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Low Earth Orbit including altitute, period, and orbital velocity.
Approx. 300 km but technically any satellite below 1500 km in altitute. Period of 90 minutes. Orbital velocity of 8 km/s.
Above most of the atmosphere, below dangerous radiation of the Van Allen belts. LEOs suffer orbital decay still within the atmosphere.

Geostationary orbit including altitute, period, and orbital velocity.
36,000 km in altitude. Period of 24 hours. Orbital velocity of 3 km/s.
Lies above the equator, and always remains above the same point on the surface of the Earth, appearing stationary in the sky.

(2009 HSC) How does the gravitational field of a planet affect the speed and direction of a space probe as it passes close to a planet?
Approaching the planet increases the gravitational force towards the planet. This causes an acceleration of the spacecraft resulting in a change in direction and a change in speed.

(2009 HSC) During a lunar eclipse, Earth moves between the Sun and the Moon. What happens to the force exerted by the Sun on the Moon when the Earth is between the two?
F_{g} is proportional to the mass of the Sun and Moon and inversely proportional to distance of separation squared. These do not change, therefore the gravitational force between the Sun and the Moon does not change.

(2009 HSC) What forces are acting on a satellite in orbit around the Earth?
Gravity is the only force acting on the satellite providing the centripetal force and this results in an inward acceleration (centripetal acceleration)

(2007 HSC) A spaceship sittingn on its launch pad is measured to have a length L. This spaceship passes an outer planet at a speed of 0.95 c. What is the length of the spaceship as observed by those in the spaceship and those on the planet?
Observers in the spaceship see no change in the spaceships length. So the spaceship has a length L. To the observer ont he planet however, they see the spaceship's length contract so they see a length shorter than L.

PRAC: Using pendulum motion to determine a value for acceleration due to gravity
 Construct pendulum using 1 m long string, attached to clamp and retor stand, with 100 g mass on the lower end as a pendulum bob.
 Measure length of pendulum, from point of attachment to centre of mass of bob.
 Hold pendulum aside and release it with 15° max deviation from vertical  string loses tension at greater angles
 Use stop watch, begin timing at extreme of pendulum's motion.
 Time ten full swings, back and forth, of the pendulum
 Divide this time measurement by ten to get average period of motion, to minimise timing errors and random factors affecting individual swings.
 Thus, using the equation, value of 'g' can be calculated.
Repeated trials with different string lengths (but need to be long as to minimise human errors when timing), more accurate timing devices or placing a mark in the background when timing, will increase ACCURACY of results.

PRAC: Reasons for possible variations between experimental 'g' value and accepted value of 9.8 ms^{2}.
 Variations may be due to experimental error or factors actually affecting 'g' including:
 Altitude  greater elevation, smaller 'g'
 Location on the Earth  Earth spins so bulges at equator, flattening at poles. Closer to Earth's poles, greater 'g'
 Density of nearby geography  Places where lithosphere is thick, or where there are dense mineral deposits, greater 'g'

Why does gravitational potential energy take on a negative value?
Gravitational fields, like many fields, have no theoretical maximum range and theoretically exist at an infinite distance away from a central mass such as a planet. Because gravitational fields obey INVERSE SQUARE LAW and decrease in strength rapidly as distance increases, at large distances, the field is so insignificant it is regarded as nonexistent. At this point the gravitational field would be gone, and the object would have no potential energy when it is such ah large distance away. Hence when the object falls towards the planet, it loses potential energy and so a negative value of potential energy results. Note with the simpler definition that potential energy equals 'mgh', this is a limited view as at an infinite distance (h), there is infinite potential energy.
Gravitational potential energy is defined as the work done to move an object from a very large distance away (infinity) to a point within a gravitational field. The work done is the energy input by the gravitational field to the object as it falls to that particular distance. Decrease in potential energy, increase in kinetic energy.

Galileo's analysis of projectile motion
 First to analyse projectile motion mathematically, by diving motion into a horizontal and vertical component, which when added provide the total motion of the object.
 realised only vertical component would change (ignoring air resistance), horizontal component remains constant.
 motion of projectiles is parabolic due to the uniform acceleration vertically combined with constant horizontal motion.

Explain the concept of escape velocity, and how the equation is derived.
Velocity required at a planet's surface to completely leave its gravitational field without further energy input. Hence it must have the same kinetic energy as the absolute value of the gravitational potential energy it has at the point of takeoff. Hence equate equations for kinetic energy and gravitational potential energy together to obtain equation for escape velocity.

Newton's concept of escape velocity
 Newton considered a firing a projectile horizontally from the top of a tower and ignored air resistance.
 The projectile will hit the ground at a certain distance.
 At faster speeds, projectil will fall at a further distance away.
 If projected with enough speed, the projectile will take longer to hit the ground, and because gravity is pulling it towards the centre of the field, the Earth's surface curves away at the same time, resulting in the projectile remaining at a constant height i.e. it is orbiting the earth.
 At even higher velocities, the circle trajectory becomes hyperbolic, and at this point, the projectile has enough velocitiy to leave the gravitational field.
 The velocity corresponding to the time when this first happens is the escape velocity.

Why is the term 'gforces' used to explain the force acting on an astronaut during launch?
 where a = acceleration on the person which may be negative.
 gforce is calculated by dividing apparent weight (mg + ma) by the true weight (mg).
Used as it is a convenient measure of the force as it allows for comparisons, and eases calculations as to the force which the human can withstand during launch.

Effect of Earth's orbital motion on the launch of a rocket
 The Earth, relative to the Sun, has an orbital velocity. This can be exploited in a rocket launch to gain a boost in velocity.
 Certain 'launch windows' with optimal times at which a rocket can be launched for the desired orbital velocity and direction which the rocket requires.
 The rocket is fired to the East into orbit, then fired out of orbit at the optimal time.

Effect of Earth's rotational motion ont he launch of a rocket
 The Earth is rotates on its axis, giving it a rotation velocity.
 Rockets that are to orbit the Earth are fired in the direction of the Earth's rotation i.e. to the East. Also launching from the equator is ideal where the surface speed is at a maximum. Rockets can then gain extra momentum, with up to an additional 0.5 km/s towards the rocket's velocity. This means to achieve orbit, rockets only need to accelerate 7.5 km/s with the additional 0.5 km/s contributed by the Earth's rotational motion.
 Less fuel is required and/ or greater payload can be carried.

What equation do you use to calculate a rocket's liftoff acceleration?
 N.B. since 'm' of rocket is decreasing due to consumption of fuel  rate of acceleration is increasing as the flight progressses, and the rocoket's velocity will increase logarithmically.

Changing acceleration of a rocket during launch and forces experienced by astronauts using Law of Conservation of Momentum
 Law of Conservation of Momentum  in a closed system the total momentum of the system remains unchanged.
 Hence in a rocket, the impulse of the exhaust gases expelling from the back, creates an equal and oposite impulse to the rocket.
 Hence the sum of the momentum of the exhaust gas and the rocket is zero i.e. m_{gas }x v_{gas} = m_{rocket} x v_{rocket}.
 As rocket travels into space, it burns fuel, so its mass decreases. But because the momentum of the exhaust is constant resulting in constant thrust, this means the rocket's velocity must rise in order to obey the Conservation of Momentum.
 Increasing in the rocket's velocitiy means acceleration is also increasing.
 This can also be seen with F = ma, where F is the thrust of the rocket engine. As it provides relatively constsant thrust, as mass decreases, 'a' must increase i.e. rocket's accleration must increase.
 As rocket is launched off, acceleration progresively increases, as it burns fuel and becomes lighter.
 For astronauts, they experience an increasing force. So as rockets lift off, thrust needs to be progressively reduced to protect occupants by using throttling systems in liquid fuel rockets or having multistages where fuel is divided into stages, where once a stage of fuel is exhaused, it is released, allowing the thrust to drop back down and prevent excessive gforces on the crew.

Forces experienced by astronauts with a multistage rocket during launch.
 Prior lift off  zero acceleration  weight force equals thrust force  experience 1g.
 During lift off  increasing thrust exceeds rocket's weight  net force upwards ont he rocket, accelerates up, gforce greater than 1. From this point on, rocket's mass decreases as fuel is consumed, acceleration increases, gforce increases and reaching max values just before rocket exhausts its fuel.
 The first stage is then shut down and jettissoned reducing gforces momentarily experiences 0 g as it coasts.
 2ndstage rocket fires, quicklky develops thrust to exceed effective weight at its altitude, and start accelerating again. gforce begins to increase marginally greater than one, gradually building to its max value again, just as second stage is exhausted.
 If there is a 3rd stage, the process is repeated.

The change in energy involved during rocket launch
 At launch, ignition of fuel begins conversion of chemical potential energy in the fuel into kinetic energy of the exhaust gases.
 The impulse from the exhaust gases deliver energy to the rocket and work is done.
 As this occurs, the rocket begins to move upward gaining both gravitational potential energy and kinetic energy.
 The chemical potential energy in the fuel continues to decrease as more fuel is consumed, being converted to produce both an increase int he kinetic energy of the rocket as it increases speed, and an increase in the gravitational potential energy as it rises higher.

Forces involved upon space
air friction continues craft descent
 Rockets on spacecraft are fired
 create a force to reduce speed
 gravitational force accelerates spacecraft towards Earth
 gravitational force increases as spacecraft comes closer i.e. F ∝ 1/r^{2}
 gravitational potential energy decreases
 spacecraft gains kinetic energy
 nearing Earth, with trajectory set for safe reentry into atmosphere with correct angle
 begins to experience increasing atmospheric drag  friction  with more atmospheric gas particles encountered
 during reentry  very large drag forces
 large amounts of heat produced
 velocity reduces significantly
 air friction continues to reduce velocity of spacecraft utnil a point is reached where drag acting equals gravitational force
 spacecraft descends at fairly steady speed
 parachutes deployed to create increase in air firction  further reduce speed  allow safe touchdown to the Earth's surface

Uses of LEOs and Geostationary satellites
 Low Earth Orbit  weather satellites, resource mapping
 Geostationary Orbit  communcation satellites as a receiving dish need only point to a fixed spot in the sky to remain in contact with the satellite.

Konstantin Tsiolkovsky
 Russian scientist
 didn't contribute directly to space travel
 was entirely theoretical and devised many ideas that were almost prophetic & extremely important to space travel
 also calculated the escape velocity from Earth into orbit was 8 km/s.
 ROCKET PROPULSION: used Newton's 3rd Law and Conservation of Momentum and applied to rockets, underlies functioning of all rockets, vital to understanding of their operation.
 LIQUID FUELS: proposed using liquid hydrogen & liquid oxygen as rocket fuels so that thrust produced by rocket could be varied. Same fuels implemented in the Saturn V rocket powering Apollo missions to the moon. Gforces could be controlled unlike in solid fuel engines.
 MULTISTAGE ROCKETS: visualised 20stage rocket that dropped stages as each stage ran out of fuel, to cut down on mass and improve efficiency. Although 20 stages was extreme, multistage rockets proved vital in highenergy launches for manned space emissions such as Apollo as well as missions with large payloads.

Define orbital velocity.
 Orbital velocity is the speed of a satellite
 It is always tangentional to the radius of its orbit.
 To derive equation: Gravitational force = Centripetal force.
 note that 'd' = orbital radius.. so radius + altitude

Derive Kepler's Law of Periods.

Orbital decay  how does it happen?
 LEO still wthin the atmosphere although above regions of high density.
 LEOs collide with the air particles that are still present, and experience friction causing heat which signifies a loss of energy. Loss in mechanical energy (orbital speed decreases and from equation, 'r' will decrease) forces them lower down in the atmosphere experiencing greater drag  more friction, more loss of energy and the cycle goes on.
By the time satellite is below 200 km in altitude, only few more hours left before reentry.
 Amount of atmospheric drag experience by satellite depends on density of the air along the orbit  varies with time of day, season, latitude and longitude and other factors  predictable.
 Unpredictable factors  fluctuations in the solar wind. An increasing amount of incoming solar radiation can heat up the outer atmosphere causing it the expand, thereby height and density in the orbital region.

Techniques for safe reentry and other issues including optimum angle for safe reentry.
 HEAT  Satellite in orbit has a lot of kinetic and potential energy. During reentry, deceleration by friction converts all this energy into heat. Tolerate heat using either ablating surface (Apollo capsules) or insulating surface (space shuttle). Ablative tiles burn off, taking heat with them. Heat also minimised by extending the time to reenter, so energy is converted to heat over a long time (space shuttle)
 GFORCES  Deceleration of a reentering spacecraft produces gforces, usually greater than those during launch. Tolerated by reclining the astronaut, so blood not forced away from brain, and by fully supporting the body. Gforces can be minimised by extending the reentry, slowing the rate of descent.
 IONISATION BLACKOUT  During reentry, the heat that builds up around the spacecraft results in the air around it becoming ionised forming a layer around the spacecraft. This blocks radio communication as they cannot penetrate ionized particles, preventing communcation between the ground and the spacecraft for the duration of the reentry.
 OPTIMUM ANGLE  Angle of reentry is critical. If too steep, descent rate too fast, spacecraft would encounter higher density atmosphere whiel retaining too much velocity. It was then experience more drag, decelerating vehicle even faster and leading to higher temperatures. This results in very minimum excess gforces, and extra heating could even destroy the whole vehicle. On the other hand, if angle too shallow, spacecraft will retain too much of its velocity and exist the atmosphere by skimming off it, returning to space. Optimum angle is between 5.2°  7.2°.
 REACHING THE SURFACE  Must touch down softly on surface of the Earth. Use of parachutes to slow descent and make gentle landing (Apollo mission), or use of wings to generate lift to glide to a gentle landing an air strip (space shuttle).

Sling shot effect
 a craft approaches a planet in the direction of its motion
 the planet's gravitational field accelerates the space probe on approach and decelerates it on departure so that the departure speed and approach speed are the same relative to the planet (the blue line)
 but relative to the sun, it has increased its velocity, as the probe takes a little of the planet's angular momentum.
 can be regarded as an elastic 'collison'

Aether properties
 According to classical wave theory and Maxwell's electromagnetism, light, being a wave, must have a medium in which to propagate. Such a medium was called the lumniferous aether and was believed to be an absolute rest frame. It:
 filled all space
 no mass
 perfectly transparent
 permeated all matter
 great elasticity to support and propagate light waves

MichelsonMorley experiment (1887)
 Earth moving around Sun hence moving through aether resulting in an 'aether wind' that would affect the speed of light to an observer on Earth.
 MM experiment analyse aether wind, then calculate velocity of Earth through space.
 APPARATUS: halfsilvered mirror to split a light beam so two beams travelled perpendiciularly through the aether for the same distance, then recombined and arriving at the interferometer to create an interference pattern. Rotating apparatus as it floated on liquid mercury, should cause shift in interference pattern, as light should have travelled at diff. speeds in each direction. The velocity of Earth would be calculated by analysing the changing interference pattern.
 However, despite extensive testing, no change in interference pattern was observed hence no change in speed of light a 'null result'. MM experiment failed to caculate velocity of Earth through aether, but led to the conclusion aether model was flawed, which eventually led to the idea that aether did not exist but at the time scientists held onto its existence for a long time.
 NB if the Earth was moving through the motionless aether than the speed of light moving into the aether head on is higher than the speed of light travelling perpendicular to the aether. However the speed of light was demonstrated to be the same in both cases.
 Also the aether wind blows in the opposite direction to the motion of the Earth.

Initial reaction of MM results by scientific community
 Depite 'null' result, scientists were slow to abandon aether concept.
 Experiment was repeated at diff. times of year, in diff. locations, but yielded same results.
 Various solutions proposed: contraction of length in direction of aether flow, a large mass could 'carry' the aether with it so that there was no relative motion and hence, aether wind, but none survived close scrutiny.
 MM experiment used highly sensitive equipment  eventually became one of the most conclusive pieces of evidence against aether theory showing there was no aether wind to change the speed of light.
 Almost 20 yeares after MM experiment in 1905, Einstein proposed special relativity stating aether model was not needed. It supported Einstein's model of light and Einstein's theory successfully accounted for the null result of the MM experiment  speed of light was constant.

In the MM experiment, why was the rotation of the apparatus necessary?
When the two light beams rejoin, they should be out of phase to each other due to the effect of the aether wind on their velocities, and hence an interference pattern can be observed at the interferometer. However, this is not enough to prove the existence of the aether, as the phase difference might be caused by the difference in length of the two different pathways the light beams have undertaken. Only when the entire apparatus is rotated 90°, a change in the interference pattern is observed, can the existence of the aether be proven, since the beam that was once travelling across the aether wind is now travelling along and against the direction of the aether wind and vice versa, showing definitively the phase difference is due to the effect of aether on the velocity of light.

What is a frame of reference?
 A framework from which measurements such as position, velocity etc. are taken by an observer.

What is an inertial frame of reference? What is a noninertial frame of reference?
 INERTIAL FRAME OF REFERENCE: one that has no net force acting, and in which all of Newton's laws hold true. It is either at rest or moving with constant velocity i.e. not accelerating. It is not possible to carry out a mechanical experiment WITHIN THE INERTIAL FRAME to determine whether the frame is moving with constant velocity or at rest. A reference to an external location must be made to determine whether it is moving with constant velocity or at rest.
 NONINERTIAL FRAME OF REFERENCE: One that IS accelerating.

Why do the laws of motion not hold for noninertial frames of reference?
 Consider a bus and a tennis ball placed on the floor of the bus. When the bus accelerates forward, the ball rolls backwards. For an observer inside the bus (noninertial frame of reference) no force is observed acting on the ball to push it back, yet the ball does not remain stationary (Newton's 1st Law violated). Here a fictitious force, that is a false backward force, needs to be introduced in order to maintain the validity of the laws of mechanics. The existence of a fictious force is one of the most distinctive features of a noninertial frame of reference and allows it to be distinguished from an inertial frame of reference. Such forces are also known as 'inertial forces'.
 Another example is to consider the ride 'Rotor' at Luna Park. To a person on the ride, they feel a force pressing them into the walls of the ride however all the objects inside the 'rotor' are stationary relative to them. Therefore, the fictitious centrifugal force is pressing them against the wall of the ride. To an observer above, they see the rider travel in a circular path because the walls of the ride exert centripetal force. Furthermore if a rider threw a ball straight into the middle of the ride, they would see that the ball would not travel in a straight line, disobeying Newton's First Law  hence Newton's laws only hold true in an inertial frame.

PRAC: Distinguishing between noninertial and inertial frames of reference.
 Pulley with a string attached to a spring balance, holding a 100 g weight.
 Apparatus was an inertial reference frame when stationary  spring balance registered 100 g.
 When rope was pulled steadily, spring balance and weight rose at a constant velocity, spring balance still indicated 100 g  showing the frame of reference was still inertial.
 When rope was pulled increasingly faster, so that spring accelerated upwards, it registered more than 100 g because according to F = ma, it was exerting extra force on the weight to cause it to accelerate upwards.
 Because this accelerating frame indicated a different value from the stationary value of 100 g, it was identified as a noninertial frame where the laws of physics do not hold as the 100 g weight was indicated to be weighing more while accelerating.

Principle of relativity  key postulates
 1905 Einstein  theory of special relativity
 First postulate  laws of physics are the same for all inertial frames of refrence
 Second postulate  speed of light is constant for all observers
 From the first postulate, this meant that all inertial frames were equal and could not be distinguished from one another i.e. there is no absolute reference frame and this is why the aether was considered by Einstein to be superfluous.
 With the second postulate  thought experiments and later physical experiments showed that as observed velocity increases, time dilates, length contracts and mass increases.

Significant of Einstein's assumption of the constancy of the speed of light
 His assumption was the critical distinction between his theory of special relativity and prior theories, that assumed length and time were constant in all reference frames.
 It led to the idea that events which are simultaneous in one reference frame may not be in another; also significance of the constancy of the speed of light meant that mass, length and time change in order for speed of light to be the same.

Identify that if 'c' is constant, space and time become relative.
Velocity = Distance / Time
Thus, if 'c' is constant, then space and time are relative, and vary depending on the frame of reference.
Since neither space nor time is absolute quantities, the theory of relativity has replaced them with the concept of a spacetime continuum. Any event then has four dimensions, three space and one time, that define its position within its frame of reference.

Length standards as defined in terms of time rather than the original metre standard.
 Orignally, in 1793 metre was defined as 1 x 10^{7} of the circumference of Earth
 then in 1889 defined as the distance between two lines on a platinumiridium bar
 TODAY metre is defined as distance traveled by light in a vacuum in 1/299,792,458 seconds. This definition assumes that the speed of light is exactly 299,792,458 metres per second. Hence this definition shows that distance is calculated based on time  a unit of distance is measured in terms of how much distance light travels in a period of time. A lightyear is another distance measured by time  distance light travels in one year.

What are some problems with the current definition of the metre?
 Does not take into account certain relativistic phenomena, such as time dilation and how the speed of light is affected by the strength of a gravitational field through which it is travelling.
 Need for an even more precise standard for length will drive any changes.

Relativity of simultaneity
 Two events which are simultaneous in one reference frame, may not necessarily be simultaneous in another refrence frame which is in relative motion to the first.
 Consider light beams that open doors in a train that travels a constant speed 0.5c. For the black man, they will open simultaneously because the distance to each door from the light source is equal. Howeverfor the white man, who sees the same train in a different frame of reference, observes the doors opening as nonsimultaneous. The observer from outside sees the train moving, so light reaches the back door faster than it reachces the front door since the train is moving forwards, the front door is moving away from the point where the light was original turned on. Hence simultaneity is dependant on the frame from which events are observed.

Equivalence betwen mass and energy
 In Einstein's special relativity, he proposed E = mc^{2} which is used to calculate the 'rest energy' of an object and also the amount of energy released if matter is destroyed and converted into pure energy.
 New definition of an object's total energy: E = E_{k} + mc^{2}. As a force acts on the object which is close to the speed of light, since it cannot exceed the speed of light, the extra energy is converted into extra mass rather than more velocitiy for the object.
 Also modification to law of Conservation of Energy and law of Conservation of Mass to come up with Law of Conservation of Mass and Energy: Matter and energy cannot be destroyed or created. They can only be transformed. opening up a whole new realm of energy study i.e. with nuclear technoliges and matter and antimatter interaction, a small amount of mass can be converted to create energy such as in nuclear fusion and fission.

Length Contraction
 As observed velocity increases, length appears to contract in the direction of motion.
 Frame being observed and the frame of observation must both be inertial frames of reference.

Time dilation
 Moving clocks appear to run slower as observed velocity increases. Hence less time has passed for the frame of reference moving at relativistic speeds (smaller t value)
 Frame being observed and frame of observation must both be inertial frames of reference.

Mass dilation
 Mass appears to increase as observed velocity increases.
 Only true when frame being observed and the frame of observation are both inertial frames of reference.

Einstein's mirror thought experiment and light bouncing experiment.
 With the 1st pic, would the black man see his face normally in the mirror held in front of him if the train was travelling at constant c? Yes, because since he was in an inertial frame, there is no way of determining whether he was moving at the constant speed c. However with vector addition, a stationary observer outsidee would see light travelling away from the black man's face at c, but as the train was moving as c as well, the observer would see light travel twice the distance in the same amount of time. Since s = d/t, in order for 's' to remain constant (since speed of light, c, is constant) then 't' must change, in order for the stationary observer to see light travelling at 'c' and for Einstein's special relativity to hold.
 With the 2nd and 3rd pics, it illustrates Einstein's 'light bouncing experiment' where light is seen to travel a longer path by the white man outside the train. Again interpretation was that time changes so that c remains constant.

Relationship betwen theory and evidence supporting it
No hypothesis can be considered a theory until there is evidence confirming that hypothesis is correct. Therefore, Einstein's conclusions were merely predictions of what would happen at relativistic speeds. There is also an unusual relationship between relativity and theory  here the theoretical prediction preceded the evidence. Ordinarily, theory is derived from observed phenomenon. But until highly advanced instruments were developed in providing evidence for Einstein's hypotheses were his ideas to become theory.

Evidence supporting Einstein's predictions such as time dilation
 Atomic clocks of great accuracy were built (can measure down to one billiointh of a second). In 1971, the HafeleKeating experiment took two synchronised atomic clocks  one put on a jet plane to fly at very high speeds for a period of time, the other left on Earth (stationary). When the jet plan returned, the time of the two atomic clocks was compared. The two clocks were no longer synchronised; time of the clock in the jet plane ran slower hence time was dilated as predicted by Einstein.
 Muon experiment  particular similar to an electron, but heavier. Stationary half life  2 microseconds, when accelerated observed half life  60 microseconds. Accelerated in a particular accelerator to speeds up to 0.9994c. This also supported why the presence of muons are detected with advanced instruments, as they travel at relativistic velocity, their time is dilated as measured by a stationary scientific laboratory; hence their halflife is lengthened, long enough for them to reach the surface of the Earth. ANOTHER WAY OF LOOKING AT IT  as muons travel down at very high velocities, distance before them appears to move at a relativistic velocity relative to them. Hence, the distance they have to travel will contract, short enough for the muons to reach the Earth's surface within the limit of their lifetime.

Implications of mass increase, time dilation and length contraction for space travel.
 As spacecraft approaches speed of light:
 mass increases  greater force required to accelerate the spaceship, more work must be done  hinders the spaceship's atempts to reach higher speeds. If somehow this mass could be converted into energy (E = mc^{2}) it could work in the spacecraft's favour.
 time dilates  occupants of the spaceship see time passing slower so their trip takes less time to complete than measured by those on Earth, hence a really long flight may only be a fraction of the time for the travelers on the spacecraft.
 length contracts  distance in getting to the destination shortens  so doesn't take as long to get to the destination

