08.19: Kepler’s Second Law about “sweeping out equal areas in equal time” cav le/ bnh5v2f- c,dak im4w9jzf b:oa4. ,iqi1n be derived most directly from wo5,ad ev iaz:v4 1,wflhk2 m-i/.b9nbq f 4icjhich conservation law?

  16.17:“All planets in the kkf)sf9a byh)/8rha3 solar system follow elliptical orbits with the Sun located at one focus of the ellipse.” This statement h 9 b3yffak)r ah)8/skis best summarized by which one of the following choices?

  99.21: What happens to the force of gravitational att t wtygf39b5 rs(i gdxr 9skm ;*;zo0mi6+e,xoraction between two small objects if the mass of each object is doubled and w, b(zf6goe*9 ts+iidy 0mgxo;x5 srr9km3;tthe distance between their centers is doubled?

  95.09 Two spherical bodies attrac;wq 2vro79.nxco ep8et each other with a gravitational force of 4.0 N. What will be the force if the distance between therpc owxvn9e;2qe87o. m is doubled?

  14.27: Two spherical, non-rotating planets, X andY, have the same uniform dew5 gy/e h/mm+ensity. Planet X has/h5mm +/eygew twice the radius of Planet Y. Let $g_x$ and $g_y$ represent the accelerations due to gravity at the surfaces of Planet X and Planet Y, respectively. What is the ratio of $g_x:g_y$?

  16.46 Two spherical, non-rotating planets,xs eo -/m/ /pe37se14 buatzgb X and Y, have the same uniform densitygb4msoe 71e p/b3ts-/u/xaze . Planet X has twice the radius of Planet Y. Let $v_x$ and $v_y$ represent the escape speed at the surfaces of Planet X and Planet Y, respectively. What is the ratio of $v_x:v_y$?

  01.16: The mass of a planet can be calculated if it is orbited by a small ku+ eqn+t:e3-5 wmtqi) lwb1e satellite by setting the gravitational force on the satellite equal to the centripetal force on the satellite. Which of the following w3e q1+ :teibk5-weum+wn tlq )ould NOT be required in this calculation?

  99.11: Assume that the Earth attracts John Glennwzp cg6k7 7kqee728xi with a gravitational force F at the surface of the Earth. When he made his famous second flight in orbit, the gravitational force on John Glenn while he was in orbit was closest to which of the fol w6zik7gkx e e2778qpclowing?

  14.30: Considering only the Moon-Eartc vsghvv1d30s )jtoh ,:i;x4rh system (ignore any influence of the Sun), which one of j) ohg3v :0,c1rdsvish vtx4; the following best expresses the magnitude of the Moon’s acceleration about the Earth?

  02.19: As a rocket blasts away from the earth with vx1*yww5 sw v9a cargo for the international space stwy9v*1w w5xsvation, which of the following graphs would best represent the gravitational force on the cargo versus distance from the surface of the Earth?

  99.33: One object at the surface of the Moon experiences the same gravitatioqxo(o e52q d*jgd-v5fnal force as a second objeco(oj2 xd5q eqd-f5 *vgt at the surface of the Earth. Which of the following would be a reasonable conclusion?

  00.24 Consider an obje4as zakzywn j2 pp(0tf2;m*o9ct that has a mass, m, and a weight, W, at the surface of the moon. If we assume the moon has a nearly uniform density, which of the following would be closest to the object’s mass and weight at a distance halfway betwee* 02pkpzfw;m stao nz( 29yj4an Moon’s center and its surface?

  96.23: A hypothetical planet hapn *s; axu:mu1hw6;d(pdwln 8s seven times the mass of Earth and twice the radius of Earth. The magnitude of the gravitational acceleration at the su;w nw 6n(du*;8ahmlp: 1upd xsrface of this planet is most nearly:

  98.24: A planet has a rao+rdlrky* on cn n/x 4ikt6-09 (qhz5fdius one-half that of Earth and a mass one-fifth the Earth’s mass. The gravitational acceleration at the surface of the (dxcr5 oz0o r*fq9iny4 kt kln +-n/6hplanet is most nearly

  08.38: Akg 1200 satellit1og (js7082(mo a)rzrkpvcs ke orbits Planet X in a circular orbit with a constant speed of 5,000m/s. The radius of orbit is 7,500,000 m. What is the magnitude of the gravitational force exerted12vmsza s ck r7po8ko 0)j(rg( on the satellite by Planet X?

  94.34: A hypothetical planet orbits a star with mass one-half the mass of:* b0zi u9fdqf our sun. The planet’s orbital radius is the same as the Earth’s. Approximately how many Earth years does it take for the planet to comple iu:90ffdqzb *te one orbit?

  97.12: Two artificial satellites, 1 and 2, are puy/s4e: du r q-x87bl2b l9nnnyt into circular orbit at the same altitude above Earth’s surface. The mass of satellite 2 is twice the mass of satellite 1. If thee2 -q/u :bnld9b synxrly 4n78 period of satellite 1 is T, what is the period of satellite 2?

  15.22 Satellite 1 makes a circular or9btpy03i zyo:u dwh9v9 rph4( bit around the Earth with a radius $r_1= R$. Satellite 2 makes a circular orbit around the Earth with a radius $r_2= 2R$. We let v represent the speed of a satellite and a represent the magnitude of a satellite’s acceleration. Which one of the following choices gives the correct relation between the speeds and accelerations of the satellites?

  98.33: In the following problem, the word “weight” refers to the force a scrjotoxes) 88.ale registe8s)o8.jet r oxrs. If the Earth were to stop rotating, but not change shape,

  10.42: A comet moves in an elliptical orbit around the sun. As theorp58f 2oot :x comet moves from aphelion po52otf :r o8x(the point on the orbit farthest from the sun) to perihelion (the point on the orbit closest to the sun), which of the following results is true?

  17.48: In the binary star system shown, the two stars follow circular orbit92+xi rwh*f3zy3tkr idad s1 kogp:;6s about the system’s center of mass. The stars are separated by a distance D that is large compared to their size and are subject only to their mutual gravitational attraction. The orbital p 2hy3go*rxk ra+s3f;wi16dpz ik : td9eriod of the star of mass M is T. Which one of the following choices represents the total mass of the binary star system?

  06.50: A rocket is in a circular orbit with speed vand orbital radius R aro ( xcs4ggcc.ju86l.ydev 5 m-hund a heavy stationary mass. An external impuj(exl46d g. hcvm-5.c8 ysguclse is quickly applied to the rocket directly opposite to the velocity and the rocket’s speed is slowed to v/2, putting the rocket into an elliptical orbit. In terms of R, the size of the semi-major axis a of this new elliptical orbit is