9.2SPACE

1. The Earth has a gravitational field that exerts a force on objects both on it and around it

1.1 Define weight as the force on an object due to a gravitational field• Every objects has a gravitational field, and the force that is applied to the object due to its gravitational field is

referred to as the object's weight. • Given that weight is a force, than Fw=ma. However, 'a' is acceleration, and for weight this is 9.8 ms-2 (acceleration

due to gravity). • The acceleration due to gravity will change from planet to planet and so the weight will change, however the

mass remains constant.

1.2 Explain that a change in gravitational potential energy is related to work done• When work is done on an object, some form of energy is converted into kinetic energy within the object. When

we move an object against a gravitational field, the energy is stored within the object as gravitational potential energy (GPE).

• The gravitational potential energy is GPE= mgh and the work done on an object is denoted by W=Fs. However, for a gravitational field the force is weight, or mg (mass x acceleration due to gravity). Therefore W=mgs. But, h=s and so W=mgH=GPE.

1.3 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

• Gravitational potential energy is the work done to move an object from a very large distance away to a point within a gravitational field.

• As we move an object away from Earth, its potential energy increases. When gravity pulls the object back towards Earth, this potential energy is converted back into kinetic energy.

• Hence, potential energy increases the further away an object is from the Earth's surface. But, the GPE is zero at an infinite distance away from an object, and so potential energy must be negative.

• Gravitational potential energy is defined as:Er = - Gm1m2 G=6.67 x 10-11Nm2kg-2

r • The change in potential energy of a mass, m, is defined as the work done (energy change) to move the mass, m1,

from its initial position to the centre of a body mass m2, its final position.• Change in potential energy is given by: ΔEp = Gm1m2(r2 - r1)

r1 r2

where r1 is the initial distance separating the centres of each mass r2 is the final distance separating the centre of each mass

1.4 Gather secondary information to predict the value of acceleration due to gravity on other planets• The strength of g can be calculated using the above formula if the mass and radius of the planet is known:

Body Mass (kg) Diameter (km) Radius (m) > km = m x 103 g (ms-2) > 3d.p. My weight (N), mass=100

Mercury 3.58 x 1023 4 878 2439 x 103 4.01 401

Venus 4.90 x 1024 12 104 6052 x 103 8.92 892

Earth 5.974 x 1024 12 756 6378 x 103 9.8 980

Moon 7.35 x 1022 3 476 1738 x 103 1.62 162

Mars 6.42 x 1023 6 795 3397.5 x 103 3.71 371

Pluto 1.27 x 1022 2 320 1160 x 103 0.63 63NB> Radius is in metres and diameter is in kilometres, make sure check units in exam if asked to find g.

1.5 Analyse information using the expression F = ma to determine the weight force for a body on Earth and for the same body on other planets

• If my mass is 100kg, then weight will be equal to mass multiplied by gravity i.e. w = mgBody Mercury Venus Earth Mars Pluto Moon

g (ms-2) 4.01 8.92 9.8 3.71 0.63 1.62

Weight (N) 401 892 980 371 63 162

2. Many factors have to be taken into account to achieve a successful rocket launch, maintain a stable orbit and return to Earth

2.1 Describe the trajectory of an object undergoing projectile motion within the Earth's gravitational field in terms of horizontal and vertical components

• An object that is thrown, launched of fired at an angle in the Earth's gravitational field follows a parabolic path (trajectory). This motion is called projectile motion.

• Its horizontal component's velocity will remain constant (neglecting air resistance) given that there are no external unbalanced forces acting upon it horizontally.

• The vertical components will undergo a constant negative acceleration of 9.ms-2. The overall velocity is the vector sum of these components.

2.2 Describe Galileo's analysis of projectile motion• Galileo worked how the position and velocity of a projectile could be calculated at any time. The horizontal and

vertical components were separated in order to do this, and then motion is the addition of the two components.• Galileo showed that all projectiles follow a parabolic motion; that all projectiles fall at the same rate, regardless of

weight; and that horizontal and vertical motion is separate, using an inclined plane. • If projectile is fired with an initial velocity, u, at an angle θ from horizontal, the initial horizontal component (x)

of velocity would be ux = ucosθ and the initial vertical component of velocity would be uy = usinθ.• Given that gravity only acts vertically downwards, the horizontal component (x) of motion has no force or

acceleration. Hence, the horizontal velocity remains constant and the horizontal position and velocity is given by: vx = ux and x=(ux)t

• The vertical component, y, must include the acceleration due to gravity, g, at all times during the flight.• Remember: At top of flight vy = 0 and the motion is symmetric which means that the upwards part is a mirror

image of the downwards part. Because of the symmetry the initial upwards velocity will be the conjugate of the final downwards velocity (uy = -vy).

E 2.3 Explain the concept of escape velocity in terms of the:- gravitational constant- mass and radius of the planet

• If a object possesses enough upward kinetic energy at least as great as the gravitational potential energy it possesses, and has a great enough velocity; then it will be going fast enough that the gravitational field of a planet will be able to slow it down, but will never be enough to stop it or turn the object around (i.e. the field will lose strength faster than the object loses speed).

• The velocity at which an object must travel to be slowed down to 0m/s at an infinite distance from the planet is defined as the escape velocity. A velocity greater than this value will allow the object to escape the planet's gravitational field.

• The velocity will vary based upon the following equation: v = √(2Gmp/rp) where v- velocity, G- gravitational constant, mp- mass of planet and rp- radius of planet.

• This equation comes from the relationship KE = GPE. Therefore, ½mrv2 = Gmrmp/rp

½v2 = Gmp/rp (mr cancels out) …..v = √(2Gmp/rp)

• Note: v∞mp /rp. Hence, as the mass increases, so does the escape velocity. As the radius of the planet increases, the escape velocity decreases.

2.4 Outline Newton's concept of escape velocity• Newton proposed that if an object was projected horizontally off a mountain, it would undergo projectile motion.• Once it reaches escape velocity, the curvature of the Earth would match the curvature of the projectile's trajectory

and so it would begin a circular orbit of Earth. • If it is projected at a speed that is significantly higher than the escape velocity, it would be able to escape the

Earth's gravitational field altogether.

2.5 Identify why the term 'g forces' is used to explain the forces acting on an astronaut during launch• The term 'g forces' is used to express apparent weight as a proportion of true weight. The 'g' stands for gravity.• True weight is a force applied by gravity upon an object, but because it is evenly spread is not felt. Apparent

weight is what an object experiences when an external force acts upon it to cause a change in its motion.• For g forces, 1g is equal to a change in velocity of 9.8m/s. Usually humans can withstand 4g, although astronauts

experience up to 10g. Under these circumstances, blood will rush to the head or feet potentially causing a black out. To combat this, the chairs are vertical and at right angles to the direction of forces causing it to be evenly spread out.

2.6 Discuss the effect of the Earth's orbital motion and its rotational motion on the launch of a rocket• The fuel required to launch a rocket into orbit can be minimised if it is launched to the east and as close to the

equator as possible. This is because the Earth rotates eastward and so a rocket launched to east will get a boost in speed from this rotation. Since the surface speed is fastest at the equator this is where the largest boost will be obtained.

• Transfer orbits between the Earth and other planets can be achieved by using the Earth's orbital velocity around Sun.

• If rocket is launched against motion of Earth's orbit it will have an overall velocity of Earth's orbital velocity minus escape velocity, and it will consequently transfer to an orbital path nearer to sun than that of Earth.

• If rocket is launched with Earth's orbit it will be travelling at the Earth's orbital velocity plus the escape velocity and hence will transfer to an orbit further away from the sun than that of Earth.

2.7 Analyse the changing acceleration of a rocket during launch in terms of the:- Law of Conservation of Momentum- Forces experienced by astronauts

• The change in momentum for the rocket equals the change in momentum for the gases (but in the opposite direction)

• It can be said that:Frocket on gases=Fgases on rocket. Given F= Δp/tΔpgases/t= Δprocket/t Since t is equal on both sides Δpgases= Δprocket

Δ(mv) gases= Δ(mv) rocket

Δ(mv) rocket+Δ(mv) gases = 0• There is no net change in momentum in the system, and so the Law of Conservation of momentum is obeyed.• It can also be said from this equation that, assuming the rate and velocity of gas released is constant, the rocket

will speed up because to compensate for mass loss (due to fuel burning) the velocity must increase to balance the equation.

• There are two forces acting upon an astronaut during launch, the thrust of the rocket (t) and the effect of gravity pulling down (w=mg). The net acceleration of astronaut can be found by: a = (T-mg)/m

• As rocket loses fuel and becomes lighter acceleration increases, thus force on astronaut will increase.

2.8 Analyse the forces involved in uniform circular motion for a range of objects, including satellites orbiting the Earth

• Uniform circular motion is circular motion with a uniform orbital speed. For an object to stay in circular motion, centripetal force must be acting upon it, which is equal to Fc = mv 2

r • This force is directed towards the centre of the circle, and when centripetal force is no longer acting upon the

object in circular motion, the object will fly off at a tangent to the circle. • In the case of a spacecraft, it is the gravitational attraction between the Earth and the spacecraft that acts to

maintain the circular motion that is the orbit.• Given that the object is always changing direction, Newton's Second Law states that it must be accelerating.

Centripetal acceleration is equal to: ac = v 2 therefore, Fc = ac x mass r

• The centripetal force on other objects is:Motion: Centripetal force is provided by:

*Whirling rock on a string The tension of the string

* Electron orbiting atomic nucleus Electronegativity (electron-nucleus electrical attraction)

* Car cornering Friction between tyres and road

* Moon revolving around Earth Moon-Earth gravitational attraction

* Satellite revolving around Earth Satellite-Earth gravitational attraction

2.9 Compare qualitatively low Earth and geostationary orbits• A low earth orbit is generally an orbit higher than approximately 250km, in order to avoid atmospheric drag, and

lower than approximately 1000km, which is altitude at which the Van Allen radiation belts start to appear. • Low earth orbits are commonly used for fast communication and for satellite imagery. Many of these satellites are

in polar orbit, so they span as the Earth rotates. • Note: The belts are regions of high radiation trapped by the Earth's magnetic field and pose significant threat to

live space travellers as well as to electronic equipment• A geostationary orbit is at an altitude which period of the orbit precisely matches that of the Earth, which

corresponds to that of approximately 35 800km. Hence, geostationary orbits will always stay at the same point in regards to Earth, making them useful as weather satellites.

2.10 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 Kepler's law of period.

• Orbital velocity is the velocity required for an object to maintain its orbit.• Kepler's Law of Periods is the relationship: r 3 for planet 1 = r 3 for planet 2 and r 3 = GM

T2 T2 T2 4∏2

• The relationship between orbital velocity, the gravitational constant, mass of the central body, mass of the satellite and the radius of the orbit is derived as follows:

2.11 Account for the orbital decay of satellites in low Earth orbit• When a satellite is in a low Earth orbit it will collide with small particles in the atmosphere and will hence

experience drag. This causes the satellites orbit to decay (or lose altitude).• As the altitude is reduced the atmosphere becomes denser and the process of orbital decay is accelerated as drag is

increased. Eventually, the satellite will re-enter the Earth's atmosphere causing it to burn up.

2.12 Discuss issues associated with the safe re-entry into the Earth's atmosphere and landing on the Earth's surface

• Heating:• As a spacecraft enters the Earth's atmosphere, kinetic and gravitational potential energy is converted into heat.

This is due to the extremely high velocity which the craft is travelling at, and the substantial amounts of friction between the craft and air molecules. If not dissipated, the heat may cause the craft to burn up.

• By presenting a blunt, flat surface to strike the atmosphere, a shock wave is created which absorbs a lot of heat. In addition, the outer layers of the spacecraft may wear away, vaporise and thus carry away heat energy.

• The space shuttle uses carbon coatings and porous tiles to absorb heat, which will not wear away through erosion or vaporisation.

• G-forces:• The deceleration during re-entry can cause high g forces to be experienced by the astronaut, which can cause

blood to rush to brain or feet.• The g forces can be minimised by increasing the re-entry time, slowing the rate of descent. This is done

through parachutes, which will increase air resistance thus slowing the rate of descent..• Connection Problems (Ionisation Blackout):

• As the spacecraft enters the atmosphere and heat builds up around the craft, atoms in the air become ionised and surround the craft, resulting in a phenomenon known as ionisation blackout.

• These ions deflect any radio signals sent to or from the craft. This can be dangerous if there is contact needed between the craft and the Earth at this phase of the flight.

2.13 Identify that there is an optimum angle for safe re-entry for a manned spacecraft into the Earth's atmosphere and the consequences of failing to achieve this angle

• Spacecraft have a re-entry window of between 5'-7'. If the craft descents at less than this angle, it will bounce off the atmosphere and go into orbit. But if it descents too steeply, the craft will burn up due to the heat of acceleration and excessive drag.

2.14 Solve problems and analyse information to calculate the actual velocity of a projectile from its horizontal and vertical components

• Equations for horizontal and vertical motion:General Form Horizontal Motion (Note: ax = 0) Vertical Motion (ay = 9.8ms-2 down)

v = u + at - vx = ux (horizontal velocity is uniform) - vy = uy + ayt

v2 = u2 + 2ar NB: r = ∆x/y - vx2 = ux

2 - vy2 = uy

2 + 2ay∆y

r = ut + ½at2 - ∆x = uxt (range) - ∆y = uyt + ½ ayt2

where 'x' is horizontal velocity of the projectile, and 'y' is the vertical velocity of the projectile!

• To split the given velocity into its vertical and horizontal components, Pythagoras can be used:

• Question 1: • (a) A cannon is fired at a velocity of 40.0ms-1 30° above horizontal. Determine the vertical and horizontal

components of this initial velocity.• Answer:

• (b) Determine the velocity after 3.0s after firing• Answer:

• Question 2:• (a) A tennis ball is struck at a velocity of 25ms-1 15o above the horizontal. Calculate the maximum height

reached by the ball• Answer:

• (b) Determine the time it takes for the ball to return to the ground (trip time):• Answer:

2.15 Identify data sources, gather, analyse and present information on the contribution of Tsiolkovsky to the development of space exploration

• Tsiolkovsky was the first person to deduce mathematically how a rocket would be launched in order for it to enter Space.

• Newton's third law, “For every action there is an equal but opposite reaction,” formed the groundwork and basis in Tsiolkovsky's reasoning that theoretically, it was plausible to use a rocket to escape the Earth's gravitational field and navigate in space.

• He successfully demonstrated that less fuel could be used to raise a larger payload into an orbital velocity. Although he did evolve the rocket powered space travel from merely an idea into a proven mathematical theory, he did not conduct any experiments which implemented the theory with the rockets that he had designed.

2.16 Solve problems and analyse information to calculate the centripetal force acting on a satellite undergoing circular motion about the Earth using Fc = mv 2 /r

• Question 1 (Calculating Fc and ac): • A rock of mass 250g is attached to the end of a 1.5m long string and whirled in a horizontal circle at 15ms -1.

Calculate the centripetal force and acceleration on the rock• Answer:

• Centripetal force:Fc = mv2/r = (0.25)(152) / 1.5 = 37.5 N

• Acceleration:Fc = mac or ac = v 2 ac = 37.5 / 0.25 r = 150 ms-2

• Question 2 (Calculating frictional force on a turning body):• A car of mass 1450kg is driven around a bend of radius 70m. Determine the frictional force required between

the tyres and the road in order to allow the car to travel at 70kmh-1. • Answer:

• Frictional forceNote: the car will travel at 70kmh-1 = 70/3.6 ms-1 = 19.4ms-1

Fc = mv2 / r = 1450 (19.42) / 70

= 7800 N NB> This is shared over all four tyres i.e. it is 1950N per tyre

2.17 Solve problems and analyse information using: r 3 = GM T2 4∏2

• Question 1:• Calculate the period of three different satellites orbiting the Earth at altitudes of (a) 250km, (b) 400km, and

(c) 40 000km

• Answer

3. The Solar System is held together by gravity

3.1 Describe a gravitational field in the region surrounding a massive object in terms of its effect on other masses• Any object that has mass will have a gravitational field. A gravitational field is any field in which in mass within

the gravitational field will experience a gravitational force.• Large bodies, such as the Earth, have a gravitational field around them which acts towards its centre. Therefore,

any mass on the surface of the body will experience the force of gravity pushing towards the body's centre. • Newton's third law states that for every force there is an equal but opposite force. Given that Earth is a large body,

it must have a gravitational field. So, when we jump, gravity is the force that pushes us back to Earth. However, we also push the Earth back up to us, Newton's third law. The reason that we do not see or feel the earth moving is because F = ma. The force the Earth experiences is equal to the force we experience, but given that our mass is substantially small as opposed to that of the Earth, the acceleration we undergo is similarly substantially greater than the Earth. While we may fall 1m to reach the Earth, the Earth will barely move to reach us.

3.2 Define Newton's Law of Universal Gravitation• Newton proposed that ‘any two objects attract each other with a force proportional to the product of their masses

and inversely proportional to the square of their separation.’• This is represented by:

3.3 Discuss the importance of Newton's Law of Universal Gravitation in understanding and calculating the motion of satellites

• The uniform circular motion that a satellite travels is due to a centripetal force, which in this circumstance is gravity. Using Newton's law of universal gravitation, the force holding the satellite in orbit can be calculated.

• Newton's law of universal gravitation can also be used to derive to important formulas: Kepler's law of Periods and to calculate orbital velocity.

• These two formulas enable scientists to calculate the required orbital velocity and altitude at which the satellite must be travelling at, to undergo and maintain uniform circular motion; and to calculate the position and velocity of a satellite at any instant.

3.4 Identify that a slingshot effect can be provided by planets for space probes• The slingshot effect involves a probe approaching a planet into a hyperbolic orbit to gain kinetic energy form the

planet's gravitational field. • The gravitational field around planets can be used to provide a spacecraft with momentum without burning fuel.

Even though the spacecraft has taken some of the planet's angular momentum, because of its huge mass there is little decrease in its velocity.

• The net effect is that the planet will lose kinetic energy as the probe gains some. The spacecraft's velocity (direction, not magnitude) will change relative to the sun.

• Basically: If a space shuttle travels toward a particular planet at precisely the right velocity and position the shuttle will begin to fall toward the planet as if in orbit but have enough velocity to just curve round the planets surface and use the force of gravity of the planet to accelerate the shuttle and make it turn.

3.5 Present information and use available evidence to discuss the factors affecting the strength of the gravitational force

• The strength of gravity field is directly proportional to the mass of the planet, and inversely proportional to the radius. This provides an approximation of the strength of the gravitational field surrounding a planet, however in different places the strength will also change

• The Earth is not a perfect sphere, and so at different places the distance from the centre to it will vary, altering the strength of the gravitational field. Rock densities and mineral deposits, and other reasons (dot point 1.4) also affect the strength of the gravitational field.

3.6 Solve problems and analyse information using Newton's Law of Universal Gravitation• Question 1 (Determining Smaller Gravitational Forces):

• Determine the gravitational force of attraction between two 250g apples on a desk 1m apart• Answer:

• Question 2 (Determining the gravitational forces between larger bodies):• Given the following data, determine the magnitude of the gravitational attraction between:

(a) Earth and the Moon(b) Earth and the SunMass of the Earth = 5.97 x 1024kg Mass of the Moon = 7.35 x 1022 kgMass of the Sun = 1.99 x 1030 kg Earth-Moon distance = 3.84 x 108m (on average) Earth- Sun Distance = 1.5 x 1011m (on average)

• Answer:

4. Current and emerging understanding about time space has been dependent upon earlier models of the transmission of light

4.1 Outline the features of the aether model for the transmission of light• The aether model was model first suggested by the Greeks and was widely accepted until the 1900s. The model

suggested that all space is filled with an invisible, massless substance called the aether.• The aether was the hypothesised medium through which light was propagated. It is invisible, filled all space, has a

low density and is transparent. It can permeate all matter and has a great elasticity in order to propagate light waves. It was also stationary in space.

• It was believed to be a solid, similar to wax, that is stiff enough to allow for the propagation of light but fluid enough for the planets to pass through.

4.2 Describe and evaluate the Michelson-Morley attempt to measure the relative velocity of the Earth through the Aether

• Two American scientists tried to prove the existence of the aether based upon the notion that if the earth was travelling through the aether, it should experience the force and flow of 'aether wind'.

• Michelson and Morley set up their experiments on a large heavy rock which they floated upon mercury. The large rock was an attempt to eliminate vibrations from external sources as these would blur the light pattern result. Floating the apparatus on mercury enabled them to rotate it to try to detect the expected interference patterns from different directions. The Michelson-Morley experiment was an extremely well thought out and conducted experiment, the problem was that you cannot prove an incorrect theory.

• The Michelson-Morley experiment attempted to prove it by having two light beams travel different paths along an apparatus. The distance that each light beam would travel would be the same, and given that the velocity of light is distance/time, and given that one beam is travelling with the aether and the other against it, the two light beams should have different velocities. Given that the distance is the same, it was anticipated that they would reach the observation point at different times. But, they both arrived at the same time under all circumstances, and so no motion of the Earth relative to the aether was detected. The idea was that if there was an aether, then light reaching the Earth from directions at 90o to each other should be travelling at different speeds relative to the Earth

• The apparatus was shifted 90' and so a change in the interference pattern was expected and, the idea being that the aether wind would affect the path of at least one of the light beams causing a different interference pattern to appear. But, no change in the interference was observed.

• The problem with detecting the aether was that no experiment worked. Because scientists were so convinced that the aether must exist, all negative results were explained away on the basis that the equipment was not sensitive enough to detect it.

4.3 Discuss the role of the Michelson-Morley experiments about making determinations about competing theories• The Michelson-Morley experiment proved the aether model to be invalid, however, it did not prove Einstein's

theory correct, it merely supported it. Einstein's theory would have predicted the results that were obtained.• But, the aether model was modified to explain these results, such as by claiming that the earth dragged the aether

along with it. The modifications minimised the inaccuracies and so the aether model continued to be popular well into the 1900s.

• Twenty years later Einstein's Theory of Relativity was proposed that did not need the aether. This has since been proven with the advancements in technology and is currently the favoured theory.

4.4 Outline the nature of inertial frames of references• A frame of references is a system in which measurements are taken, which are all relative to a certain frame for

reference. • An inertial frame of reference is a frame of reference moving at a constant velocity or stationary ( non-

accelerating) where Newton's First Law is obeyed.

• A non-inertial frame of reference is a frame which is accelerating. Observers in these frames will have forces acting upon them, and so Newton's First Law does not hold true in these frames.

4.5 Discuss the principle of relativity• Relativity did not begin with Einstein, but had in fact been around in various forms since Galileo's time. Newton

extended it and further was added by Poincare to include the laws of electromagnetism.• The principle of relativity states that it is impossible to detect the motion of an inertial frame of reference and that

the only way motion of an inertial frame of reference can be measured is from an external frame of references, i.e. the principle states that all non-accelerated motion is relative and cannot be detected without reference to an outside point, and that the speed of light is constant in the same medium.

• Einstein's theory of relativity had two postulates:• The law of physics is the same in all inertial frames of reference• The speed of light is constant in the same medium, and dependent of the velocity of the source or the observer

4.6 Describe the significance of Einstein's assumption of the constancy of the speed of light• This assumption explained the null result of Michelson-Morley and showed that the aether was not necessary. It

also suggests that nothing can travel faster than the speed of light.• This assumption also allowed Einstein to propose his theories of time dilation, length contraction and mass

dilation, which is shown through his thought experiment: If a person is sitting in a train that is travelling at the speed of light, and they hold up a mirror in front of them and look into it, would they be able to see their reflection? Einstein could only see two possible answers:• No, he would not see his reflection. This would be because the train was already going as fast as light can

travel. Therefore, the light leaving his face would not be able to reach the mirror in order to return as a reflection. By not being able to see his reflection, he would immediately know that the train was travelling at the speed of light, without reference to an outside point. This is a violation of the principle of relativity predicted by the aether model.

• Yes, he would be able to see his reflection, and so the principle of relativity is not violated. This means that the light leaving his face travels at the usual speed of light, as measured by him on the train. But it would mean that an observer standing on the ground should measure the speed of light as 2c, twice the usual value.

• Einstein could not accept that an optical experiment could violate the principle of relativity while a mechanical one could not. He decided that therefore that the aether model is wrong, the principle of relativity is never violated and he would see his reflection in the mirror.

• Given that Einstein believed that the speed of light is absolute in the same medium, then he realised that given that speed equals distance/time, then the two people watching the same event observe different distances and time intervals, and when they are divided it will always give you the same value for c. Hence, time and distance become relative, it is only the speed of light that is absolute.

4.7 Identify that if c is constant then space and time become relative • Conventionally, space is relative to the observer and time is constant. In the theory of relativity time becomes

relative as well as space. This means, depending on the velocity of the observers, time passes differently for different observers.

• For example, if a man is sitting in a train travelling at c and looks into the window he will see his reflection. If an outside observer looks into the train they will see the light travel twice as fast to reach that window. If c is constant this means that time slows down inside the train according to the outside observer as c=d/t

• Depending on your frame of reference, then your perception of the speed of light must change. However, c is absolute, so Einstein realised that distance and time change. But when that distance is divided over time, the value of c will always be the same regardless of your frame of reference. Hence, time and distance become relative, and the speed of light is the only factor that remains absolute.

4.8 Discuss the concept that length standards are defined in terms of time in contrast to the original meter standard• Up until recently, the meter was defined as the distance between two marks on a platinum-iridium bar in Paris.

But now the definition of the speed of light as well as the definition of a second have become increasingly accurate than our definition of the metre.

• So now the metre is defined as the distance travelled by a beam of light in a vacuum in 1/c seconds. As such the speed of light has been set at a given number of metres per second, so as our measurements become more accurate our definition of the metre will be revised, while c will remain constant. This also means that the metre is the same for any frame of reference, meaning that it is unaffected by length contraction and time dilation.

4.9 Explain qualitatively and quantitatively the consequence of special relativity in relation to:- The relativity of simultaneity

• This refers to Einstein's contention that if an observer sees two event to be simultaneous then any other observer, in a different frame of reference, may not judge them to be simultaneous.

• Einstein's thought experiment (train):• An operator of a lamp rides in the middle of a specially-rigged train carriage. The doors at either end of the

carriage are light operated. When the operator is along-side an observer on the embankment, he turns on the lamp. Light from the lamp travels forward and backward, and opens the doors.

• The operator of the lamp, who is the observer in the rest frame of reference, will see the two doors open simultaneously. The distance of each door from the lamp is the same and light travels at the same speed, c, both forward and backward so that each door receives that light at the same time and they open simultaneously.

• After the lamp is turned on but before the light has reached the doors, the train has moved so that the front door is now further away and the back door closer to the initial pulse of light. The observer on the embankment sees the light travelling both forward and backward at the same speed, c, so that the back door receives the light first and is seen to open before the front door.

- The equivalence between mass and energy• If force is applied to an object then work is done on an object, that is energy is applied. This energy would take in

the form of kinetic energy and it increases as the object speeds up, but, as it reaches c the object doesn’t speed up and instead the object acquires extra mass (mass dilation).

• Einstein made an inference here and stated that the mass of the object contained this extra energy. Thus, mass and energy are interchangeable. This is shown in the equation: E = Ek + mc2, however, when an object is stationary it has no kinetic energy and so it the relationship is expressed using Einstein's famous equation: E = mc2

- Length contraction• From simultaneity, it can be proven that lengths must contract within a fast moving object. Einstein proved this

with another trains-and-mirrors thought experiment. • This is shown through:

- Mass Dilation• As objects cannot continue to accelerate past the speed of light, when they reach very high speeds, their mass

begins to increase to slow acceleration. Thus, the mass of a moving object is greater than when it is at rest.• This is expressed through:

- Time Dilation• Due to time dilation, time passes slower in a moving frame than in a stationary frame. This cannot be noticed by

an observer in the moving frame. To them, time passes more quickly outside the frame.• This was shown through a ‘light-clock’ experiment. In a moving frame, the light must travel further for the clock

to tick, thus, an observer sees that time passes more slowly in the moving system. • This is represented in:

4.10 Discuss the implications of mass increase, time dilation and space contraction for space travel• Mass increase means that a space craft will not be able to travel at or above the speed of light. As an aircraft gains

momentum and speed, the heavier it will get and so a greater amount of force is required to accelerate it (Newton's Second Law, F = ma). Also, to accelerate the body until is is travelling at the speed of light, it will have infinite mass and so it will require infinite energy, which is impossible.

• For length contraction, it is best to use Einstein’s Relativity Postulate that states, the laws of physics are the same for observers in all inertial reference frames. No frame is preferred. This means that the spaceship speeding though space at a constant velocity could equally say that they in the spaceship are stationary and the rest of the space is speeding past the craft. In this respect, the space will contract in length and hence the spaceship will have less length to travel in order to reach the destination.

• Time dilation and length contraction help space travel as, if relativistic speeds can be achieved then the length needed to travel will become less and as time slows people can travel further in their lifetime, however, if they return to Earth people would have aged much more.

• If man could travel to relativistic speeds such as half the speed of light, man would be able to reach alpha centauri (our nearest star) in approximately 8 years, however due to time dilation less time appears to pass on the space ship according to observers on earth, and the length between earth and alpha centauri would have contracted considerably causing the journey to take much less time. If the journey took 8 years then it may seem like 5 years to the people on the spacecraft, and so theoretically it is possible to travel to stars thousands of light years away within the lifetime of an astronaut if the spacecraft can be accelerated close to the speed of light.

4.11 Gather and process information to interpret the results of the Michelson-Morley experiment• Nothing was known about the aether prior to the conduction of the Michelson-Morley experiment, however

properties were predicted.• In the Michelson-Morley experiment, they achieved a null result as no interferene patterns could be found. His

was not due to a poor experiment, as it was quite the contrary, but they could not prove an incorrect hypothesis.• No conclusion could be drawn as there were no results. Whilst this disproves the theory of the aether, it cannot be

used as evidence to support Einstein's theory of relativity, Einstein would have merely predicted the results.

4.12 Analyse and interpret some of Einstein's thought experiments involvoing mirrors and trains and discuss the relationship between thought and reality

• Einstein's first thought experiment involved trains and mirrors. Einstein wondered: “Suppose I am sitting in a train travelling at the speed of light. If I hold a mirror in front of me, will I see my reflfection?”. There are two possibilities:• No, he would not see his reflection. This would be because the train was already going as fast as light can

travel. Therefore, the light leaving his face would not be able to reach the mirror in order to return as a reflection. By not being able to see his reflection, he would immediately know that the train was travelling at the speed of light, without reference to an outside point. This is a violation of the principle of relativity predicted by the aether model.

• Yes, he would be able to see his reflection, and so the principle of relativity is not violated. This means that the light leaving his face travels at the usual speed of light, as measured by him on the train. But it would mean that an observer standing on the ground should measure the speed of light as 2c, twice the usual value.

• Einstein could not accept that an optical experiment could violate the principle of relativity while a mechanical one could not. He then decided that if the principal of relativity is true and can never be violated, then:

• The aether must be wrong• He would see his reflection• The speed of light, c, is constant regardless of the motion of the observer

• In order to make the third statement true, Einstein concluded that it is not the speed of light that is changing, but time. In other words, the stationary observer and the moving observer perceive time differently.

• Using these ideas, Einstein put forward his theory of relativity:• All motion is relative- the principle of relativity holds in all situations• The speed of light is constant regardless of the observer's frame of reference• The aether is not needed to explain light and, in fact, does not exist

• The standard of length was the distance between two lines one metre apart on a platinum-iridium alloy bar. However, time, length and mass all become relative. Because the speed of light is constant, the new definition of one metre is taken as the distance light travels in 1/299 792 458 of a second, given that the speed of light is 299 792 458ms-1.

4.13 Analyse information to dicuss the relationship between theory and the evidence supporting it, using Einstein's predictions based on relativity that were made many years before evidence was available to support it

• As technology advanced, evidence was soon becoming available to support Einstein's predictions. Evidence that support Einstein's theory includes:• Atomic clocks able to keep time to an unprecedented accuracy, one clock was flown around the world on a jet

plane at extremely fast speeds, and the other clock remained on Earth. When the plane got back to Earth, they compared the two clocks and discovered they had different times. (Remember, fast clocks run slow). This is due to time dilation as predicted by Einstein: as the spacecraft is travelling very fast, from the Earth, its time dilates and so for every minute on Earth, its equivalent minute may equal to three Earth minutes as an example. Hence, clock on the plane is travelling very slow compared to the atomic clock that remained on Earth.

• Muons are created in the upper atmosphere and live on a few microseconds. Theoretically, they should not reach the Earth, but they do. As they travel at very fast speeds, time dilation occurs meaning that their lifespan is prolonged relative to the Earth, and distance contracts so it has less distance to travel. Due to time dilation and length contraction, muons are able to reach the Earth.

• Although there was no evidence to support Einstein's theories at the time that he first proposed them, this did not mean that they were incorrect.

4. 14 Solve problems and analyse information using E = mc 2 , and the formulas for mass dilation, time dilation and length contraction