SpaceContents1. The Earth has a gravitational field that exerts a force on objects both on it and around it1Define weight as the force on an object due to a gravitational field1Explain that a change in gravitational potential energy is related to work done2Define gravitational potential energy as the work done to move an object from a very large distance away to a point in a gravitational field3EP: gravitational potential energy32. Many factors have to be taken into account to achieve a successful rocket launch, maintain a stable orbit and return to Earth4Describe the trajectory of an object undergoing projectile motion within the Earths gravitational field in terms of horizontal and vertical components4Describe Galileos analysis of projectile motion4Explain the concept of escape velocity in terms of the:5 Gravitational constant5 Mass and radius of the planet55Outline Newtons concept of escape velocity5Identify why the term g forces is used to explain the forces acting on an astronaut during launch6Discuss the effect of the Earths orbital motion and its rotational motion on the launch of a rocket6Analyse the changing acceleration of a rocket during launch in terms of the:7 Law of Conservation of Momentum7 Forces experienced by astronauts7Analyse the forces involved in uniform circular motion for a range of objects, including satellites orbiting the Earth7Compare qualitatively low Earth and geo-stationary orbits7Define the term orbital velocity and the quantitative and qualitative relationship between orbital velocity, the gravitational constant, mass of the central body, mass of the satellite and the radius of the orbit using Keplers Law of Periods7Account for the orbital decay of satellites in low Earth orbit8Discuss issues associated with safe re-entry into the Earths atmosphere and landing on the Earths surface9Identify that there is an optimum angle for safe re-entry for a manned spacecraft into the Earths atmosphere and the consequences of failing to achieve this angle93. The Solar System is held together by gravity10Describe a gravitational field in the region surrounding a massive object in terms of its effects on other masses in it10Define Newtons Law of Universal Gravitation:10Discuss the importance of Newtons Law of Universal Gravitation in understanding and calculating the motion of satellites11Identify that a slingshot effect can be provided by planets for space probes114. Current and emerging understanding about time and space has been dependent upon earlier models of the transmission of light12Outline the features of the aether model for the transmission of light12Describe and evaluate the Michelson Morley attempt to measure the relative velocity of the Earth through the aether12Discuss the role of the Michelson Morley experiments in making determinations about competing theories13Outline the nature of inertial frames of reference13Discuss the principle of relativity13Describe the significance of Einsteins assumption of the constancy of the speed of light13Identify that if c is constant then space and time become relative13Discuss the concept that length standards are defined in terms of time in contrast to the original metre standard13Explain qualitatively and quantitatively the consequence of special relativity in relation to:14The relativity of simultaneity14The equivalence between mass and energy14Length contraction14Time dilation14Mass dilation15Discuss the implications of mass increase, time dilation and length contraction for space travel16

1. The Earth has a gravitational field that exerts a force on objects both on it and around it Define weight as the force on an object due to a gravitational field Weight is the force on an object due to a gravitational field (a region where a mass experiences a force due to gravity)

W: weight (N) m: mass (kg) g: acceleration due to gravity (ms-2) The acceleration due to gravity can vary depending on: Geographical location (crust density, near poles or equator) Altitude Planetary bodyExplain that a change in gravitational potential energy is related to work done The force of attraction between two objects becomes 0 when the distance is infinity thus EP is 0 when the distance is infinityEP increases as distance increases and since EP is 0 at infinity, the EP has a negative value for any distance smaller than that The change in EP is equal to the work done to move the object from one point to another

Define gravitational potential energy as the work done to move an object from a very large distance away to a point in a gravitational field EP is the work done needed to move an object from one point to another in a gravitational field when the EP of an object at an infinite distance is taken to be 0

EP: gravitational potential energy G: universal gravitational constant (6.67 x 10-11 N m2 kg-2) m1: mass of object 1 (kg) m2: mass of object 2 (kg) r: distance (m)

2. Many factors have to be taken into account to achieve a successful rocket launch, maintain a stable orbit and return to Earth Describe the trajectory of an object undergoing projectile motion within the Earths gravitational field in terms of horizontal and vertical components A projectile is any object launched into the air (rockets are not included because thrusters are used throughout the flight) A projectiles parabolic trajectory can be split into two components: Horizontal component: a projectile will not accelerate in its motion in the x-axis due to no net force (uniform velocity) Vertical component: a projectile will always be affected by the acceleration due to gravity (uniform acceleration)

Describe Galileos analysis of projectile motion The motion of a projectile can be regarded as two separate and independent motions superimposed upon each other Explain the concept of escape velocity in terms of the: Gravitational constantEscape velocity is proportional to the gravitational constant Mass and radius of the planet Escape velocity is proportional the mass of the planet and is inversely proportional the radius of the planet The escape velocity is the initial velocity required to completely escape the Earths gravitational field when launched vertically upwards. The total of kinetic energy and the gravitational potential energy will equal to 0 as an object goes towards infinity.

G: universal gravitational constant (6.67 x 10-11 N m2 kg-2) m: mass of the planet (kg) r: radius of the planet (m)Outline Newtons concept of escape velocity When a projectile is launched and its initial velocity is fast enough, it could never fall back to the ground due to the curved surface therefore it orbits the Earth Identify why the term g forces is used to explain the forces acting on an astronaut during launch G-force is a term used to express a persons apparent weight as a multiple of their true weight

Apparent weight (what we feel): the sum of the contact forces resisting true weight An astronaut has an upward reaction force (mg) and upward force from the rocket (ma) hence the g-force experienced by the astronaut is:

Discuss the effect of the Earths orbital motion and its rotational motion on the launch of a rocket The Earths rotational motion as well as revolving around the sun can be used in a way to give the rocket higher orbital velocities relative to the sun. The rocket should be launched in the direction of the Earths rotation (towards east) and at a certain time period throughout the year to achieve a desired course relative to the sun.

Analyse the changing acceleration of a rocket during launch in terms of the: Law of Conservation of MomentumUsing the Law of Conservation of Momentum, the change in momentum (impulse) of the gases is equal to the change in momentum of the rocket but in opposite direction. This means that the force of the gas propelled backwards is equal to the force of the rocket forwards. Whenever there is a force, there is acceleration hence the rocket accelerates increasingly due to the changing mass of the rocket (as fuel is used) and g decreases slightly with higher altitudes

Forces experienced by astronauts As acceleration increases, the g-force experienced by the astronauts increases as well Analyse the forces involved in uniform circular motion for a range of objects, including satellites orbiting the Earth Since it is in a uniform circular motion, the centripetal force involved is the gravitational attraction between the Earth and the object

Compare qualitatively low Earth and geo-stationary orbitsLow Earth orbits are higher than 250km, avoiding atmospheric drag, but lower than 1000km below the Van Allen radiation belts (high radiation trapped by the magnetic field). Geostationary orbits are at an altitude where the period of the orbit matches that of the Earth; if over the equator it will appear stationary in the sky.

Define the term orbital velocity and the quantitative and qualitative relationship between orbital velocity, the gravitational constant, mass of the central body, mass of the satellite and the radius of the orbit using Keplers Law of Periods Orbital velocity is the instantaneous speed and direction of an object during circular motion

Orbital velocity:

Keplars Law of Periods:

Thus the orbital velocity can be changed to:

Or another derivation:

Account for the orbital decay of satellites in low Earth orbit The thin atmosphere still causes friction with the satellite which causes the satellite to slow down or reduce its velocity. Since force stays the same, the radius has to decrease thus the satellite spirals back down to Earth. As the satellite gets lower there is increasing air density and thus increasing the rate of descent.

Discuss issues associated with safe re-entry into the Earths atmosphere and landing on the Earths surface De-orbit manoeuvre: the spacecraft has to enter the atmosphere at a shallow angle otherwise it would generate too much heat and g-forces during re-entry but not too shallow otherwise it will bounce off the atmosphere.Extreme heat: the spacecraft will have a lot of kinetic energy converted into heat from friction in the atmosphere potentially melting the framework. Heat shields and certain materials are used.Decelerating g-forces: the astronauts inside the spacecraft will experience high g-forces due to higher rates of deceleration. To increase tolerance, astronauts lie down, always face upwards and supporting chairs. Ionisation blackout: there is a loss of communication due to a surrounding layer of non-penetrable ionised atoms as heat builds up. Reaching the surface: how the spacecraft or astronauts reach the surface; through parachuting or landing the spacecraft.

Identify that there is an optimum angle for safe re-entry for a manned spacecraft into the Earths atmosphere and the consequences of failing to achieve this angle To de-orbit, the spacecraft must enter the atmosphere at a certain angle to prevent high amounts of generated heat and g-forces (if the angle is greater) and to prevent it bouncing off the atmosphere (if the angle is lower)

3. The Solar System is held together by gravity

Describe a gravitational field in the region surrounding a massive object in terms of its effects on other masses in it A gravitational field is the region around a large mass (planet) where another mass will experience a gravitational force towards the centre. When two massive bodies are near each other, they combine to form complex gravitational field.

Define Newtons Law of Universal Gravitation: The attractive force (F) between the centres of two masses (m1 and m2) a distance (r) apart

F: force (N) G: Universal Graviational Constant (6.67 x10-11 N m2 kg-2) m1: mass of body 1 (kg) m2: mass of body 2 (kg) r: distance between the centre (m)

Discuss the importance of Newtons Law of Universal Gravitation in understanding and calculating the motion of satellites The orbital velocity equation could also be derived from Newtons Law of Universal Gravitation and centripetal force showing that gravity has a direct influence on the motion of satellites.

Identify that a slingshot effect can be provided by planets for space probesA slingshot effect allows space probes to change in velocity without using too much fuel by using a planets gravitational field

4. Current and emerging understanding about time and space has been dependent upon earlier models of the transmission of lightOutline the features of the aether model for the transmission of light The luminiferous aether was a medium in which electromagnetic waves (including light) travelled through. It filled space, had low density, was transparent and had great elasticity.

Describe and evaluate the Michelson Morley attempt to measure the relative velocity of the Earth through the aetherLight from a source is split into two rays, one ray going against the aether wind then back and the other ray going perpendicular to the wind. The apparatus was rotated 90o to interpose the rays to see if there was a difference. It was a good test to detect aether wind if there was then one ray would reach the sensor before the other.Discuss the role of the Michelson Morley experiments in making determinations about competing theoriesThis proved the aether model wrong and led to the development of other scientific theories to replace it such as Einsteins theory of Special Relativity. However, at the time the aether model was not rejected but rather modified to suit the results obtained from the experiments.

Outline the nature of inertial frames of reference Inertial frames of reference are non-accelerated environments (stationary or moving at uniform velocity)

Discuss the principle of relativity In an inertial frame of reference, no mechanical experiments or observations can be done to determine whether you are stationary or uniformly moving. Motion cannot be detected without a reference to an outside point.

Describe the significance of Einsteins assumption of the constancy of the speed of light The luminiferous aether is no longer needed to explain the fact that the speed of light will always be observed as the same regardless of the observers motion.

Identify that if c is constant then space and time become relative

For the speed of light c to be constant or absolute, the distance (space) and time has to change thus space and time become relative to the motion of the observer.

Discuss the concept that length standards are defined in terms of time in contrast to the original metre standard The metre is currently defined as the distance travelled by light in a vacuum during of a secondExplain qualitatively and quantitatively the consequence of special relativity in relation to:The relativity of simultaneitySimultaneous events occurring in one frame may not be simultaneous in another frame

The equivalence between mass and energyInfinite mass requires infinite force. A moving object acquires mass due to the energy from the work done to it. The rest energy is the energy of a stationary object:

E: rest energy (J) M: mass (kg) C: speed of light (3 x 108 ms-1) There is an equivalence of mass and energy given by the formula

Length contraction

L0: length measured from the rest frame Lv: length measured from a different frame of reference v: relative speed of the two frames of reference c: speed of lightLv is always smaller than L0; a moving object shortens its length in the direction of motion

Time dilation

t0: time taken in the rest frame of reference tv: time taken as seen from the frame of reference in relative motion to the rest frame v: relative speed of the two frames of reference c: speed of lightSince the speed of light c is the same in any frame of reference time dilation occurs. The time measured in the rest frame is t0. The measurement of this time from any other inertial reference frame in relative motion is tv and is always greater than t0. Or simply put, moving clocks are slower.

Mass dilation

m0: mass taken in the rest frame of reference mv: mass taken as seen from the frame of reference in relative motion to the rest frame v: relative speed of the two frames of reference c: speed of lightThe Law of Conservation of Momentum still applies and mass is dilated to account for the different velocities due to time dilation. The mass in the rest frame is m0 and this measurement in another inertial frame in relative motion is mv and is always greater. In other words, a moving object increases in mass when observed from a reference frame in relative motion.

Discuss the implications of mass increase, time dilation and length contraction for space travelTime dilation and length contraction would have effects for people on space travel, assuming they travel using great speeds (e.g. 0.1c). For example, the time measured on the moving ship would actually be shorter than the time measured on Earth and the distance measured by the ship is also shorter than the distance measured from Earth. This could mean that space travel has reasonable travelling times for the passengers. However, to reach great accelerations and speeds it requires very large amounts of energy which is not possible using current technologies.

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