gravitation (1) [compatibility mode]

8/8/2019 Gravitation (1) [Compatibility Mode]

1/26

GravitationGravitation

Generated by Foxit PDF Creator Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.


2/26

6-1 Newtons Law of Universal Gravitation

If the force of gravity is being exerted onobjects on Earth, what is the origin of that

force?

Newtons realization was

that the force must comefrom the Earth.

He further realized that

this force must be what

keeps the Moon in itsorbit.



3/26

Newtons Law of Universal Gravitation

Therefore, the gravitational force must be proportional to both

masses.

By observing planetary orbits, Newton also concluded that the

gravitational force must decrease as the inverse of the square of the

distance between the masses.

In its final form, the law of universal gravitation reads:

where



4/26



5/26

F= gravitational force(N)

m = mass of object(kg)

r= separation between objects(m)

G = universal gravitation constant

2

21

rmGmF

Law of Universal GravitationLaw of Universal Gravitation

Every object attracts every other object with anEvery object attracts every other object with anattractive force which is directly proportional to theattractive force which is directly proportional to the

masses and inversely proportional to the square ofmasses and inversely proportional to the square of

the separation between themthe separation between them



6/26



7/26

The orbits of the planets are elliptical (not circular) withthe Sun at one focus of the ellipse.

KeplersKeplers First LawFirst Law



8/26

Kepler's Second Law

A line connecting the Sun and a planet sweeps out equal areas in equaltimes.

Translation: planets move faster when closer to theSun.

slowerfaster



9/26

Recall that the external net torque on a systemequals the time rate of change of

angular momentum of the system; that is,.

Therefore, because torque is zero , the

angular momentum L of the planet is a constant of the

motion:



10/26

Kepler's Third Law

The square of a planet's orbital period is proportional to the cube of itssemi-major axis.

T2 is proportional to R3

Translation: The further the planet is fromthe sun, the longer the period.


G t d b F it PDF C t F it S ft


11/26


Generated by Foxit PDF Creator Foxit Software


12/26




13/26

At what point in an elliptical orbit does a planet have

the greatest speed?




14/26

Circular Motion & SatellitesCircular Motion & Satellites(a) What is the velocity of moon orbiting the Earth ? The(a) What is the velocity of moon orbiting the Earth ? The

moon is 242,000 miles from earth. (b) What is the period ofmoon is 242,000 miles from earth. (b) What is the period of

the moons rotation about the Earth ?the moons rotation about the Earth ?

Earth Fcgmoon

Fcentripetal = Fgravitymv2/r = mg

V2/r = g

v = (r x g )1/2




15/26




16/26

yhttp://www.foxitsoftware.com For evaluation only.

Generated by Foxit PDF Creator Foxit Softwareh // f i f F l i l


17/26

Gravitational Field Strength g

M

m

r

2

r

GMmF

2r

GM

g

From Newtons 2nd Law

F = mgg = acceleration due to gravity (m/s2)

g = gravitational field strength (N/kg)

m

Fg

http://www.foxitsoftware.com For evaluation only.

Generated by Foxit PDF Creator Foxit Softwarehtt // f it ft F l ti l


18/26


Generated by Foxit PDF Creator Foxit Softwarehttp://www foxitsoftware com For evaluation only


19/26

Gravitational Potential V

In general

V = potential difference(J/kg)

r

Vg

A Point in space has Potential

An Object placed there has Potential Energy

Potential Energy = potential x mass

r

GMmEP

For a radial field

V = gravitational potential at a distance

r from mass M

r

GMV




20/26

That is, the gravitational potential energy

associated with anypair of particles of masses m1 and m2

separated by a distance r is




21/26




22/26

Escape VelocityEscape Velocity

p y



23/26

TOTAL ENERGY OF THE SYSTEM

p y



24/26

Calculate the escape speed from the Earth for a 5 000-kg

spacecraft, and determine the kinetic energy it must have at

the Earths surface in order to move infinitely far away from

the Earth.



25/26

Calculate the escape speed from the Earth for a 5 000-kg

spacecraft, and determine the kinetic energy it must have at

the Earths surface in order to move infinitely far away from

the Earth.



26/26

gravitation (1) [compatibility mode]

Documents