Solution: Orbiting the MoonSuppose a spacecraft orbits the

Problem 1CQ The batter in a baseball game hits a homerun. As he circles the bases, is his angular velocity positive or negative?

Problem 1P What is the angular position in radians of the minute hand of a clock at (a) 5:00, (b) 7:15, and (c) 3:35?

Problem 2CQ Viewed from somewhere in space above the north pole, would a point on the earth’s equator have a positive or negative angular velocity due to the earth’s rotation?

Problem 2P A child on a merry-go-round takes 3.0 s to go around once. What is his angular displacement during a 1.0 s time interval?

Problem 3P What is the angular speed of the tip of the minute hand on a clock, in rad/s?

Problem 3CQ A cyclist goes around a level, circular track at constant speed. Do you agree or disagree with the following statement? “Since the cyclist’s speed is constant, her acceleration is zero.” Explain.

Problem 4CQ In uniform circular motion, which of the following quantities are constant: speed, instantaneous velocity, centripetal acceleration, the magnitude of the net force?

Problem 4P An old-fashioned vinyl record rotates on a turntable at 45 rpm. What are (a) the angular speed in rad/s and (b) the period of the motion?

Problem 5CQ A particle moving along a straight line can have nonzero acceleration even when its speed is zero (for instance, a ball in free fall at the top of its path). Can a particle moving in a circle have nonzero centripetal acceleration when its speed is zero? If so, give an example. If not, why not?

Problem 5P The earth’s radius is about 4000 miles. Kampala, the capital of Uganda, and Singapore are both nearly on the equator. The distance between them is 5000 miles. a. Through what angle do you turn, relative to the earth, if you fly from Kampala to Singapore? Give your answer in both radians and degrees. b. The flight from Kampala to Singapore takes 9 hours. What is the plane’s angular speed relative to the earth?

Problem 6CQ Would having four-wheel drive on a car make it possible to drive faster around corners on an icy road, without slipping, than the same car with two-wheel drive? Explain.

Problem 6P A Ferris wheel rotates at an angular velocity of 0.036 rad/s. At t = 0 min, your friend Seth is at the very top of the ride. What is Seth’s angular position at t = 3.0 min, measured counterclockwise from the top? Give your answer as an angle in degrees between 0° and 360°.

Problem 7CQ Large birds like pheasants often walk short distances. Small birds like chickadees never walk. They either hop or fly. Why might this be?

Problem 7P A turntable rotates counterclockwise at 78 rpm. A speck of dust on the turntable is at ? = 0.45 rad at t = 0 s. What is the angle of the speck at t = 8.0 s? Your answer should be between 0 and 2? rad.

Problem 8CQ When you drive fast on the highway with muddy tires, you can hear the mud flying off the tires into your wheel wells. Why does the mud fly off?

Problem 8P A fast-moving superhero in a comic book runs around a circular, 70-m-diameter track five and a half times (ending up directly opposite her starting point) in 3.0 s. What is her angular speed, in rad/s?

Problem 9CQ A ball on a string moves in a vertical circle as in Figure Q6.7. When the ball is at its lowest point, is the tension in the string greater than, less than, or equal to the ball’s weight? Explain. (You may want to include a free-body diagram as part of your explanation.)

Problem 9P Figure 9 shows the angular position of a potter’s wheel. a. What is the angular displacement of the wheel between t = 5 s and t = 15 s? b. What is the angular velocity of the wheel at t = 15 s? FIGURE 9

Problem 10CQ Give an everyday example of circular motion for which the centripetal acceleration is mostly or completely due to a force of the type specified: (a) Static friction. (b) Tension.

Problem 10P The angular velocity (in rpm) of the blade of a blender is given in Figure 10. a. If ? = 0 rad at t = 0 s, what is the blade’s angular position at t = 20 s? b. At what time has the blade completed 10 full revolutions? FIGURE 10

Problem 11CQ Give an everyday example of circular motion for which the centripetal acceleration is mostly or completely due to a force of the type specified: (a) Gravity. (b) Normal force.

Problem 11P A 5.0-m-diameter merry-go-round is turning with a 4.0 s period. What is the speed of a child on the rim?

Problem 12CQ It’s been proposed that future space stations create “artificial gravity” by rotating around an axis. (The space station would have to be much larger than the present space station for this to be feasible.) a. How would this work? Explain. b. Would the artificial gravity be equally effective throughout the space station? If not, where in the space station would the residents want to live and work?

Problem 12P The blade on a table saw spins at 3450 rpm. Its diameter is 25.0 cm. What is the speed of a tooth on the edge of the blade, in both m/s and mph?

Problem 13CQ A car coasts at a constant speed over a circular hill. Which of the free-body diagrams in Figure Q6.11 is correct? Explain.

Problem 13P The horse on a carousel is 4.0 m from the central axis. a. If the carousel rotates at 0.10 rev/s , how long does it take the horse to go around twice? b. How fast is a child on the horse going (in m/s)?

Problem 14CQ Riding in the back of a pickup truck can be very dangerous. If the truck turns suddenly, the riders can be thrown from the truck bed. Why are the riders ejected from the bed?

Problem 14P The radius of the earth’s very nearly circular orbit around the sun is . Find the magnitude of the earth’s (a) velocity and (b) centripetal acceleration as it travels around the sun. Assume a year of 365 days.

Problem 15CQ Variation in your apparent weight is desirable when you ride a roller coaster; it makes the ride fun. However, too much variation over a short period of time can be painful. For this reason, the loops of real roller coasters are not simply circles like Figure 6.16a. A typical loop is shown in Figure Q6.15. The radius of the circle that matches the track at the top of the loop is much smaller than that of a matching circle at other places on the track. Explain why this shape gives a more comfortable ride than a circular loop.

Problem 15P Your roommate is working on his bicycle and has the bike upside down. He spins the 60-cm-diameter wheel, and you notice that a pebble stuck in the tread goes by three times every second. What are the pebble’s speed and acceleration?

Problem 16CQ A small projectile is launched parallel to the ground at height h = 1 m with sufficient speed to orbit a completely smooth, airless planet. A bug rides in a small hole inside the projectile. Is the bug weightless? Explain.

Problem 16P To withstand “g-forces” of up to 10g, caused by suddenly pulling out of a steep dive, fighter jet pilots train on a “human centrifuge.” 10g is an acceleration of . If the length of the centrifuge arm is 12 m, at what speed is the rider moving when she experiences 10g?

Problem 17CQ Why is it impossible for an astronaut inside an orbiting space station to go from one end to the other by walking normally?

Problem 17P Figure P6.13 is a bird’s-eye view of particles on a string moving in horizontal circles on a tabletop. All are moving at the same speed. Rank in order, from largest to smallest, the tensions .

Problem 18CQ If every object in the universe feels an attractive gravitational force due to every other object, why don’t you feel a pull from someone seated next to you?

Problem 18P A 200 g block on a 50-cm-long string swings in a circle on a horizontal, frictionless table at 75 rpm. a. What is the speed of the block? b. What is the tension in the string?

Problem 19CQ A mountain climber’s weight is slightly less on the top of a tall mountain than at the base, though his mass is the same. Why?

Problem 19P A 1500 kg car drives around a flat 200-m-diameter circular track at 25 m/s. What are the magnitude and direction of the net force on the car? What causes this force?

Problem 20CQ Is the earth’s gravitational force on the sun larger than, smaller than, or equal to the sun’s gravitational force on the earth? Explain.

Problem 20P A fast pitch softball player does a “windmill” pitch, illustrated in Figure P6.18, moving her hand through a circular arc to pitch a ball at 70 mph. The 0.19 kg ball is 50 cm from the pivot point at her shoulder. At the lowest point of the circle, the ball has reached its maximum speed. a. At the bottom of the circle, just before the ball leaves her hand, what is its centripetal acceleration? b. What are the magnitude and direction of the force her hand exerts on the ball at this point?

Problem 21MCQ A ball on a string moves around a complete circle, once a second, on a frictionless, horizontal table. The tension in the string is measured to be 6.0 N. What would the tension be if the ball went around in only half a second? A. 1.5 N B. 3.0 N C. 12 N D. 24 N

Problem 21P baseball pitching machine works by rotating a light and stiff rigid rod about a horizontal axis until the ball is moving toward the target. Suppose a 144 g baseball is held 85 cm from the axis of rotation and released at the major league pitching speed of 85 mph. a. What is the ball’s centripetal acceleration just before it is released? b. What is the magnitude of the net force that is acting on the ball just before it is released?

Problem 22MCQ As seen from above, a car rounds the curved path shown in Figure Q6.22 at a constant speed. Which vector best represents the net force acting on the car?

Problem 22P You’re driving your pickup truck around a curve with a radius of 20 m. A box in the back of the truck is pressed up against the wall of the truck. How fast must you drive so that the force of the wall on the box equals the weight of the box?

Problem 23MCQ Suppose you and a friend, each of mass 60 kg, go to the park and get on a 4.0-m-diameter merry-go-round. You stand on the outside edge of the merry-go-round, while your friend pushes so that it rotates once every 6.0 s. What is the magnitude of the (apparent) outward force that you feel? A. 7 N B. 63 N C. 130 N D. 260 N

Problem 23P The passengers in a roller coaster car feel 50% heavier than their true weight as the car goes through a dip with a 30 m radius of curvature. What is the car’s speed at the bottom of the dip?

Problem 24MCQ The cylindrical space station in Figure Q6.25 , 200 m in diameter, rotates in order to provide artificial gravity of g for the occupants. How much time does the station take to complete one rotation? A. 3 s B. 20 s C. 28 s D. 32 s

Problem 24P You hold a bucket in one hand. In the bucket is a 500 g rock. You swing the bucket so the rock moves in a vertical circle 2.2 m in diameter. What is the minimum speed the rock must have at the top of the circle if it is to always stay in contact with the bottom of the bucket?

Problem 25MCQ Two cylindrical space stations, the second four times the diameter of the first, rotate so as to provide the same amount of artificial gravity. If the first station makes one rotation in the time T , then the second station makes one rotation in time A. T/4 B. 2 T C. 4 T D. 16 T

Problem 25P As a roller coaster car crosses the top of a 40-m-diameter loop-the-loop, its apparent weight is the same as its true weight. What is the car’s speed at the top?

Problem 26MCQ A newly discovered planet has twice the mass and three times the radius of the earth. What is the free-fall acceleration at its surface, in terms of the free-fall acceleration g at the surface of the earth?

Problem 26P A typical laboratory centrifuge rotates at 4000 rpm. Test tubes have to be placed into a centrifuge very carefully because of the very large accelerations. a. What is the acceleration at the end of a test tube that is 10 cm from the axis of rotation? b. For comparison, what is the magnitude of the acceleration a test tube would experience if stopped in a 1.0-ms-long encounter with a hard floor after falling from a height of 1.0 m?

Problem 27MCQ Suppose one night the radius of the earth doubled but its mass stayed the same. What would be an approximate new value for the free-fall acceleration at the surface of the earth?

Problem 27P A satellite orbiting the moon very near the surface has a period of 110 min. Use this information, together with the radius of the moon from the table on the inside of the back cover, to calculate the free-fall acceleration on the moon’s surface.

Problem 28MCQ Currently, the moon goes around the earth once every 27.3 days. If the moon could be brought into a new circular orbit with a smaller radius, its orbital period would be A. More than 27.3 days. B. 27.3 days. C. Less than 27.3 days.

Problem 28P The centers of a 10 kg lead ball and a 100 g lead ball are separated by 10 cm. a. What gravitational force does each exert on the other? b. What is the ratio of this gravitational force to the weight of the 100 g ball?

Problem 29MCQ Two planets orbit a star. You can ignore the gravitational interactions between the planets. Planet 1 has orbital radius and planet 2 has . Planet 1 orbits with period . Planet 2 orbits with period

Problem 29P The gravitational force of a star on an orbiting planet 1 is F1 Planet 2, which is twice as massive as planet 1 and orbits at twice the distance from the star, experiences gravitational force F2. What is the ratio F2/F1 ?

Problem 30MCQ A particle undergoing circular motion in the xy-plane stops on the positive y-axis. Which of the following does not describe its angular position? A. ?/2rad B. ? rad C. 5?/2 rad D. ?3?/2 rad

Problem 30P The free-fall acceleration at the surface of planet 1 is . The radius and the mass of planet 2 are twice those of planet 1. What is the free-fall acceleration on planet 2?

Problem 31MCQ Questions concern a classic figure-skating jump called the axle. A skater starts the jump moving forward as shown in Figure, leaps into the air, and turns one-and-a-half revolutions before landing. The typical skater is in the air for about 0.5 s, and the skater’s hands are located about 0.8 m from the rotation axis. FIGURE 31 What is the approximate angular speed of the skater during the leap? A. 2 rad/s ________________ B. 6 rad/s ________________ C. 9 rad/s ________________ D. 20 rad/s

Problem 31P What is the ratio of the sun’s gravitational force on you to the earth’s gravitational force on you?

Problem 32MCQ Questions concern a classic figure-skating jump called the axel. A skater starts the jump moving forward as shown in Figure, leaps into the air, and turns one-and-a-half revolutions before landing. The typical skater is in the air for about 0.5 s, and the skater’s hands are located about 0.8 m from the rotation axis. FIGURE 31 The skater’s arms are fully extended during the jump. What is the approximate centripetal acceleration of the skater’s hand? A. 10 m/s2 ________________ B. 30 m/s2 ________________ C. 300 m/s2 ________________ D. 450 m/s2

Problem 32P Suppose the free-fall acceleration at some location on earth was exactly . What would it be at the top of a 1000-m-tall tower at this location? (Give your answer to five significant figures.)

Problem 33MCQ Questions concern a classic figure-skating jump called the axle. A skater starts the jump moving forward as shown in Figure, leaps into the air, and turns one-and-a-half revolutions before landing. The typical skater is in the air for about 0.5 s, and the skater’s hands are located about 0.8 m from the rotation axis. FIGURE 31 What is the approximate speed of the skater’s hand? A. 1 m/s ________________ B. 3 m/s ________________ C. 9 m/s ________________ D. 15 m/s

Problem 33P a. What is the gravitational force of the sun on the earth? b. What is the gravitational force of the moon on the earth? c. The moon’s force is what percent of the sun’s force?

Problem 34P What is the free-fall acceleration at the surface of (a) Mars and (b) Jupiter?

Problem 35P Planet X orbits the star Omega with a “year” that is 200 earth days long. Planet Y circles Omega at four times the distance of Planet X. How long is a year on Planet Y?

Problem 36P Satellite A orbits a planet with a speed of 10,000 m/s. Satellite B is twice as massive as satellite A and orbits at twice the distance from the center of the planet. What is the speed of satellite B?

Problem 37P The Space Shuttle is in a 250-miie-high orbit. What are the shuttle’s orbital period, in minutes, and its speed?

Problem 38P The asteroid belt circles the sun between the orbits of Mars and Jupiter. One asteroid has a period of 5.0 earth years. What are the asteroid’s orbital radius and speed?

Problem 39P An earth satellite moves in a circular orbit at a speed of 5500 m/s. What is its orbital period?

Problem 40GP How fast must a plane fly along the earth’s equator so that the sun stands still relative to the passengers? In which direction must the plane fly, east to west or west to east? Give your answer in both km/h and mph. The radius of the earth is 6400 km.

Problem 41GP The car in Figure P6.51 travels at a constant speed along the road shown. Draw vectors showing its acceleration at the three points A, B, and C, or write . The lengths of your vectors should correspond to the magnitudes of the accelerations.

Problem 42GP In the Bohr model of the hydrogen atom, an electron orbits a proton at a distance of . The proton pulls on the electron with an electric force of . How many revolutions per second does the electron make?

Problem 43GP A 75 kg man weighs himself at the north pole and at the equator. Which scale reading is higher? By how much? Assume the earth is a perfect sphere. Explain why the readings differ.

Problem 44GP A 1500 kg car takes a 50-m-radius unbanked curve at 15 m/s. What is the size of the friction force on the car?

Problem 45GP A 500 g ball swings in a vertical circle at the end of a 1.5-m-long string. When the ball is at the bottom of the circle, the tension in the string is 15 N. What is the speed of the ball at that point?

Problem 46GP Suppose the moon were held in its orbit not by gravity but by a massless cable attached to the center of the earth. What would be the tension in the cable? See the inside of the back cover for astronomical data.

Problem 47GP A 30 g ball rolls around a 40-cm-diameter L-shaped track, shown in Figure 47, at 60 rpm. Rolling friction can be neglected. a. How many different contact forces does the track exert on the ball? Name them. b. What is the magnitude of the net force on the ball? FIGURE 47

Problem 48GP A 5.0 g coin is placed 15 cm from the center of a turntable. The coin has static and kinetic coefficients of friction with the turntable surface of . The turntable very slowly speeds up to 60 rpm. Does the coin slide off?

Problem 49GP A conical pendulum is formed by attaching a 500 g ball to a 1.0-m-long string, then allowing the mass to move in a horizontal circle of radius 20 cm. Figure 49 shows that the string traces out the surface of a cone, hence the name. a. What is the tension in the string? b. What is the ball’s angular velocity, in rpm? Hint: Determine the horizontal and vertical components of the forces acting on the ball, and use the fact that the vertical component of acceleration is zero since there is no vertical motion. FIGURE 49

Problem 50GP In an old-fashioned amusement park ride, passengers stand inside a 3.0-m-tall, 5.0-m-diameter hollow steel cylinder with their backs against the wall. The cylinder begins to rotate about a vertical axis. Then the floor on which the passengers are standing suddenly drops away! If all goes well, the passengers will “stick” to the wall and not slide. Clothing has a static coefficient of friction against steel in the range 0.60 to 1.0 and a kinetic coefficient in the range 0.40 to 0.70. What is the minimum rotational frequency, in rpm, for which the ride is safe?

Problem 51GP The 0.20 kg puck on the frictionless, horizontal table in Figure P6.59 is connected by a string through a hole in the table to a hanging 1.20 kg block. With what speed must the puck rotate in a circle of radius 0.50 m if the block is to remain hanging at rest?

Problem 52GP While at the county fair, you decide to ride the Ferris wheel. Having eaten too many candy apples and elephant ears, you find the motion somewhat unpleasant. To take your mind off your stomach, you wonder about the motion of the ride. You estimate the radius of the big wheel to be 15 m, and you use your watch to find that each loop around takes 25 s. a. What are your speed and magnitude of your acceleration? b. What is the ratio of your apparent weight to your true weight at the top of the ride? c. What is the ratio of your apparent weight to your true weight at the bottom?

Problem 53GP A car drives over the top of a hill that has a radius of 50 m. What maximum speed can the car have without flying off the road at the top of the hill?

Problem 54GP A 100g ball on a 60-cm-long string is swung in a vertical circle whose center is 200 cm above the floor. The string suddenly breaks when it is parallel to the ground and the ball is moving upward. The ball reaches a height 600 cm above the floor. What was the tension in the string an instant before it broke?

Problem 55GP While a person is walking, his arms (each with typical length 70 cm measured from the shoulder joint) swing through approximately a 45° angle in 0.50 s. As a reasonable approximation, we can assume that the arm moves with constant speed during each swing. a. What is the acceleration of a 1.0 g drop of blood in the fingertips at the bottom of the swing? b. Draw a free-body diagram for the drop of blood in part a. c. Find the magnitude and direction of the force that the blood vessel must exert on the drop of blood. d. What force would the blood vessel exert if the arm were not swinging?

The two identical pucks in Figure 56 rotate together on a frictionless, horizontal table. They are tied together by strings 1 and 2, each of length . If their common angular speed is , what are the tensions in the two strings?

Problem 57GP The ultracentrifuge is an important tool for separating and analyzing proteins in biological research. Because of the enormous centripetal accelerations that can be achieved, the apparatus (see Figure 6.18) must be carefully balanced so that each sample is matched by another on the opposite side of the rotor shaft. Failure to do so is a costly mistake, as seen in Figure P6.64. Any difference in mass of the opposing samples will cause a net force in the horizontal plane on the shaft of the rotor. Suppose that a scientist makes a slight error in sample preparation, and one sample has a mass 10 mg greater than the opposing sample. If the samples are 10 cm from the axis of the rotor and the ultracentrifuge spins at 70,000 rpm, what is the magnitude of the net force on the rotor due to the unbalanced samples?

Problem 58GP The Space Shuttle orbits 300 km above the surface of the earth. a. What is the force of gravity on a 1.0 kg sphere inside the Space Shuttle? b. The sphere floats around inside the Space Shuttle, apparently “weightless.” How is this possible?

Problem 59GP A sensitive gravimeter at a mountain observatory finds that the free-fall acceleration is less than that at sea level. What is the observatory’s altitude?

Problem 60GP Suppose we could shrink the earth without changing its mass. At what fraction of its current radius would the free-fall acceleration at the surface be three times its present value?

Problem 61GP Planet Z is 10,000 km in diameter. The free-fall acceleration on Planet Z is . a. What is the mass of Planet Z? b. What is the free-fall acceleration 10,000 km above Planet Z’s north pole?

Problem 62GP What are the speed and altitude of a geostationary satellite (see Example 6.15) orbiting Mars? Mars rotates on its axis once every 24.8 hours.

Problem 63GP a. What is the free-fall acceleration on Mars? b. Estimate the maximum speed at which an astronaut can walk on the surface of Mars.

Problem 64GP How long will it take a rock dropped from 2.0 m above the surface of Mars to reach the ground?

Problem 65GP A 20 kg sphere is at the origin and a 10 kg sphere is at (x, y) = (20 cm, 0 cm). At what point or points could you place a small mass such that the net gravitational force on it due to the spheres is zero?

Problem 66GP a. At what height above the earth is the free-fall acceleration 10% of its value at the surface? b. What is the speed of a satellite orbiting at that height?

Problem 67GP Mars has a small moon, Phobos, that orbits with a period of 7 h 39 min. The radius of Phobos’ orbit is . Use only this information (and the value of G) to calculate the mass of Mars.

Problem 68GP You are the science officer on a visit to a distant solar system. Prior to landing on a planet you measure its diameter to be 1.80 X 107 m and its rotation period to be 22.3 h. You have previously determined that the planet orbits 2.20 X 1011 m from its star with a period of 402 earth days. Once on the surface you find that the free-fall acceleration is 12.2 m/s2. What are the masses of (a) the planet and (b) the star?

Problem 69GP Europa, a satellite of Jupiter, is believed to have a liquid ocean of water (with a possibility of life) beneath its icy surface. In planning a future mission to Europa, what is the fastest that an astronaut with legs of length 0.70 m could walk on the surface of Europa? Europa is 3100 km in diameter and has a mass of .

Problem 70GP In Problems you are given the equation (or equations) used to solve a problem. For each of these, you are to a. Write a realistic problem for which this is the correct equation. The last two questions should involve real planets. Be sure that the answer your problem requests is consistent with the equation given. b. Finish the solution of the problem. 60 N = (0.30 kg)?2(0.50 m)

Problem 71GP In Problems you are given the equation (or equations) used to solve a problem. For each of these, you are to a. Write a realistic problem for which this is the correct equation. The last two questions should involve real planets. Be sure that the answer your problem requests is consistent with the equation given. b. Finish the solution of the problem. (1500 kg) (9.80 m/s2)?l 1,760 N = (1500 kg)v2/(200m)

Problem 72GP In Problems you are given the equation (or equations) used to solve a problem. For each of these, you are to a. Write a realistic problem for which this is the correct equation. The last two questions should involve real planets. Be sure that the answer your problem requests is consistent with the equation given. b. Finish the solution of the problem.

Problem 73GP In Problems you are given the equation (or equations) used to solve a problem. For each of these, you are to a. Write a realistic problem for which this is the correct equation. The last two questions should involve real planets. Be sure that the answer your problem requests is consistent with the equation given. b. Finish the solution of the problem.

Problem 74PP Orbiting the Moon Suppose a spacecraft orbits the moon in a very low, circular orbit, just a few hundred meters above the lunar surface. The moon has a diameter of 3500 km, and the free-fall acceleration at the surface is . The direction of the net force on the craft is A. Away from the surface of the moon. B. In the direction of motion. C. Toward the center of the moon. D. Nonexistent, because the net force is zero.

Problem 75PP Orbiting the Moon Suppose a spacecraft orbits the moon in a very low, circular orbit, just a few hundred meters above the lunar surface. The moon has a diameter of 3500 km, and the free-fall acceleration at the surface is . How fast is this spacecraft moving? A. 53 m/s B. 75 m/s C. 1700 m/s D. 2400 m/s

Problem 76PP Orbiting the Moon Suppose a spacecraft orbits the moon in a very low, circular orbit, just a few hundred meters above the lunar surface. The moon has a diameter of 3500 km, and the free-fall acceleration at the surface is . How much time does it take for the spacecraft to complete one orbit? A. 38 min B. 76 min C. 110 min D. 220 min

Problem 77PP Orbiting the Moon Suppose a spacecraft orbits the moon in a very low, circular orbit, just a few hundred meters above the lunar surface. The moon has a diameter of 3500 km, and the free-fall acceleration at the surface is . The material that comprises the side of the moon facing the earth is actually slightly more dense than the material on the far side. When the spacecraft is above a more dense area of the surface, the moon’s gravitational force on the craft is a bit stronger. In order to stay in a circular orbit of constant height and speed, the spacecraft could fire its rockets while passing over the denser area. The rockets should be fired so as to generate a force on the craft A. Away from the surface of the moon. B. In the direction of motion. C. Toward the center of the moon. D. Opposite the direction of motion.