08.19: Kepler’s Second Law about “sweeping out equal areas in ew.om vtcc,li (6i(fi )qual time” can be derived most directly from wh, mti(i( .fv 6w)oilccich conservation law?

  16.17:“All planets in the so:n; yjf1 z5ruxlar system follow elliptical orbits with the Sun located at one focus of the ellipse.” This statement is best summarized by which one of the fol ;yfnur:jx 15zlowing choices?

  99.21: What happens to the force of gravitational attraction between twht2iae4ukg*ec-re:8 gc+ tn* o small objects if the mass of each object is doubledc iehkeg:*+rne4 *tgcu a-82t and the distance between their centers is doubled?

  95.09 Two spherical bodies attract each other with a gravitational fotyi /2, ugp*rerce of 4.0 N. What will be the i ,yp/2g rteu*force if the distance between them is doubled?

  14.27: Two spherical, non-rotating planets, X andY, hav; f 4rmk8-rir qwg tck5lr5b5j/2q:ice the same uniform densityw4ktc8-mfr5b; q5i r5glqkjirr:/c 2. Planet X has 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, X and Y, have the same pqj.5y*o63p n hz+uec uniform density. Planet X has twice the radius 6.p+euo5hc j3 p zynq*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/ 2yqqcxczp4j9,u1 mj be calculated if it is orbited by a small satellite by setting the gravitational force on the satellite equal to the centripetal force on the satellite. Which of the following would N zq12 x ,mcqjyjpc/4u9OT be required in this calculation?

  99.11: Assume that the Earth attracts John Glenn with a gravitational+x9wvu5nvy )5xo el2k;jzo f4 force F at the surface of thex+52n ovxv y k5)4ow;juzl e9f 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 following?

  14.30: Considering only the Moon-Earth system (ignore any influence of the Sunmrkm rt4xh3b1v ,,ew1 ), which one of the following best expresses the magnitude of the Moon’s acceleration atrr3 weh,bk4 x vm1,1mbout the Earth?

  02.19: As a rocket blasts away from the;3( u.hc2 y2;gm xgvlq.0 isk4cpj hpz earth with a cargo for the international space station, which of the following graphs would best represent the gravitational force on the cargo versus distance from the surface svkihq 2 m0lgp.cjzg . p3(cx y;2;4uhof the Earth?

  99.33: One object at the surface of the Moonygj.pe52d4r q4urc0 h experiences the same gravitational force as a second object at j2u 5hy gdq40e4.rpcrthe surface of the Earth. Which of the following would be a reasonable conclusion?

  00.24 Consider an object that has a mass, m, as s1ro9b ibej6evqk .3a ;1rs6nd a weight, W, at the surface of the moon. If we assume the moon has a nearl9ao rsjkbe1i36rssq.1v; eb 6 y uniform density, which of the following would be closest to the object’s mass and weight at a distance halfway between Moon’s center and its surface?

  96.23: A hypothetical planet has seven times thh m718*vpz a.n+x3zpb onk(eae mass of Earth and twice the radius of Earth. The magnitude of the gravitational acceleration at the surface of this k7 (+3bx8ap hz en* zo1n.apmvplanet is most nearly:

  98.24: A planet has a radius one-half that pswe.9w (bb0 lrc g5-hof Earth and a mass one-fifth the Earth’s mass. The gravitational acceleration at the surflww h-s95gr . bb(ce0pace of the planet is most nearly

  08.38: Akg 1200 satellite orbits Plv29g6w(w/is defcb ny;;5vg xanet 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 gravitationfg;c dbxv (v6e/ 5 wwinsyg;29al force exerted on the satellite by Planet X?

  94.34: A hypothetical planet orbito:b vx;t qxq+7s a star with mass one-half the mass of our sun. The planet’s orbital radius is the same as the Earth’s. A:;qtxx o7qbv+ pproximately how many Earth years does it take for the planet to complete one orbit?

  97.12: Two artificial satellites, 1 and 2, ar7sfa 7f9z/hare put into circular orbit at the same altitude above Earth’s surface. The mass of satellite 2 is twice the mass of satellite 1. If the period of satellite 1 is T, what isa 9/7zf rfash7 the period of satellite 2?

  15.22 Satellite 1 makes a circular orbit mw:plw:k,d1a//(+e cnyv yrf 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 followizo ly2g9l4 5 7*b/mu, boz/fvnjhf5t ing problem, the word “weight” refers to the force a scale registers. If 7/* vbtl ozi /2fzgh o9lun,yb4jm5f5the Earth were to stop rotating, but not change shape,

  10.42: A comet moves in an elliptical orbit aroujic l8e).*kjl nd the sun. As the comet moves from aphelion (the point on the orbit farthest from thk*cl) le8j .ije 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 circu4 /mu u/ s ozlo;f57whqcg7mh(lar orbits 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 mutuaq/cmhus og/4zuw(h;m f7 5ol7l gravitational attraction. The orbital period 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 spehhr45 fm4uc6z4ysv 1oed vand orbital radius R around a heavy stationary mass. An external impulse is quickly applied to the rocket directl1r46hu mv4z hoc45ysfy 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