Problem 13.1DQ: A student wrote: The only reason an apple falls downward to meet the earth instead of the earth... Problem 13.2DQ: If all planets had the same average density, how would the acceleration due to gravity at the... Problem 13.3DQ: Is a pound of butler on the earth the same amount as a pound of butter on Mars? What about a... Problem 13.4DQ: Example 13.2 (Section 13.1) shows that the acceleration of each sphere caused by the gravitational... Problem 13.5DQ: When will you attract the sun more: today at noon, or tonight at midnight? Explain. Problem 13.6DQ: Since the moon is constantly attracted toward the earth by the gravitational interaction, why doesnt... Problem 13.7DQ Problem 13.8DQ: A planet makes a circular orbit with period T around a star. If the planet were to orbit at the same... Problem 13.9DQ: The sun pulls on the moon with a force that is more than twice the magnitude of the force with which... Problem 13.10DQ: Which takes more fuel: a voyage from the earth to the moon or from the moon to the earth? Explain. Problem 13.11DQ Problem 13.12DQ: Does the escape speed for an object at the earths surface depend on the direction in which it is... Problem 13.13DQ: If a projectile is fired straight up from the earths surface, what would happen if the total... Problem 13.14DQ: Discuss whether this statement is correct: In the absence of air resistance, the trajectory of a... Problem 13.15DQ: The earth is closer to the sun in November than in May. In which of these does it move faster in its... Problem 13.16DQ: A communications firm wants to place a satellite in orbit so that it is always directly above the... Problem 13.17DQ Problem 13.18DQ: What would Keplers third law be for circular orbits if an amendment to Newtons law of gravitation... Problem 13.19DQ: In the elliptical orbit of Comet Hailey shown in Fig. 13.21a, the suns gravity is responsible for... Problem 13.20DQ: Many people believe that orbiting astronauts feel weightless because they are beyond the pull of the... Problem 13.21DQ: As part of their training before going into orbit, astronauts ride in an airliner that is flown... Problem 13.1E: What is the ratio of the gravitational pull of the sun on the moon to that of the earth on the moon?... Problem 13.2E: CP Cavendish Experiment. In the Cavendish balance apparatus shown in Fig. 13.4, suppose that m1 =... Problem 13.3E: Rendezvous in Space! A couple of astronauts agree to rendezvous in space after hours. Their plan is... Problem 13.4E: Two uniform spheres, each with mass M and radius R, touch each other. What is the magnitude of their... Problem 13.5E: Two uniform spheres, each of mass 0.260 kg, are fixed at points A and B (Fig. E13.5). Find the... Problem 13.6E: Find the magnitude and direction of the net gravitational force on mass A due to masses B and C in... Problem 13.7E: A typical adult human has a mass of about 70 kg. (a) What force does a full moon exert on such a... Problem 13.8E: An 8.00-kg point mass and a 12.0-kg point mass are held in place 50.0 cm apart. A particle of mass m... Problem 13.9E Problem 13.10E: The point masses m and 2m lie along the x-axis, with m at the origin and 2m at x = L. A third point... Problem 13.11E: At what distance above the surface of the earth is the acceleration due to the earths gravity 0.980... Problem 13.12E: The mass of Venus is 81.5% that of the earth, and its radius is 94.9% that of the earth, (a) Compute... Problem 13.13E: Titania, the largest moon of the planet Uranus, has 18 the radius of the earth and 11700 the mass of... Problem 13.14E: Rhea, one of Saturns moons, has a radius of 764 km and an acceleration due to gravity of 0.265 m/s2... Problem 13.15E: Calculate the earths gravity force on a 75-kg astronaut who is repairing the Hubble Space Telescope... Problem 13.16E Problem 13.17E: Use the results of Example 13.5 (Section 13.3) to calculate the escape speed for a spacecraft (a)... Problem 13.18E: Ten days after it was launched toward Mars in December 1998, the Mars Climate Orbiter spacecraft... Problem 13.19E: A planet orbiting a distant star has radius 3.24 106 m. The escape speed for an object launched... Problem 13.20E Problem 13.21E Problem 13.22E: Aura Mission. On July 15, 2004, NASA launched the Aura spacecraft to study the earths climate and... Problem 13.23E: Two satellites are in circular orbits around a planet that has radius 9.00 106m. One satellite has... Problem 13.24E: International Space Station. In its orbit each day, the International Space Station makes 15.65... Problem 13.25E Problem 13.26E Problem 13.27E: The star Rho1 Cancri is 57 light-years from the earth and has a mass 0.85 times that of our sun. A... Problem 13.28E: In March 2006. two small satellites were discovered orbiting Pluto, one at a distance of 48,000 km... Problem 13.29E: The dwarf planet Pluto has an elliptical orbit with a semi-major axis of 5.91 1012 m and... Problem 13.30E: Hot Jupiters. In 2004 astronomers reported the discovery of a large Jupiter-sized planet orbiting... Problem 13.31E: Planets Beyond the Solar System. On October 15, 2001, a planet was discovered orbiting around the... Problem 13.32E: A uniform, spherical, 1000.0-kg shell has a radius of 5.00 m. (a) Find the gravitational force this... Problem 13.33E: A uniform, solid, 1000.0-kg sphere has a radius of 5.00 m. (a) Find the gravitational force this... Problem 13.34E: CALC A thin, uniform rod has length L and mass M. A small uniform sphere of mass m is placed a... Problem 13.35E Problem 13.36E: A Visit to Santa. You decide to visit Santa Claus at the north pole to put in a good word about your... Problem 13.37E: The acceleration due to gravity at the north pole of Neptune is approximately 11.2 m/s2. Neptune has... Problem 13.38E: Mini Black Holes. Cosmologists have speculated that black holes the size of a proton could have... Problem 13.39E Problem 13.40E: In 2005 astronomers announced the discovery of a large black hole in the galaxy Markarian 766 having... Problem 13.41P: Neutron stars, such as the one at the center of the Crab Nebula, have about the same mass as our sun... Problem 13.42P: Four identical masses of 8.00 kg each are placed at the corners of a square whose side length is... Problem 13.43P: Three uniform spheres are fixed at the positions shown in Fig. P13.43. (a) What are the magnitude... Problem 13.44P: CP Exploring Europa. There is strong evidence that Europa, a satellite of Jupiter, has a liquid... Problem 13.45P: A uniform sphere with mass 50.0 kg is held with its center at the origin, and a second uniform... Problem 13.46P: Mission to Titan. On December 25, 2004, the Huygens probe separated from the Cassini spacecraft... Problem 13.47P Problem 13.48P: At a certain instant, the earth, the moon, and a stationary 1250-kg spacecraft lie at the vertices... Problem 13.49P Problem 13.50P: CP Submarines on Europa. Some scientists are eager to send a remote-controlled submarine to Jupiters... Problem 13.51P: What is the escape speed from a 300-km-diameter asteroid with a density of 2500 kg/m3? Problem 13.52P: A landing craft with mass 12,500 kg is in a circular orbit 5.75 105 m above the surface of a... Problem 13.53P: Planet X rotates in the same manner as the earth, around an axis through its north and south poles,... Problem 13.54P: (a) Suppose you are at the earths equator and observe a satellite passing directly overhead and... Problem 13.55P: CP An astronaut, whose mission is to go where no one has gone before, lands on a spherical planet in... Problem 13.56P: CP Your starship, the Aimless Wanderer, lands on the mysterious planet Mongo. As chief... Problem 13.57P: CP You are exploring a distant planet. When your spaceship is in a circular orbit at a distance of... Problem 13.58P: The 0.100-kg sphere in Fig. P13.58 is released from rest at the position shown in the sketch, with... Problem 13.59P: An unmanned spacecraft is in a circular orbit around the moon, observing the lunar surface from an... Problem 13.60P: Mass of a Comet. On July 4, 2005, the NASA spacecraft Deep Impact fired a projectile onto the... Problem 13.61P: Falling Hammer. A hammer with mass m is dropped from rest from a height h above the earths surface.... Problem 13.62P Problem 13.63P Problem 13.64P Problem 13.65P Problem 13.66P: The planet Uranus has a radius of 25,360 km and a surface acceleration due to gravity of 9.0 m/s2 at... Problem 13.67P Problem 13.68P: A rocket with mass 5.00 103 kg is in a circular orbit of radius 7.20 106 m around the earth. The... Problem 13.69P: A 5000-kg spacecraft is in a circular orbit 2000 km above the surface of Mars. How much work must... Problem 13.70P Problem 13.71P: CALC Planets are not uniform inside. Normally, they are densest at the center and have decreasing... Problem 13.72P: One of the brightest comets of the 20th century was Comet Hyakutake, which passed close to the sun... Problem 13.73P: CALC An object in the shape of a thin ring has radius a and mass M. A uniform sphere with mass m and... Problem 13.74P: CALC A uniform wire with mass M and length L is bent into a semicircle. Find the magnitude and... Problem 13.75P Problem 13.76P: DATA For each of the eight planets Mercury to Neptune, the semi-major axis a of their orbit and... Problem 13.77P: DATA For a spherical planet with mass M, volume V, and radius R, derive an expression for the... Problem 13.78P: DATA For a planet in our solar system, assume that the axis of orbit is at the sun and is circular.... Problem 13.79CP: Interplanetary Navigation. The most efficient way to send a spacecraft from the earth to another... Problem 13.80CP: CP Tidal Forces near a Black Hole. An astronaut inside a spacecraft, which protects her from harmful... Problem 13.81CP: CALC Mass M is distributed uniformly over a disk of radius a. Find the gravitational force... Problem 13.82PP: EXOPLANETS. As planets with a wide variety of properties are being discovered outside our solar... Problem 13.83PP: EXOPLANETS. As planets with a wide variety of properties are being discovered outside our solar... Problem 13.84PP: EXOPLANETS. As planets with a wide variety of properties are being discovered outside our solar... format_list_bulleted