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9.2 S p a c e

9.2 S p a c e. 1. Gravitational fields. Weight. Weight is the force on an object due to a gravitational field. The rest mass of an object remains constant irrespective of the gravitational field. The weight of an object changes as the gravitational field changes: F W = mg

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9.2 S p a c e

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  1. 9.2 Space

  2. 1. Gravitational fields

  3. Weight • Weight is the force on an object due to a gravitational field. • The rest mass of an object remains constant irrespective of the gravitational field. • The weight of an object changes as the gravitational field changes: FW = mg Where,FW = weight (N)‏ m= mass (kg)‏ g= gravitational acceleration (ms-2)‏ • The mass of an astronaut at rest on Earth remains the same on another planet • The weight of an astronaut on another planet will depend on the planet's gravitational field

  4. Calculating weight • The reading on the scale is 57 kg. Although the scale actually measures weight (it measures a force), scales are traditionally calibrated in the units for mass. • The weight of the person on the scales can be calculated using : FW = mg FW = weight N; m = 57kg and g= 9.8ms-2 FW = 57 x 9.8 = 558.6 N • The value of g on Venus is 8.9ms-2 . On Venus, this person would still have a mass of 57 kg but her weight would be 447 N (57 x 8.9 )‏

  5. Gravitational Potential Energy • The change in gravitational potential energy is related to the work done: Work: W = Fs (force used to move an object from the surface to a height of s metres)‏ In a gravitational field: F= Fw = mg Therefore W = mgs Potential energy near the Earth's surface is given by: Ep = mgh The two expressions are clearly identical W = Ep

  6. Gravitational Potential Energy • Gravitational potential energy is the work done to move an object from a very large distance away to a specific point in a gravitational field. • When a rocket is launched into space, work is done on the rocket hence the rocket's gravitational energy increases • When a meteor approaches the Earth its gravitational potential energy decreases (as the meteor speeds-up, potential energy is converted into kinetic energy ) • The lowest Ep in the gravitational field surrounding a planet is at the surface of the planet. • The highest Ep is when that of object is at an 'infinite' distance from Earth. Its gravitational energy due to Earth's gravitational at infinity is zero. • It follows that all other values of Ep must be negative G = 6.67300 × 10-11 m3 kg-1 s-2 (Universal gravitation constant)‏

  7. Ep example problem • Calculate the energy that was required to move The Hubble Telescope (11 110 kg) to its parking orbit (559 km)‏ • To do this we have to find the change in energy from its value on the surface to its value in orbit

  8. Determination of g To use a simple pendulum to determine the value of g. • The equipment used is shown to the left. • Displace the pendulum through a small angle ( < 10 o) and set it swinging. • Using a stop watch measure the time taken for ten periods (a period is a full swing from A to B and back to A)‏ • Repeat a number of times and find the average period (T) for that length (L)‏ • Repeat steps 3 to 6 for at least three different lengths. • Plot T2 vs. L. • The gradient of the line is: T2 / L • Using the formula adjacent and the gradient of the line, work out a value for g

  9. Variations from 9.8 ms-2 • The pendulum experiment generally yields fairly accurate results , ranging from 9.5 to 10 ms-2 for g. • Experimental errors occur in any experiment. In this case there are errors in measurement as well as errors inherent in the equipment used. • The average gravitational acceleration at the surface of the Earth is 9.80 ms-2. It can vary by a total of up to about 1%. This is largely due to a combination of 3 factors: Latitude: • Gravity is an average 9.78 ms-2 at the equator. It is about 0.5% higher at the poles at an average 9.83 ms-2. This is due to a combination of effects: • The spin of the Earth creates an outward force that is greatest at the equator. The difference is small, but enough to make the launch of space rockets cheaper near the equator than near the poles for most orbits. • The Earth's diameter at the equator is about 12,756 km . The distance from pole to pole is about 12,713 km This means that the surface at the equator is further away from the centre of the Earth. Elevation: • Gravity decreases with distance from the centre of the Earth. Gravity is about 0.2% lower at the top of Mount Everest than at sea level Crust thickness and Density: • Variations in the density and thickness of rocks in the Earth's lithosphere cause local variations in gravity. The denser the rock, the higher the value of g.

  10. gfor other planets • The gravitational force exerted by a planet at its surface is related to its mass and its radius. • The radius and mass of a planet can be derived from astronomical observation. • g for any planet (including Earth) can be estimated using the formula:

  11. Revision questions - 1 • Define weight • Explain the relationship between a change in gravitational potential energy and the work done • Define gravitational potential energy • Describe an investigation you performed to determine a value for the acceleration due to gravity using pendulum motion • Identify reasons for possible variations of g from the value of 9.8 ms-2 • Identify the data you would need in order to predict the value of g on other planets and describe how you would use it. • Calculate the work required to lift a 35 000 kg rocket to an altitude of 1 200 km • An astronaut lands on a new planet where the value of g is 10.67 ms-2. If the weight of the astronaut on Earth was 796 N determine his weight on the new planet

  12. 2. Rocket Launch

  13. Projectile motion • Projectile motion is considered as a motion in two dimensions: horizontal and vertical. • The horizontal velocity is constant if we ignore air resistance. • The vertical velocity is changed by the action of the acceleration due to gravity “g” which points directly downward at all times (toward the centre of the Earth or planet)‏ • The trajectory is parabolic (if we ignore air resistance).‏ • If the projectile starts and finishes at the same level, then the time to maximum height is at ½ of the time of flight. • At maximum height the vertical velocity is zero • If the initial velocity is upward and is taken as positive then downward is the negative direction. Hence g must be negative.

  14. Projectile motion • The two velocities are the component vectors of the projectile velocity at any one time during the flight. • The horizontal component (x direction) remains constant throughout. • The vertical motion (y direction) is uniformly accelerated downward by -g. • At any time during the flight the velocity and/or the displacement of the projectile can be calculated by finding the vertical and horizontal components and then using Pythagoras and trigonometry • The time of flight is the same for both motions and is used to tie them together.

  15. Projectile motion • Horizontal motion is described by: Where, t = time of flight; x = range • Vertical motion is described by: • Where at maximum height; uy = 0

  16. Projectile motion - a worked example An object is fired at 100 ms-1 at an angle of 47o near the edge of a cliff face, which is 58 m above sea level. Find how far from the bottom of the cliff the object will enter the sea. Step 1 do a sketch of the problem. Step 2 resolve the initial velocity into the two components ux and uy ux=100cos47 = 68.1998 ms-1 and uy=100sin47 = 73.1353 ms-1 Step 3 find the time to point H vy=uy+ayt 0=73.1353 + (-9.8)t t = 7.4628 s Step4 find height of point H vy2 = uy2 +2ayy 0 = (73.1353)2 + 2(-9.8)y y = 272.8965 m H from sea level = 272.8965 + 58 = 330.8965 Step 5 find time to impact from point H (y = - 330.8965 m)‏ y=ut+1/2at2 - 330.8965= 0t + ½ (-9.8)t2 t = 8.2176 s Step 6 find the total time of flight t = 7.4628 + 8.2176 = 15.6804 s NB: the above can be done in one step using the 'quadratic formula' ony=uyt+1/2at2 with y = -58 and uy= 73.1353 Step 7 find the horizontal distance traveled x=uxt x = 68.1988 x 15.6804 x =1069.38446352 =1070 m(do not round-off to significant figures until the final answer)‏

  17. Projectiles – an investigation • An example of an investigation is the construction of a small catapult. You will need to research the subject and then come-up with your own design. • You will need to calibrate it by firing an object a number of times. Keep a full record of all your experiments in a log book. • On the side of your catapult you will need to attach some sort of scale that will allow you to bring back the arm reproducibly at different points to achieve different ranges. • Find the maximum range for your machine. Then try to set your arm so the it will propel the object ¾ of the way, ½ way and ¼ of the way. For each position validate your results by repetition. • For each position estimate angle of flight, maximum height time of flight using a camcorder or the video recorder on a mobile phone. From these calculate the initial velocity of the object • Next, set your self a fixed distance to aim at (e.g. 60% of your maximum range). Set your catapult using your calibrations and check how accurate you were. • Finally, write a report on your investigation. When you submit it for marking, include your log book.

  18. Galileo Galilei • Before Galileo, it was believed that a projectile would travel in a straight line until it ran out of “impetus” and then it would fall straight down. • Using both experiment and mathematics, Galileo showed that the path of a projectile is a parabola. • Galileo rolled an inked bronze ball down an inclined plane onto a table. The ball thus accelerated, rolled over the table-top with uniform motion and then fell off the edge of the table. Where it hit the floor, it left a small mark. The mark allowed Galileo to measure the height and horizontal distance for different velocities.

  19. Galileo Galilei • Using a thought experiment, Galileo also showed that all objects will fall under the influence of gravity at the same rate irrespective of their masses (if there is no air resistance)‏ • He didn't actually drop objects from the leaning tower of Pisa as legend describes. • Galileo's discovery was demonstrated by the Apollo mission astronauts in the vacuum of the Moon. • They dropped a feather and a hammer at the same time - as expected, both the feather and the hammer hit the lunar surface exactly at the same time! (A short clip of this is available on YouTube)‏

  20. Escape velocity (speed)‏ • For a given gravitational potential energy, the escape velocity is the minimum speed an object (without propulsion) needs to have so that its kinetic energy equals the gravitational potential energy. • An object on the surface of a planet will need a kinetic energy equal to the gravitational potential energy at the surface of the planet. For the Earth's surface that kinetic energy results from a speed of about 11,100 ms-1 • The concept does not directly apply to rockets as they are propelled by their engines and accelerating. But at the instant the propulsion stops, the vehicle can only escape if its speed is greater than or equal to the escape velocity for that position. • It would apply to an object fired by gun in an attempt to, say, reach the Moon. Much like Jules Verne's “moon gun” described in his 1865 novel From the Earth to the Moon. • Escape velocity is proportional to the square root of the planet's mass and inversely proportional to the square root of the distance from its centre, but is not affected by the object's mass.

  21. Newton's escape velocity • Newton's thought experiment related to firing a gun pointing horizontally, on top of a very high mountain. At lower muzzle velocities the cannon ball would fall to the ground in a parabolic trajectory as shown by Galileo. • As the gun's muzzle velocity is increased the ball will hit further and further, but eventually, because the Earth is round it will end up not being able to hit the ground at all (because, as it falls, the surface of the Earth curves away from it. • The ball would complete a circular orbit around the Earth and if the gun was moved in time and there was no air resistance the ball would be in a circular orbit around the Earth • If the ball was fired at even higher speeds the orbit would become an ellipse. • At speeds above escape velocity the trajectory would become a hyperbola and the ball would leave forever.

  22. G-forces • An acceleration of 1g is equal to standard gravity (9.80 ms-2)‏ • G force = (a – g) /g • Human tolerances depend on the magnitude of the G-force, the length of time it is applied, the direction it acts, the location of application, and the posture of the body • A constant 16 g for a minute can be Fatal. • Astronauts and test pilots are tested for their ability to withstand high G's in special equipment.

  23. G forces and the Apollo space craft* 1. Launch with ignition of the S-IC. Note how the acceleration rapidly rises with increasing engine efficiency and reduced fuel load. 2. Cut-off of the centre engine of the S-IC. 3. Outboard engine cut-off of the S-IC at a peak of 4g. 4. S-II stage ignition. Note the reduced angle of the graph for although the mass of the first stage has been discarded, the thrust of the S-II stage is nearly one tenth of the final S-IC thrust. 5. Cut-off of the centre engine of the S-II. 6. Change in mixture ratio caused by the operation of the PU valve. The richer mixture reduces the thrust slightly. 7. Outboard engine cut-off of the S-II at a peak of approximately 2.7g. 8. S-IVB stage ignition. Note again the reduced angle of the graph caused by the thrust being cut by a fifth. 9. With the cut-off of the S-IVB's first burn, the vehicle is in orbit.. The 4g reached during boost is not the highest that will be experienced during the mission. Entry through the Earth's atmosphere decelerates the Command Module at about 6½g.] *http://history.nasa.gov/ap15fj/01launch_to_earth_orbit.htm

  24. Robert H. Goddard • Robert H Goddard ( 1882 – 1945), was an American physics professor and scientist. He was a pioneer of controlled, liquid-fueled rocketry. • In 1926 he launched the world's first liquid-fueled rocket and from 1930 to 1935, he launched rockets that attained higher speeds and higher altitudes. • His work in this field was revolutionary, he is recognized as one of the fathers of modern rocketry. • In 1914, his first two (of 214) patents were accepted and registered. The first, described a multi-stage rocket. The second, described a rocket fueled with gasoline and liquid nitrous oxide. • In 1919, the Smithsonian Institution published Goddard's advanced treatment on rocketry: “A Method of Reaching Extreme Altitudes”. In it he describes his mathematical theories of rocket flight, his experiments with solid-fuel rockets, and the possibilities he saw of exploring the earth's atmosphere and beyond. This book is regarded as one of the pioneering works of the science of rocketry. • On Sept. 16, 1959, the U.S. Congress authorized the issue of a gold medal in the honor of Professor Robert H. Goddard

  25. Launching a rocket from Earth • Earth orbits the Sun at a speed of 107,000 kmh-1 Launching a rocket in the same direction as Earth's movement, will provide a big boost in relative speed (to the Sun) and save a lot of fuel. • Earth rotates toward the East, one complete turn each day. This means that at the equator, Earth's surface has a linear speed of about 1600 kmh-1. For this reason most launch sites are located near the equator and rockets are launched toward the east, thus obtaining a 'free' boost from Earth's rotational motion. • The eastward launch time is chosen to give the rocket the time to accelerate as it goes partway around Earth. • For interplanetary travel, it is important to chose the right time of the year (i.e. the position of the Earth in its orbit) to launch. This is known as a “launch-window”

  26. Off the pad and into orbit

  27. Rockets can't fly in a vacuum ... • On January 12, 1920 a front-page story in The New York Times editorial delighted in heaping scorn on the proposal that travel to the Moon was possible. It expressed disbelief that: “Professor Goddard actually does not know of the relation of action to reaction, and the need to have something better than a vacuum against which to react" ! • Of course the newspaper was completely wrong (and that is not news). The action-reaction relationship is between the rocket and the gases emitted, and not between the rocket and air. • This is an example of how the Law of Conservation of Momentum, which is Newton's third law, can be used to analyse rocket motion. • For a rocket at rest, the momentum of the system (rocket + fuel) is zero. According to the Law of Conservation of Momentum this must be preserved. • The mass of fuel burned / second is much less than the mass of the rocket, but due to the explosive nature of rocket fuel, the velocity of the hot exhaust gases will be far greater than the velocity of the rocket • As fuel is burnt the mass of the rocket diminishes but its velocity increases. The momentum of the system remains zero.

  28. Forces on astronauts • Two forces act on an astronaut during launch: the thrust (T) and the astronaut's own weight (mg). • Newton’s second law is used to arrive at the relationship between the acceleration of the rocket and the forces on the astronaut, • The astronaut experiences this acceleration as an apparent increase in his/her weight of a magnitude that depends on the rocket's acceleration. An acceleration of 4g is experienced as a four-fold increase in weight. • Once the rocket reaches a stable orbit a 'weightlessness' is experienced. The astronauts are not really weightless but are continuously falling (in free-fall) toward the centre of the Earth with an acceleration of g (for that altitude)‏ • During re-entry the spacecraft must be decelerated as quickly and as safely as possible. The acceleration of g downward is opposed by air resistance, which at high speeds can cause the space ship to heat-up to dangerous temperature. • The re-entry trajectory is long and shallow to decrease the re-entry g-forces on the astronauts, to decrease the speed of the aircraft and so avoid burn-up or impact at a fatally damaging speed.

  29. Circular orbits • Any object that is moving in a circular path at a uniform speed is accelerating toward the centre of the circular path (its speed is constant, but its direction is constantly changing).‏ The acceleration is called centripetal (centre-pointing) and is associated with a force called the centripetal force: Fc = mac (m= mass of the object in circular motion)‏ For circular motion it can be shown that: ac = v2 / r (v = instantaneous tangential speed; r = radius of circle)‏ Therefore , Fc = mv2 / r • For a rock at the end of a string that is being rotated in uniform circular motion, the Fc is the tension in the string. For a satellite or planet in uniform circular orbit, the Fc is the gravitational attraction between the satellite / planet (m) and the central body (M). Hence: Fc = Fg mv2 / r = G M m / r2 v2= G M / r • 'v' is the orbital velocity of the satellite, it is independent of its mass, but dependent on the mass of the central body (planet or star).

  30. Geostationary orbits A satellite in a geostationary orbit (GO) has an orbital period equal to one sidereal day (23 hours 56 minutes). From the ground, a satellite in GO appears fixed in the sky because its period is the same as the Earth's. A satellite in GO will have an altitude above the upper van Allen belts of approximately 35 800 km. An object in GO will need an orbital velocity of about 11,000 km h-1. Satellites in GO are mainly country- specific communications and weather satellites. Two types of orbits Low Earth orbits • A low Earth orbit (LEO) is an orbit that lies between the Earth’s upper atmosphere and the lower van Allen radiation belts. The average altitude for a LEO is from 200 km to 1,000 km above the surface of the Earth. • An object in LEO will need an orbital velocity of approximately 28.000 km h-1 to maintain the orbit, • Objects in LEO will have orbital periods of about 90 minutes. • The space shuttle, the Hubble space telescope and the International Space-station are in LEO's

  31. What happened to Skylab? • Skylab was a space research laboratory constructed by NASA and was launched in 1973. • In mid 1979 it re-entered the atmosphere and landed in fiery chunks around the Balladonia Hotel/Motel (Western Australia). There were no injuries. • Jimmy Carter, the US President at the time, personally rang the Balladonia Hotel/Motel to apologise to the shaken but not injured staff and guests. • What went wrong? • Through a process called 'orbital decay' satellites in Low Earth Orbits are slowed down by the friction with the very thin air of the upper atmosphere. This friction results in a loss kinetic energy. • The satellite drops down to lower altitude and gains kinetic energy at the expense of gravitational potential energy. It will now be moving faster but a faster velocity means increased friction. At this lower altitude, the air is even denser. The loss in kinetic energy now is even greater, so the process picks up speed and the satellite is soon on a no-return path down to Earth. • Most satellites in LEO are small enough to burn up from air-friction before reaching the ground. Skylab was just too big (88,900 kg) and pieces of it managed to hit the ground in WA. • The Hubble Space telescope (11,100 kg) orbits in a LEO too and if it is not re-boosted by a shuttle or other means, it will re-enter the Earth's atmosphere sometime between 2010 and 2032.

  32. Keppler's Law of Periods (3rd)‏ • Notice that, • With a system of planets or satellites rotating a central body, the right hand side of the equation remains constant and does not depend on the individual masses of the rotating bodies but only on the mass of the central body • If the ratio of the (radius)3 to the (period)2 is known for one body, it will be the same for all the other bodies rotating around the same central star or planet.

  33. Orbital velocity, the gravitational constant, mass of the central body, mass of the satellite and the radius of the orbit Mass of the satellite and radius of the orbit can be related to the period of the orbit. Keppler's law can be used to find the relationship between orbital velocity and orbital period. Orbital velocity is the rectilinear, instantaneous speed tangential to the orbital path in the direction of movement.

  34. Re-entry • For spacecraft needing to re-enter the Earth's atmosphere safely, there is only a small angular window available. • If the angle is too shallow the spacecraft will bounce on the atmosphere like a flat stone on a pond of water; if the angle is too steep the spacecraft will suffer too much drag from the air and will burn up and the deceleration will be too rapid. • The angles differ for different orbits and different spacecraft: for the Apollo capsule the window was between 5o and 7o but for the space shuttle orbiter it is between 1o and 1.5o. • There are other consideration for a safe re-entry and a safe landing. • Spacecraft in orbit have kinetic energy, as the craft descends even more kinetic energy is produced as it loses gravitational potential energy. On re-entry, some of this energy is converted into a lot of heat by air friction. The effect of this heat can be minimized by 2 methods: • By the use of an ablative shield (substances that will burn at a very high temperature and thus use-up the heat, like on the Apollo capsule underside). • By using a long and gradual decent with a heat- insulating shield on the underside (the space shuttle uses this method).‏

  35. Re-entry • The heat generated also causes a general radio black-out with the craft as the over-heated air molecules become ionized. For a period of time the craft cannot be contacted and the crew cannot be warned of any dangerous situations that might be developing e.g. being off-course • The orbit speeds are in excess of 20 000 km h-1 to decrease from that speed down to a tolerable impact velocity in a distance of just 200 or so km would need very high decelerations (work it out). Hence the re-entry trajectory has too be very shallow resulting in a long path, even then the deceleration is very high and the G-forces on the astronauts can be considerably higher than launch G-forces. • Safe impact with the surface is achieved by the use of parachutes deployed at correct altitudes, by splashing in water rather than on hard ground or by gliding down to an airport tarmac like glider (space shuttle)‏

  36. Revision questions - 2 • Describe the trajectory of an object undergoing projectile motion within the Earth’s gravitational field in terms of horizontal and vertical components • Calculate the maximum height, the time of flight and the range of an object with an initial velocity of 30 ms-1 that is projected at 3 different angles: 30o; 45o and 60o • Describe a first-hand investigation you performed to analyse data and to calculate initial and final velocity, maximum height reached, range and time of flight of a projectile. • Describe Galileo’s contribution to projectile motion. • Explain the concept of escape velocity. • Outline Newton’s concept of escape velocity. • Identify why the term ‘g forces’ is used to explain the forces acting on an astronaut during launch • Present information on the contribution of one of the following to the development of space exploration: Tsiolkovsky, Oberth, Goddard, Esnault-Pelterie, O’Neill or von Braun

  37. Revision questions - 3 • Discuss the effect of the Earth‘s motion in space on the launch of a rocket. • Describe the changing acceleration of a 2 stage rocket during launch. • Describe the forces experienced by astronauts during launch. • Describe the forces involved with uniform circular motion. • Compare low Earth and Geostationary orbits • Account for the orbital decay of satellites in low Earth orbit. • Calculate the orbital speed and period of a satellite orbiting at an altitude of 350 km above the Earth's surface. Explain why this is not a Geostationary orbit. • The average radius of Earth's orbit is 149,600,000 km and its period of rotation is 365.26 days. If Jupiter rotates the Sun in 4332.71 Earth days, calculate the average distance of Jupiter from the Sun • Define the term orbital velocity and using Keppler's 3rd law find its relationship to the period of the orbit • Outline issues that relate to a safe re-entry and touch down for a manned spacecraft in parking orbit around the Earth. Identify which of these would not apply to a safe landing on the Moon's surface

  38. 3. Gravity

  39. Gravity • Gravity is the force of attraction between two or more masses. • Each mass is thought of having an infinite gravitational field surrounding it in space • The gravitational force exerted by an object is proportional to its mass. • The strength of the field obeys the inverse- square law (it diminishes as the inverse of the square of the distance from the centre of mass). • Gravity is the weakest of the four known forces, but large bodies like the Sun and the planets exert strong gravitational fields because of their large masses • Gravity holds the planets and satellites in their orbits it even stops the thermonuclear fusion reaction in the Sun from exploding it apart. • Gravity shapes the structure and evolution of stars, galaxies, and the entire universe...

  40. Newton's Law Newton's Law of Universal gravitation states” “Every object in the universe attracts every other object with a force directed along the line joining the centres of mass of the two objects. The force point toward each object and is proportional to the product of their masses and inversely proportional to the distance separating their centres”. G = 6.67300 × 10-11 m3 kg-1 s-2 (Universal gravitation constant)‏

  41. Newton's law and the motion of satellites • As previously shown; Newton's Law of gravitation is needed to derive an expression for the orbital velocity of a satellite in near circular orbit (it is also used for elliptical orbits but the math involved is beyond our scope)‏. • Newton's Law can also be used to derive Keppler's third law. • With these two laws the path or orbit of any satellite or planet can be analyzed and calculated. Predictions can be made as to its future positions to the extent that spacecraft can find them in the vastness of space.

  42. Slingshot • The slingshot effect is also know as a 'flyby' or as a 'gravity assist' trajectory. It consists of piloting or directing the spacecraft close to a planet in order to achieve a change in the direction or a change in velocity without the expenditure of fuel. • Depending on the direction of approach of the spacecraft relative to the planet's motion, a spacecraft' s velocity can be increased (if the destination is further on) or decreased (if a parking orbit is the aim) • In a gravity-assist trajectory, momentum is transferred from the orbiting planet to a spacecraft approaching it (it's not unlike an elastic collision between two billiard balls, except one of the balls is millions of times more massive than the other!)‏ • Both gain/lose the same amount of momentum but the planet shows negligible change in its velocity as it is so massive, whereas the spacecraft shows a significant change in it's speed (and / or direction)‏ • Voyager 2 in its flyby with Jupiter increased its speed from 10 kms-1 to almost 30 kms-1 without burning any fuel!

  43. Variations in gravitational force • Gravitational force depends on the mass and is inversely proportional to distance. • A body which has twice the mass of another will have twice the gravitational force at the same distance • Doubling the distance from a mass will reduce its gravitational force to a quarter • The value of g on a planet's surface with the same radius as Earth's but ½ the mass will be 9.8 / 2 = 4.9 ms-2 • The value of g on a planet's surface with the same mass as Earth's but ½ the radius will be 4 x 9.8 = 39.2 ms-2 • On a local level, because g depends on mass, the denser rocks will exert a higher gravitational force. • Satellites can measure the surface variation of g for the Earth and have produced colourful maps. They show that where the crust is thinnest, the ocean floor, g is smallest.

  44. Revision questions - 4 • Define Newton’s Law of Universal Gravitation. • Discuss the importance of Newton’s Law of Universal Gravitation in understanding and calculating the motion of satellites. • Identify that a slingshot effect can be provided by planets for space probes. • Discuss the factors that affect the strength of the gravitational force. • The International Space Station presently has a total mass of approximately 227,000 kg and is in a LEO at an average altitude of 350 km. Calculate: • The value of g at this altitude • The orbital velocity of the ISS • Its period of rotation • The work done to place it into orbit • Its kinetic energy • The r3 / T2 ratio for the ISS and hence the period of rotation of the Moon. (Moon – Earth distance = 3 x 10 5 km)‏ • Describe a gravitational field in the region surrounding a massive object in terms of its effects on other masses in it

  45. 4. “c”

  46. To aether or not to aether? • In 1801 Thomas Young performed the double-slit experiment and proved the wave nature of light. All waves known at that time needed a medium in which to propagate, e.g. sound cannot travel in a vacuum. But, no medium could be found for the propagation of light and light was known to travel in a vacuum. • The luminiferous aether or ether was hypothesized as being the medium that pervaded the entire universe (even solid objects) and that it was the medium through which all electromagnetic waves propagated. • The aether was given a set of properties: • The aether should: fill all of space and be stationary in space; be perfectly transparent; permeate all matter; have a low density and have great elasticity, it must be very light but almost incompressible to allow light to travel so fast. • Yet, it must allow solid bodies to pass through it freely, without any resistance, or the planets would be slowing down. • It is the relative motion of the Earth through the ether that Michelson and Morley tried to measure.

  47. M & M - Detecting the Aether Wind • The thought behind the Michelson-Morley (M&M) experiment is better understood by considering these two sketches of two swimmers (a similar drawing was included in their original paper)‏ • Swimmers A and B both swim at exactly the same speed of 5 m/s. They both start and return at point X. • In sketch 1 (no current)- both start and return at the same time. • In sketch 2 (a 3 m/s current) • Swimmer A takes 12.5s to swim to Y (@ 8 m/s) and 50s to swim back to X (@ 2 m/s). A total of 62.5s • Swimmer B has to take an angled course to point P (because of the current) in order to return to the same point. The course is longer (125 m) and it takes him 25s for both trips a total of 50s • The river represents the aether; the two swimmers represent Earth moving along and across the aether. The movement of the solar system through the aether is the current. • M&M designed equipment using an interferometer that was calculated to be up to 40 times more accurate than was needed.

  48. M & M 's experiment • The paths A and B are represented by the swimmers A and B in the preceding example. As the Experiment is rotated their respective arrival times at the interferometer screen should change in the presence of an aether current. This change will be easily detected by a shift in the interference fringes produced. • Even though the experiment was repeated many times, at different times of the year (position in Earth's orbit) and at different altitudes.NO SIGNIFICANT CHANGE WAS EVER DETECTED! A null result, conclusion: NO AETHER ??

  49. M&M' s null result • Albert Michelson and Edward Morley were experienced and rigorous scientists (Michelson had just succeeded in making the most accurate measurement of the speed of light of the time – a figure that is accurate to this day). • Their experiment was well planned, well constructed and provided reproducible results. They were not satisfied in repeating it a few times but actually repeated it many times in different locations and at different times during the year. • Both were firm believers in the aether theory, so if there was any bias at all, it would have been for a positive result, not a null one. Both were very reluctant in reaching the only conclusion possible from their results: that the existence of the aether was severely in doubt. Both received the Nobel prize for this fundamental “ null” experiment. • Many other physicists over the years (to this day!) have had trouble in letting the aether theory go and many modifications of the aether theory have been tested, but to date each test has failed. • Some years after the Michelson-Morley experiments, Albert Einstein proposed his theory of special relativity. Even though Einstein did not set out to prove that the aether did not exist, a result of his theory was that the aether is not needed. • In contrast to the aether theory, Einstein's special theory of relativity has had confirmation from many of experiments.

  50. Inertial frames of reference. • An inertial frame of reference is one that is at rest or that is moving at constant velocity • A non-inertial frame of reference is one that is accelerating. • By definition all inertial frames of reference are identical – all will produce the same results to experiments carried out in them • Also by definition any mechanical experiment carried out in an inertial frame of reference will provide NO information regarding the state of uniform motion or rest of the frame. • i.e. You cannot tell whether you are moving or not unless you look at another inertial frame of reference and then you can measure your relative speeds. • This is known as Galilean Relativity. Galileo was the first to recognize that any observation within the inertial frame of reference would not help to find out whether the frame of reference was at rest or moving at a steady velocity. • Einstein took Galilean Relativity a step forward, by including electromagnetism. He proposed that any electromagnetic experiment would also give the same results in any inertial frame of reference.

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