Solution:<\/strong><\/span>
\nNo The force of Earth\u2019s gravity is practically as strong in orbit as it is on the surface of Earth The astronauts experience weightlessness because they are in constant free fall.<\/p>\nChapter 12 Gravity Q.1P<\/strong>
\nCE System A has masses m and m separated by a distance r; system B has masses m and 2m separated by a distance 2r; system C has masses 2m and 3m separated by a distance 2r, and system D has masses 4m and 5m separated by a distance 3r. Rank these systems in order of increasing gravitational force. Indicate ties where appropriate.
\nSolution:<\/strong><\/span>
\n<\/p>\nChapter 12 Gravity Q.2CQ<\/strong>
\nWhen a person passes you on the street, you do not feel a gravitational tug. Explain.
\nSolution:<\/strong><\/span>
\n<\/p>\nChapter 12 Gravity Q.2P<\/strong>
\nIn each hand you hold a 0.16-kg apple. What is the gravitational force exerted by each apple on the other when their separation is (a) 0.25 m and (b) 0.50 m?
\nSolution:<\/strong><\/span>
\n
\n<\/p>\nChapter 12 Gravity Q.3CQ<\/strong>
\nTwo objects experience a gravitational attraction. Give a reason why the gravitational force between them does not depend on the sum of their masses.
\nSolution:<\/strong><\/span>
\nThe force of gravity between two point masses m1 and m2, separated by a distance r, is attractive and of magnitude
\n
\nwhere G is the universal gravitational constant.
\nGravity exerts an action-reaction pair of forces on m1 and m2. That is, the force exerted by gravity on m1 is equal in magnitude but opposite in direction to the force exerted on m2. It is dependent on the product of masses. If the gravitational force depended on the sum of the two masses, it would predict a non-zero force even when one of the masses is zero. That is, there would be a gravitational force between a mass and a point in empty space, which is certainly not what we observed.<\/p>\nChapter 12 Gravity Q.3P<\/strong>
\nA 6.1-kg bowling ball and a 7.2-kg bowling ball rest on a rack 0.75 m apart. (a) What is the force of gravity exerted on each of the balls by the other ball? (b) At what separation is the force of gravity between the balls equal to 2.0 \u00d7 10?9N?
\nSolution:<\/strong><\/span>
\n<\/p>\nChapter 12 Gravity Q.4CQ<\/strong>
\nImagine bringing the tips of your index fingers together. Each finger contains a certain finite mass, and the distance between them goes to zero as they come into contact. From the force law F = Gm1m2\/r2 one might conclude that the attractive force between the fingers is infinite, and, therefore, that your fingers must remain forever stuck together. What is wrong with this argument?
\nSolution:<\/strong><\/span>
\nAs the tips of the fingers approach one another, we can think of them as being two small spheres that touch each other. Even though the two spheres touch each other, the distance between the centers is not zero. This is always a finite number. Therefore, the force between the spheres is always finite, even they touch each other. As such, the two fingers simply experience the finite force of two point masses separated by a finite distance.<\/p>\nChapter 12 Gravity Q.4P<\/strong>
\nA communications satellite with a mass of 480 kg is in a circular orbit about the Earth. The radius of the orbit is 35,000 km as measured from the center of the Earth. Calculate (a) the weight of the satellite on the surface of the Earth and (b) the gravitational force exerted on the satellite by the Earth when it is in orbit.
\nSolution:<\/strong><\/span>
\n
\n<\/p>\nChapter 12 Gravity Q.5CQ<\/strong>
\nDoes the radius vector of Mars sweep out the same amount of area per time as that of the Earth? Why or why not?
\nSolution:<\/strong><\/span>
\nNo. The amount of area swept out per time varies from planet to planet because the linear speeds of planets are different.<\/p>\nChapter 12 Gravity Q.5P<\/strong>
\nThe Attraction of Ceres Ceres, the largest asteroid known, has a mass of roughly 8.7 \u00d7 1020 kg. If Ceres passes within 14,000 km. of the spaceship in which you are traveling, what force does it exert on you? (Use an approximate value for your mass, and treat yourself and the asteroid as point objects.)
\nSolution:<\/strong><\/span>
\n<\/p>\nChapter 12 Gravity Q.6CQ<\/strong>
\nWhen a communications satellite is placed in a geosynchronous orbit above the equator. it remains fixed over a given point on the ground. Is it possible to put a satellite into an orbi t so that it remains fixed above the North Pole? Explain
\nSolution:<\/strong><\/span>
\nINot possiblel because a satellite will appear stationary only when it revolves in an orbit that is concentric and coplanar with the equatorial plane, has a period of revolution of 24 hours, and
\nhas a sense of revolution from the west to the east of Earth. As the north pole is away from the equatorial plane. it will not be possible to put a geostationary satellite over the north pole.<\/p>\nChapter 12 Gravity Q.6P<\/strong>
\nIn one hand you hold a 0.11-kg apple, in the other hand a 0.24-kg orange. The apple and orange are separated by 0.85 m. What is the magnitude of the force of gravity that (a) the orange exerts on the apple and (b) the apple exerts on the orange?
\nSolution:<\/strong><\/span>
\n<\/p>\nChapter 12 Gravity Q.7CQ<\/strong>
\nThe Mass of Pluto On June 22, 1978, James Christy made the first observation of a moon orbiting Pluto. Until that lime the mass of Pluto was not known, but with the discovery of its moon, Charon, its mass could be calculated with some accuracy. Explain.
\nSolution:<\/strong><\/span>
\n<\/p>\nChapter 12 Gravity Q.7P<\/strong>
\nIP A spaceship of mass m travels from the Earth to the Moon along a line that passes through the center of the Earth and the center of the Moon. (a) At what distance from the center of the Earth is the force due to the Earth twice the magnitude of the force due to the Moon? (b) How does your answer to part (a) depend on the mass of the spaceship? Explain.
\nSolution:<\/strong><\/span>
\n
\n<\/p>\nChapter 12 Gravity Q.8CQ<\/strong>
\nRockets arc launched into space from Cape Canaveral in an easterly direction Is there an advantage to launching to the east versus launching to the west? Explain
\nSolution:<\/strong><\/span>
\nEarth revolves from west to east (counterclockwise) about its polar axis. Therefore, all the particles on Earth have a velocity from west to east. This velocity is at a maximum along the
\nequatorial line, as y = Rw,where R is the radius of Earth and w is the angular velocity of Earth\u2019s revolution about its polar axis.
\nICape Canaveral is situated at the equator so when a rocket is launched from west to east in this place. the maximum linear velocity is added to the launching velocity of the rocket Because of this. launching becomes easied<\/p>\nChapter 12 Gravity Q.8P<\/strong>
\n
\nSolution:<\/strong><\/span>
\n
\n
\n
\n
\n
\n<\/p>\nChapter 12 Gravity Q.9CQ<\/strong>
\nOne day in the future you may take a pleasure cruise to the Moon While there you might climb a lunar mountain and throw a rock horizontally from its summit If. in principle, you could throw the rock fast enough, it might end up hitting you in the back Explain.
\nSolution:<\/strong><\/span>
\nIon the Moon. where there is no atmosphere, a rock can orbit at any altitudel where it clears the mountains \u2014 as long as it has sufficient speed If we could give a rock enough speed. it would orbit the Moon and return to us from the other side (behind).<\/p>\nChapter 12 Gravity Q.9P<\/strong>
\n
\nSolution:<\/strong><\/span>
\n
\n<\/p>\nChapter 12 Gravity Q.10CQ<\/strong>
\nApollo astronauts orbiting the Moon at low altitude noticed occasional changes \u00a1n their orbit that they attributed to localized concentrations of mass below the lunar surface. Just what effect would such \u2018Thascons\u201d have on their orbit?
\nSolution:<\/strong><\/span>
\nAs the astronauts approach a mass concentration, its increased gravitational attraction would increase the speed of the craft Similarly, as they pass the mass concentration, its ravitationaI attraction is in the backward direction, which decreases their speed I<\/p>\nChapter 12 Gravity Q.10P<\/strong>
\n
\nSolution:<\/strong><\/span>
\n
\n
\n
\n
\n<\/p>\nChapter 12 Gravity Q.11CQ<\/strong>
\nIf you light a candle on the space shuttle\u2014which would not be a good idea\u2014would it burn the same as on the Earth? Explain
\nSolution:<\/strong><\/span>
\nNo. In the weightless environment of the shuttle, there is no convection which is required to bring fresh oxygen to the flame. Without convection, a flame usually goes out very quickly. In carefully controlled experiments on the shuttle, however, small flames have been maintained for considerable times These \u201cweightless\u201d flames are spherical in shape. as opposed to the tear- shaped flames on Earth<\/p>\nChapter 12 Gravity Q.11P<\/strong>
\nIP Three 6.75-kg masses are at the corners of an equilateral triangle and located in space far from any other masses. (a) If the sides of the triangle are 1.25 m long, find the magnitude of the net force exerted on each of the three masses. (b) How does your answer to part (a) change if the sides of the triangle are doubled in length?
\nSolution:<\/strong><\/span>
\n
\n
\n<\/p>\nChapter 12 Gravity Q.12CQ<\/strong>
\nThe force exerted by the Sun on the Moon is more than twice the force exerted by the Earth on the Moon. Should the Moon be thought of as orbiting the Earth or the Sun? Explain.
\nSolution:<\/strong><\/span>
\n<\/p>\nChapter 12 Gravity Q.12<\/strong>
\n
\nSolution:<\/strong><\/span>
\n
\n
\n
\n
\n
\n<\/p>\nChapter 12 Gravity Q.13CQ<\/strong>
\n
\nSolution:<\/strong><\/span>
\nThe net force acting on the moon is always directed toward the Sun, never away from the Sun. Therefore, the Moon\u2019s orbit must always curve toward the Sun. It curves sharply toward the Sun when Earth is between the Moon and the Sun, and curves only slightly toward the Sun when the Moon is between the Sun and Earth.<\/p>\nChapter 12 Gravity Q.13P<\/strong>
\nSuppose that three astronomical objects (1, 2, and 3) are observed to lie on a line, and that the distance from object 1 to object 3 is D. Given that object 1. has four times the mass of object 3 and seven times the mass of object 2, find the distance between objects 1 and 2 for which the net force on object 2 is zero.
\nSolution:<\/strong><\/span>
\n
\n
\n<\/p>\nChapter 12 Gravity Q.14P<\/strong>
\nFind the acceleration due to gravity on the surface of (a) Mercury and (b) Venus.
\nSolution:<\/strong><\/span>
\n
\n<\/p>\nChapter 12 Gravity Q.15P<\/strong>
\nAt what altitude above the Earth’s surface is the acceleration due to gravity equal to g\/2?
\nSolution:<\/strong><\/span>
\n<\/p>\nChapter 12 Gravity Q.16P<\/strong>
\nTwo 6-7-kg bowling balls, each with a radius of 0.11 m, are in contact with one another. What is the gravitational attraction between the bowling balls?
\nSolution:<\/strong><\/span>
\n
\n
\n<\/p>\nChapter 12 Gravity Q.17P<\/strong>
\nWhat is the acceleration due to Earth’s gravity at a distance from the center of the Earth equal to the orbital radius of the Moon?
\nSolution:<\/strong><\/span>
\n<\/p>\nChapter 12 Gravity Q.18P<\/strong>
\nGravity on Titan Titan is the larges t moon o f Saturn and the only moon in the solar system known to have a substantial atmosphere. Find the acceleration due to gravity on Titan’s surface, given that its mass is 1.35 \u00d7 1023 kg and its radius is 2570 km.
\nSolution:<\/strong><\/span>
\n<\/p>\nChapter 12 Gravity Q.19P<\/strong>
\nIP At a certain distance from the center of the Earth, a 4.6-kg object has a weight of 2.2 N. (a) Find this distance, (b) If the object is released at this location and allowed to fal\u00ef toward the Earth, what is its initial acceleration? (c) If the object is now moved twice as far from the Earth, by what factor does its weight change? Explain, (d) By what factor does its initial acceleration change? Explain.
\nSolution:<\/strong><\/span>
\n
\n
\n<\/p>\nChapter 12 Gravity Q.20P<\/strong>
\nTine acceleration due to gravity on the Moon’s surface is known to be about one-sixth the acceleration due to gravity on the Earth. Given that the radius of the Moon is roughly one-quarter that of the Earth, find the mass of the Moon in terms of the mass of the Earth.
\nSolution:<\/strong><\/span>
\n
\n<\/p>\nChapter 12 Gravity Q.21P<\/strong>
\nIP An Extraterrestrial Volcano Several volcanoes have been observed erupting on the surface of Jupiter’s closest Galilean moon, lo. Suppose that material ejected from one of these volcanoes reaches a height of 5.00 km a fter being projected straight upward with an initial speed of 134 m\/s. Given that the radius of lo is 1820 km, (a) outlinca strategy thatallows you to calculate the mass of To. (b) Use your strategy to calculate Io’s mass.
\nSolution:<\/strong><\/span>
\n
\n<\/p>\nChapter 12 Gravity Q.22P<\/strong>
\nIP Verne’s Trip to the Moon In his novel From the Earth to the Moon, Jules Verne imagined that astronauts inside a spaceship would walk on the floor of the cabin when the force exerted on the ship by the Earth was greater than the force exerted by the Moon. When the force exerted by the Moon was greater, he thought the astronauts would walk on the ceiling of the cabin, (a) At what distance from the center of the Earth would the forces exerted on the spaceship by the Earth and the Moon be equal? (b) Explain why Verne’s description of gravitational effects is incorrect.
\nSolution:<\/strong><\/span>
\n
\n
\n<\/p>\nChapter 12 Gravity Q.23P<\/strong>
\nConsider an asteroid with a radius of 19 km and a mass of 3.35 X 1015 kg. Assume the asteroid is roughly spherical, (a) What is the acceleration due to gravity on the surface of the asteroid? (b) Suppose the asteroid spins about an axis through its center, like the Earth, with a rotational period T. What is the smallest value T can have before loose rocks on the asteroid’s equator begin to fly off the surface?
\nSolution:<\/strong><\/span>
\n
\n
\n<\/p>\nChapter 12 Gravity Q.24P<\/strong>
\nCE Predict\/Explain The Speed of the Earth The orbital speed of the Earth is greatest around January 4 and least around July 4. (a) Is the distance from the Earth to the Sun on January 4 greater than, less than, or equal to its distance from the Sun on July 4? (b) Choose the best explanation from among the following:
\nI. The Earth’s orbit is circular, with equal distance from, the Sun at all times.
\nII. The Earth sweeps out equal area in equal time, thus it must be closer to the Sun when it is moving faster.
\nIII. The greater the speed of the Earth, the greater its distance from the Sun.
\nSolution:<\/strong><\/span>
\na) The distance from the Earth to the Sun on January 4, is less than the distance from the Sun on July 4.
\nb) The Earth sweeps out equal area in equal time, thus it must be closer to the sun when it is moving faster.<\/p>\nChapter 12 Gravity Q.25P<\/strong>
\nC E A satellite orbits the Earth in a circular orbit of radius r. At some point its rocket engine is fired in such a way that its speed increases rapidly by a small amount. As a result, do the (a) apogee distance and (b) perigee distance increase, decrease, or stay the same?
\nSolution:<\/strong><\/span>
\nUse the concept of orbital transfer to place the satellite into a new orbit.
\n(a)
\nThe decelerating or accelerating rockets at some point in the circular orbit of the satellite would allow the satellite into a new orbit which is not a circle. The new orbit is an ellipse. The largest distance between the Earth and the satellite in an elliptical orbit is called the apogee distance. In the case of transfer of orbits, the apogee distance increases if the speed of the rocket increases a while in the original orbit.
\n(b)
\nThe smallest distance between the Earth and the satellite in an elliptical orbit is nothing but the perigee distance. In case of transfer of orbits, the perigee distance doesn\u2019t change and equal to the radius of the original circular orbit.<\/p>\nChapter 12 Gravity Q.26P<\/strong>
\ng Repeat the previous problem., only this time with the rocket engine of the satellite fired in such a way as to slow the satellite.
\nSolution:<\/strong><\/span>
\n(A) The satellite drops into an elliptical orbit that brings it closer to Earth.
\n(B) The apogee distance remains unchanged.
\n(C) The perigee distance is reduced.<\/p>\nChapter 12 Gravity Q.27P<\/strong>
\nCE Predict\/Explain The Earth-Moon Distance Is Increasing Laser reflectors left on the surface of the Moon by the Apollo astronauts show that the average distance from the Earth to the Moon is increasing at the rate of 3.8 cm per year. (a) As a result, will the length of the month increase, decrease, or remain the same? (b) Choose the best expianation from among the following: I. The greater the radius of an orbit, the greater the period,
\nwhich implies a longer month.
\nII. The length of the month will remain the same due to conservation of angular momentum,
\nIII. The speed of the Moon is greater with increasing radius; therefore, the length of the month will be less.
\nSolution:<\/strong><\/span>
\na) If the average distance increases, then the length of the month also increases.
\nb) The period depends upon the radius. Greater the radius, greater will be the period. Option (1) is correct.<\/p>\nChapter 12 Gravity Q.28P<\/strong>
\nApollo Missions On Apollq missions to the Moon, the command module orbited at an altitude of 110 km above the lunar surface. How long did it take for the command module to complete one orbit?
\nSolution:<\/strong><\/span>
\n<\/p>\nChapter 12 Gravity Q.29P<\/strong>
\nFind the orbital speed of a satellite in a geosynchronous circular orbit 3.58 X 107 m above the surface of the Earth.
\nSolution:<\/strong><\/span>
\n
\n<\/p>\nChapter 12 Gravity Q.30P<\/strong>
\nAn Extrasolar Planet In July of 1999 a planet was reported to be orbiting the Sun-like star Iota Horologii with a period of 320 days. Find the radius of the planet’s orbi t, assuming that iota Horologii has the same mass as the Sun. (This planet is presumably similar to Jupiter, but it may have large, rocky moons that enjoy a relatively pleasant climate.)
\nSolution:<\/strong><\/span>
\n<\/p>\nChapter 12 Gravity Q.31P<\/strong>
\nPhobos, one of the moons of Mars, orbits at a distance of 9378 km from the center of the red planet. What is the orbital period of Phobos?
\nSolution:<\/strong><\/span>
\n<\/p>\nChapter 12 Gravity Q.32P<\/strong>
\n\u00b7 The largest moon in the solar system is Ganymede, a moon of Jupiter. Ganymede orbits at a distance of 1.07 X 109 m from the center of Jupiter with an orbital period of about 6.18 X 10′ s. Using this information, find the mass of Jupiter.
\nSolution:<\/strong><\/span>
\n<\/p>\nChapter 12 Gravity Q.33P<\/strong>
\nIP Am Asteroid with Its Own Moon The asteroid 243 Ida has its own small moon, Dactyl. (See the photo on p. 390) (a) Outline a strategy to find the mass of 243 Ida, given that the orbital radius of Dactyl is 89 km arid its period is 19 hr. (b) Use your strategy to calculate the mass of 243 Ida.
\nSolution:<\/strong><\/span>
\n<\/p>\nChapter 12 Gravity Q.34P<\/strong>
\nGPS Satellites GPS (Global Positioning System) satellites orbit at an altitude of 2.0 x 107 m. Find (a) the orbital period, and (b) the orbital speed of such a satellite.
\nSolution:<\/strong><\/span>
\n
\n<\/p>\nChapter 12 Gravity Q.35P<\/strong>
\nIP Two satellites orbit the Earth, with satellite 1 at a greater altitude than satellite 2. (a) Which satellite has the greater orbital speed? Explain, (b) Calculate the orbital speed of a satellite that orbits at an altitude of one Earth radius above the surface of the Earth, (c) Calculate the orbital speed of a satellite that orbits at an altitude of two Earth radii above the surface of the Earth.
\nSolution:<\/strong><\/span>
\n
\n<\/p>\nChapter 12 Gravity Q.36P<\/strong>
\nIP Calculate the orbital periods of satellites that orbit (a) one Earth radius above the surface of the Earth and (b) two Earth radii above the surface of the Earth, (c) How do your answers to parts (a) and (b) depend on the mass of the satellites? Explain, (d) How do your answers to parts (a) and (b) depend on the mass of the Earth? Explain.
\nSolution:<\/strong><\/span>
\n
\n<\/p>\nChapter 12 Gravity Q.37P<\/strong>
\nS P The Martian moon Deimos has an orbital period that is greater than the other Martian moon, Phobos. Both moons have approximately circular orbits, (a) Is Deimos closer to or farther from Mars than Phobos? Explain, (b) Calculate the distance from the center of Mars to Deimos given that its orbital period is 1.10 \u00d7 105 s.
\nSolution:<\/strong><\/span>
\n<\/p>\nChapter 12 Gravity Q.38P<\/strong>
\nBinary Stars Centauri A and Centauri B are binary stars with a separation of 3.45 \u00d7 1012 m and an orbital period of 2.52 \u00d7 109 s. Assuming the two stars are equally massive (which is approximately the case), determine their mass.
\nSolution:<\/strong><\/span>
\n
\n
\n<\/p>\nChapter 12 Gravity Q.39P<\/strong>
\nFind the speed of Centauri A and Centauri B, using the information given in the previous problem.
\nSolution:<\/strong><\/span>
\n
\n<\/p>\nChapter 12 Gravity Q.40P<\/strong>
\nSputnik The first artificial satellite to orbit the Earth was Sputnik I, Saunched October 4,1957. The mass of Sputnik 1 was 83.5 kg, and its distances from the center of the Earth at apogee and perigee were 7330 km-and 6610 km, respectively. Find the difference in gravitational potential energy for Sputnik I as it moved from apogee to perigee.
\nSolution:<\/strong><\/span>
\n<\/p>\nChapter 12 Gravity Q.41P<\/strong>
\nCE Predict\/Explain (a) Is the amount of energy required to get a spacecraft from the Earth to the Moon greater than, less than, or equal to the energy required to get the same spacecraft from the Moon to the Earth? (b) Choose the best explanation from among the following:
\nI. The escape speed of the Moon is less than that of the Earth; therefore, less energy is required to leave the Moon.
\nII. The situation is symmetric, and hence the same amount of energy is required to travel in either direction.
\nIII. It takes more energy to go from the Moon to the Earth because the Moon is orbiting the Earth.
\nSolution:<\/strong><\/span>
\nUse the concept of escape speed of the planet. The escape speed of the planet is the minimum speed at which the object frees from the gravitational attraction of the planet.
\n(a)
\nThe escape speed of an object launched from the planet depends only on the mass and size of the planet, but not on the mass of the object. The escape speed of the Earth is much greater than that of the Moon. Since the kinetic energy is directly proportional to the square of the velocity, the more energy is required to launch the spacecraft from the Earth to the Moon than that required to launch the spacecraft from the Moon to the Earth.
\n(b)
\nThe option (I) is correct.<\/p>\nChapter 12 Gravity Q.42P<\/strong>
\n
\nSolution:<\/strong><\/span>
\n
\n
\n<\/p>\nChapter 12 Gravity Q.43P<\/strong>
\nCalculate the gravitational potential energy of a 8.8-kg mass (a) on the surface of the Earth and (b) at an altitude of 350 km. (c) Take the difference between the results for parts (b) and (a), and compare with nigh, where h = 350 km.
\nSolution:<\/strong><\/span>
\n
\n<\/p>\nChapter 12 Gravity Q.44P<\/strong>
\nTwo 0.59-kg basketballs, each with a radius of 12 cm, are just touching. How much energy is required to change the separation between the centers of the basketballs to (a) 1.0 m and (b) 10.0 m? (Ignore any other gravitational interactions.)
\nSolution:<\/strong><\/span>
\n<\/p>\nChapter 12 Gravity Q.45P<\/strong>
\nFind the minimum kinetic energy needed for a 39,000-kg rocket to escape (a) the Moon or (b) the Earth.
\nSolution:<\/strong><\/span>
\n
\n<\/p>\nChapter 12 Gravity Q.46P<\/strong>
\nCE Predict\/Explain Suppose the Earth were to suddenly shrink to half its current diameter, with its mass remaining constant, (a) Would the escape speed of the Earth increase, decrease, or stay the same? (b) Choose the best explanation from among the following:
\nI. Since the radius of the Earth would be smaller, the escape speed would also be smaller.
\nII. The Earth would have the same amount of mass, and hence its escape speed would be unchanged.
\nIII. The force of gravity would be much stronger on the surface of the compressed Earth, leading to a greater escape speed.
\nSolution:<\/strong><\/span>
\na) The escape speed of the earth increases.
\nb) The force of gravity would be much stronger on the surface of compressed Earth, leading to a greater escape speed. Option (III) is correct.<\/p>\nChapter 12 Gravity Q.47P<\/strong>
\nCE Is the energy required to launch a rocket vertically to a height h greater than, less than, or equal to the energy required to prit the same rocket into orbit at the height hi Explain.
\nSolution:<\/strong><\/span>
\nThe energy required to launch a rocket vertically to a height h is equal to the potential energy of the rocket at that height. However, for a rocket to be put into orbit at a height h, both kinetic energy and potential energy are required. So the energy required for the rocket to be put into orbit is greater than the energy required to launch a rocket vertically to the same height.<\/p>\nChapter 12 Gravity Q.48P<\/strong>
\nSuppose one of the Global Positioning System satellites has a speed of 4.46 km\/s at perigee and a speed of 3.64 km\/s at apogee. If the distance from the center of the Earth to the satellite at perigee is 2.00 \u00d7 104 lem, what is the corresponding distance at apogee?
\nSolution:<\/strong><\/span>
\n
\n<\/p>\nChapter 12 Gravity Q.49P<\/strong>
\n
\nSolution:<\/strong><\/span>
\n<\/p>\nChapter 12 Gravity Q.50P<\/strong>
\n\u00b7 Referring to Example 12-1, if the Millennium Eagle is at rest at point A, what is its speed at point B?
\n