org/wiki/Gravitational_potentialhttp://en.wikipedia.org/wiki/Gravitational_potentialhttp://en.wikipedia.org/wiki/Gravitational_potentialhttp://en.wikipedia.org/wiki/Barycentric_Coordinate_Timehttp://en.wikipedia.org/wiki/Barycentric_Coordinate_Timehttp://en.wikipedia.org/wiki/Barycentric_Coordinate_Timehttp://en.wikipedia.org/w/index.php?title=Barycentric_coordinates_(astronomy)&action=edit§ion=6http://en.wikipedia.org/w/index.php?title=Barycentric_coordinates_(astronomy)&action=edit§ion=6http://en.wikipedia.org/w/index.php?title=Barycentric_coordinates_(astronomy)&action=edit§ion=6http://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)#cite_note-barycenter-4http://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)#cite_note-barycenter-4http://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)#cite_note-barycenter-4http://en.wikipedia.org/wiki/Small_Solar_System_bodyhttp://en.wikipedia.org/wiki/Semi-major_axishttp://en.wikipedia.org/wiki/Semi-major_axishttp://en.wikipedia.org/wiki/Astronomical_unithttp://en.wikipedia.org/wiki/Astronomical_unithttp://en.wikipedia.org/wiki/Astronomical_unithttp://en.wikipedia.org/wiki/Apoapsishttp://en.wikipedia.org/wiki/Apoapsishttp://en.wikipedia.org/wiki/C/2006_P1http://en.wikipedia.org/wiki/C/2006_P1http://en.wikipedia.org/wiki/Comet_Hyakutakehttp://en.wikipedia.org/wiki/Comet_Hyakutakehttp://en.wikipedia.org/wiki/C/2006_M4_(SWAN)http://en.wikipedia.org/wiki/C/2006_M4_(SWAN)http://en.wikipedia.org/wiki/(308933)_2006_SQ372http://en.wikipedia.org/wiki/(308933)_2006_SQ372http://en.wikipedia.org/wiki/(308933)_2006_SQ372http://en.wikipedia.org/wiki/(87269)_2000_OO67http://en.wikipedia.org/wiki/(87269)_2000_OO67http://en.wikipedia.org/wiki/(87269)_2000_OO67http://en.wikipedia.org/wiki/90377_Sednahttp://en.wikipedia.org/wiki/90377_Sednahttp://en.wikipedia.org/wiki/2007_TG422http://en.wikipedia.org/wiki/2007_TG422http://en.wikipedia.org/wiki/2007_TG422http://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)#cite_note-Kaib2009-5http://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)#cite_note-Kaib2009-5http://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)#cite_note-Kaib2009-5http://www.iisc.ernet.in/http://www.iisc.ernet.in/http://www.iisc.ernet.in/http://en.wikipedia.org/wiki/Elliptic_orbithttp://en.wikipedia.org/wiki/Elliptic_orbithttp://en.wikipedia.org/wiki/Elliptic_orbithttp://en.wikipedia.org/wiki/Binary_starhttp://en.wikipedia.org/wiki/Binary_starhttp://en.wikipedia.org/wiki/Binary_starhttp://en.wikipedia.org/wiki/Sunhttp://en.wikipedia.org/wiki/Sunhttp://en.wikipedia.org/wiki/Earthhttp://en.wikipedia.org/wiki/Earthhttp://en.wikipedia.org/wiki/File:Orbit4.gifhttp://en.wikipedia.org/wiki/File:Orbit5.gifhttp://en.wikipedia.org/wiki/File:Orbit4.gifhttp://en.wikipedia.org/wiki/File:Orbit5.gifhttp://en.wikipedia.org/wiki/Earthhttp://en.wikipedia.org/wiki/Sunhttp://en.wikipedia.org/wiki/Binary_starhttp://en.wikipedia.org/wiki/Elliptic_orbithttp://www.iisc.ernet.in/http://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)#cite_note-Kaib2009-5http://en.wikipedia.org/wiki/2007_TG422http://en.wikipedia.org/wiki/90377_Sednahttp://en.wikipedia.org/wiki/(87269)_2000_OO67http://en.wikipedia.org/wiki/(308933)_2006_SQ372http://en.wikipedia.org/wiki/C/2006_M4_(SWAN)http://en.wikipedia.org/wiki/Comet_Hyakutakehttp://en.wikipedia.org/wiki/C/2006_P1http://en.wikipedia.org/wiki/Apoapsishttp://en.wikipedia.org/wiki/Astronomical_unithttp://en.wikipedia.org/wiki/Semi-major_axishttp://en.wikipedia.org/wiki/Small_Solar_System_bodyhttp://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)#cite_note-barycenter-4http://en.wikipedia.org/w/index.php?title=Barycentric_coordinates_(astronomy)&action=edit§ion=6http://en.wikipedia.org/wiki/Barycentric_Coordinate_Timehttp://en.wikipedia.org/wiki/Gravitational_potentialhttp://en.wikipedia.org/wiki/Telemetryhttp://en.wikipedia.org/wiki/Barycentric_coordinates_(astronomy)#cite_note-3http://en.wikipedia.org/wiki/General_relativityhttp://en.wikipedia.org/wiki/General_relativityhttp://en.wikipedia.org/wiki/Classical_mechanicshttp://en.wikipedia.org/w/index.php?title=Barycentric_coordinates_(astronomy)&action=edit§ion=5 -
7/30/2019 Center of Gravity vs Center of Mass
12/25
12
Indian Statistical Institute
Top 20 Scientific Research Institutes in India
1. Indian Institute of Science (Bangalore)
2. National Physical Laboratory (New Delhi)
3. Defence Research Development Organisation (New Delhi)
4. Institute of Physics (Bhubhaneswar)
5. Tata Institute of Fundamental Research (Mumbai)
6. Inter-University Centre for Astronomy and Astrophysics (Pune)
7. National Centre for Radio Astrophysics (Pune)8. Inter-University Consortium for DAE Facilities (Indore) Jawaharlal Nehru Centre for Advanced Scientific
Research (Bangalore)
9. Institute of Mathematical Sciences (Chennai)
10. Centre for Advanced Technology (Indore)
11. Indian Spare Research Organisation- (1) Physical Research Laboratory (Ahmedabad); and (2) Space
Physics Laboratory (Thiruvananthapuram)
12. Mehta Research Institute of Mathematics and Mathematical Physics (Allahabad)
13. Bhabha Atomic Research Centre (Mumbai)
14. Physical Research Laboratory (Ahmedabad)
15. Saha Institute of Nuclear Physics (Kolkata) S N Bose National Centre for Basic Sciences (Kolkata)
16. Raman Research Institute (Bangalore)17. Indira Gandhi Centre for Atomic Research (Kalpakkam, Tamil Nadu)
18. Atomic Minerals Directorate for Exploration and Research (Hyderabad).
19. Indian Institute of Astrophysics (Bangalore)
20. Institute of Plasma Research (Gandhinagar)
Launch Vehicles are used to transport and putsatellitesor spacecrafts into space. In India, the launch
vehicles development programme began in the early 1970s. The first experimental Satellite Launch
Vehicle (SLV-3) was developed in 1980. An Augmented version of this,ASLV, was launched successfully in
1992. India has made tremendous strides in launch vehicle technology to achieve self-reliance in satellite
launch vehicle programme with the operationalisation of Polar Satellite Launch Vehicle (PSLV) and
Geosynchronous Satellite Launch Vehicle (GSLV).PSLV represents ISRO's first attempt to design and develop an operational vehicle that can be used to
orbit application satellites. While SLV-3 secured for India a place in the community of space-faring
nations, the ASLV provided the rites of passage into launch vehicle technology for ISRO. And with PSLV, a
new world-class vehicle has arrived. PSLV has repeatedly proved its reliability and versatility by
launching 55satellites / spacecrafts ( 26 Indian and 29Foreign Satellites) into a variety of orbits so far.
ISRO also makes the Rohini series of sounding rockets used by the Indian and international scientific
community to launch payloads to various altitudes for atmospheric research and other scientific
investigations. These rockets are also used to qualify some of the critical systems used for advanced
launch vehicles.
Landmark achievements in ISRO's Launch Vehicle Development
PSLVhas 21 consecutively successful flights out of 22 launches
PSLV used for launching a total of 27 satellites for foreign customers under commercial
agreements, demonstrating its multi-satellite launch capability
PSLVused to launchSpace capsule Recovery Experiment(SRE-1),Chandrayaan-1and
http://www.isro.org/satellites/satelliteshome.aspxhttp://www.isro.org/satellites/satelliteshome.aspxhttp://www.isro.org/satellites/satelliteshome.aspxhttp://www.isro.org/Launchvehicles/launchvehicles.aspx#SLV3http://www.isro.org/Launchvehicles/launchvehicles.aspx#SLV3http://www.isro.org/Launchvehicles/launchvehicles.aspx#SLV3http://www.isro.org/Launchvehicles/launchvehicles.aspx#ASLVhttp://www.isro.org/Launchvehicles/launchvehicles.aspx#ASLVhttp://www.isro.org/Launchvehicles/launchvehicles.aspx#ASLVhttp://www.isro.org/pdf/foreignsatellite.pdfhttp://www.isro.org/pdf/foreignsatellite.pdfhttp://www.isro.org/pdf/foreignsatellite.pdfhttp://www.isro.org/Launchvehicles/PSLV/pslv.aspxhttp://www.isro.org/Launchvehicles/PSLV/pslv.aspxhttp://www.isro.org/Launchvehicles/PSLV/pslv.aspxhttp://www.isro.org/Launchvehicles/PSLV/pslv.aspxhttp://www.isro.org/Launchvehicles/PSLV/pslv.aspxhttp://www.isro.org/satellites/sre-1.aspxhttp://www.isro.org/satellites/sre-1.aspxhttp://www.isro.org/satellites/sre-1.aspxhttp://www.isro.org/satellites/chandrayaan-1.aspxhttp://www.isro.org/satellites/chandrayaan-1.aspxhttp://www.isro.org/satellites/chandrayaan-1.aspxhttp://www.isro.org/satellites/chandrayaan-1.aspxhttp://www.isro.org/satellites/sre-1.aspxhttp://www.isro.org/Launchvehicles/PSLV/pslv.aspxhttp://www.isro.org/Launchvehicles/PSLV/pslv.aspxhttp://www.isro.org/Launchvehicles/PSLV/pslv.aspxhttp://www.isro.org/pdf/foreignsatellite.pdfhttp://www.isro.org/Launchvehicles/launchvehicles.aspx#ASLVhttp://www.isro.org/Launchvehicles/launchvehicles.aspx#SLV3http://www.isro.org/satellites/satelliteshome.aspx -
7/30/2019 Center of Gravity vs Center of Mass
13/25
13
ISRO's exclusive meteorological satellite,KALPANA-1, proving its versatility
GSLVwith four successful flights of seven launches can launch 2 to 2.5 tonne satellite into Geo-
synchronous Transfer Orbit (GTO)
Successful testing of indigenously developed cryogenic upper stage on November 15, 2007.
ISRO's Launch Fleet at a Glance
ISRO developed two experimental satellite launch vehicles,SLV-3andASLV
Polar Satellite Launch Vehicle(PSLV)commissioned in 1997
Geosynchronous Satellite Launch Vehicle (GSLV-Mk I) commissioned after second successful
flight in May 2003
GSLV - MK II will use indigenously developed cryogenic Upper Stage
GSLV - MK IIIis under development
SLV-3
http://www.isro.org/satellites/kalpana-1.aspxhttp://www.isro.org/satellites/kalpana-1.aspxhttp://www.isro.org/satellites/kalpana-1.aspxhttp://www.isro.org/Launchvehicles/GSLV/gslv.aspxhttp://www.isro.org/Launchvehicles/GSLV/gslv.aspxhttp://www.isro.org/Launchvehicles/launchvehicles.aspx#SLV3http://www.isro.org/Launchvehicles/launchvehicles.aspx#SLV3http://www.isro.org/Launchvehicles/launchvehicles.aspx#SLV3http://www.isro.org/Launchvehicles/launchvehicles.aspx#ASLVhttp://www.isro.org/Launchvehicles/launchvehicles.aspx#ASLVhttp://www.isro.org/Launchvehicles/launchvehicles.aspx#ASLVhttp://www.isro.org/Launchvehicles/PSLV/pslv.aspxhttp://www.isro.org/Launchvehicles/PSLV/pslv.aspxhttp://www.isro.org/Launchvehicles/GSLVMARKIII/mark3.aspxhttp://www.isro.org/Launchvehicles/GSLVMARKIII/mark3.aspxhttp://www.isro.org/Launchvehicles/GSLVMARKIII/mark3.aspxhttp://www.isro.org/Launchvehicles/PSLV/pslv.aspxhttp://www.isro.org/Launchvehicles/launchvehicles.aspx#ASLVhttp://www.isro.org/Launchvehicles/launchvehicles.aspx#SLV3http://www.isro.org/Launchvehicles/GSLV/gslv.aspxhttp://www.isro.org/satellites/kalpana-1.aspx -
7/30/2019 Center of Gravity vs Center of Mass
14/25
14
Satellite Launch Vehicle-3 (SLV-3), India's first experimental satellite
launch vehicle was successfully launched on July 18, 1980 from SHAR
Centre Sriharikota, when Rohini satellite, RS-1, was placed in orbit. SLV-3
was a 22 m long, all solid, four stage vehicle weighing 17 tonnes capable
of placing 40 kg class payloads in low earth orbit.
It employed an open loop guidance (with stored pitch programme) to
steer the vehicle in flight along pre-determined trajectory. The first
experimental flight of SLV-3, in August 1979, was only partiallysuccessful. Apart from the July 1980 launch, there were two more
launches held in May 1981 and April 1983, orbiting Rohini satellites
carrying remote sensing sensors.
ASLV
Augmented Satellite Launch Vehicle (ASLV) was developed to act as a low
cost intermediate vehicle to demonstrate and validate critical
technologies. With a lift off weight of 40 tonnes, the 23.8 m tall ASLV was
configured as a five stage, all-solid propellant vehicle, with a mission of
orbiting 150 kg class satellites into 400 km circular orbits. The strap-on
stage consisted of two identical 1m diameter solid propellant motors,Under the ASLV programme four developmental flights were conducted.
The first developmental flight took place on March 24, 1987 and the
second on July 13, 1988. ASLV-D3 was successfully launched on May 20,
1992, when SROSS-C (106 kg) was put into an orbit of 255 x 430 km.
ASLV-D4, launched on May 4, 1994, orbited SROSS-C2 weighing 106 kg. It
had two payloads, Gamma Ray Burst (GRB) Experiment and Retarding
Potentio Analyser (RPA) and functioned for seven years. ASLV provided
valuable inputs for further development.
The Polar Satellite Launch Vehicle,usually known by its abbreviation PSLV is the first operational launch
vehicle of ISRO. PSLV is capable of launching 1600 kg satellites in 620 km sun-synchronous polar orbit and
1050 kg satellite in geo-synchronous transfer orbit. In the standard configuration, it measures 44.4 m tall,
with a lift off weight of 295 tonnes. PSLV has four stages using solid and liquid propulsion systems alternate
-
7/30/2019 Center of Gravity vs Center of Mass
15/25
15
The first stage is one of the largest solid propellant boosters in the world and carries 139 tonnes of propella
A cluster of six strap-ons attached to the first stage motor, four of which are ignited on the ground and two
are air-lit.
The reliability rate of PSLV has been superb. There had been 21 continuously successful flights of PSLV, till
September 2012 . With its variant configurations, PSLV has proved its multi-payload, multi-mission capabili
in a single launch and its geosynchronous launch capability. In the Chandrayaan-mission, another variant of
PSLV with an extended version of strap-on motors, PSOM-XL, the payload haul was enhanced to 1750 kg in620 km SSPO. PSLV has rightfully earned the status of workhorse launch vehicle of ISRO.
Typical Parameters of PSLV
Lift-off
weight295 tonne
Pay Load
1600 kg in to 620 km Polar
Orbit,
1060 kg in to Geosynchronous
Transfer Orbit (GTO)
Height 44 metre
PSLV Milestones
PSLV-C21launched SPOT 6 and PROITERES on September 09, 2012 (Successful)
PSLV-C19launchedRISAT-1on April 26, 2012 (Successful)
PSLV-C18launchedMegha-Tropiques,SRMSat,VesselSat-1andJugnuon October 12, 2011
(Successful)
PSLV-C17launchedGSAT - 12on July 15, 2011 (Successful)
PSLV-C16launchedRESOURCESAT - 2,YOUTHSATandX-SATon April 20, 2011 (Successful)
PSLV-C15launchedCARTOSAT-2B,ALSAT-2A, NLS 6.1 & 6.2andSTUDSATon July 12, 2010
(Successful)
PSLV-C14launchedOceansat - 2andSix Nanosatelliteson September 23, 2009 (Successful)
PSLV-C12launchedRISAT-2andANUSATon April 20, 2009 (Successfully)
PSLV-C11launchedCHANDRAYAAN-I, on October 22, 2008 (Successful)
PSLV-C9launchedCARTOSAT-2A,IMS-1and Eightnano-satellites on April 28, 2008
(Successful)
PSLV-C10launched TECSAR on January 23, 2008 (Successful)
PSLV-C8launched AGILE on April 23, 2007 (Successful)
http://www.isro.org/pslv-c21/PSLV-C21.aspxhttp://www.isro.org/pslv-c21/PSLV-C21.aspxhttp://www.isro.org/pslv-c19/PSLV-C19.aspxhttp://www.isro.org/pslv-c19/PSLV-C19.aspxhttp://www.isro.org/satellites/RISAT-1.aspxhttp://www.isro.org/satellites/RISAT-1.aspxhttp://www.isro.org/satellites/RISAT-1.aspxhttp://www.isro.org/pslv-c18/PSLV-C18.aspxhttp://www.isro.org/pslv-c18/PSLV-C18.aspxhttp://www.isro.org/satellites/megha-tropiques.aspxhttp://www.isro.org/satellites/megha-tropiques.aspxhttp://www.isro.org/satellites/megha-tropiques.aspxhttp://www.isro.org/satellites/srmsat.aspxhttp://www.isro.org/satellites/srmsat.aspxhttp://www.isro.org/satellites/srmsat.aspxhttp://www.isro.org/satellites/vesselsat-1.aspxhttp://www.isro.org/satellites/vesselsat-1.aspxhttp://www.isro.org/satellites/vesselsat-1.aspxhttp://www.isro.org/satellites/jugnu.aspxhttp://www.isro.org/satellites/jugnu.aspxhttp://www.isro.org/satellites/jugnu.aspxhttp://www.isro.org/pslv-c17/PSLV-C17.aspxhttp://www.isro.org/pslv-c17/PSLV-C17.aspxhttp://www.isro.org/satellites/gsat-12.aspxhttp://www.isro.org/satellites/gsat-12.aspxhttp://www.isro.org/satellites/gsat-12.aspxhttp://www.isro.org/pslv-c16/PSLV-C16.aspxhttp://www.isro.org/pslv-c16/PSLV-C16.aspxhttp://www.isro.org/satellites/resourcesat-2.aspxhttp://www.isro.org/satellites/resourcesat-2.aspxhttp://www.isro.org/satellites/resourcesat-2.aspxhttp://www.isro.org/satellites/youthsat.aspxhttp://www.isro.org/satellites/youthsat.aspxhttp://www.isro.org/satellites/youthsat.aspxhttp://www.isro.org/satellites/x-sat.aspxhttp://www.isro.org/satellites/x-sat.aspxhttp://www.isro.org/satellites/x-sat.aspxhttp://www.isro.org/pslv-c15/PSLV-C15.aspxhttp://www.isro.org/pslv-c15/PSLV-C15.aspxhttp://www.isro.org/satellites/cartosat-2b.aspxhttp://www.isro.org/satellites/cartosat-2b.aspxhttp://www.isro.org/satellites/cartosat-2b.aspxhttp://www.isro.org/satellites/alsat-nls.aspxhttp://www.isro.org/satellites/alsat-nls.aspxhttp://www.isro.org/satellites/alsat-nls.aspxhttp://www.isro.org/satellites/alsat-nls.aspxhttp://www.isro.org/satellites/alsat-nls.aspxhttp://www.isro.org/satellites/studsat.aspxhttp://www.isro.org/satellites/studsat.aspxhttp://www.isro.org/satellites/studsat.aspxhttp://www.isro.org/pslv-c14/PSLV-C14.aspxhttp://www.isro.org/pslv-c14/PSLV-C14.aspxhttp://www.isro.org/satellites/oceansat-2.aspxhttp://www.isro.org/satellites/oceansat-2.aspxhttp://www.isro.org/satellites/oceansat-2.aspxhttp://www.isro.org/satellites/cubesat-rubin.aspxhttp://www.isro.org/satellites/cubesat-rubin.aspxhttp://www.isro.org/satellites/cubesat-rubin.aspxhttp://www.isro.org/pslv-c12/PSLV-C12.aspxhttp://www.isro.org/pslv-c12/PSLV-C12.aspxhttp://www.isro.org/satellites/RISAT-2.aspxhttp://www.isro.org/satellites/RISAT-2.aspxhttp://www.isro.org/s