08.19: Kepler’s Second Law about “sweeping out equal areas in equal e2.+l53(hsx ydcwbm5tc z/f o time” can be derived most d(b5t 2wz/cocfdxe .h5s m+y 3lirectly from which conservation law?

  16.17:“All planets in the solar syste w 5(qipajgk/-m follow elliptical orbits with the Sun located at one focus of the ellipse.” Thija i5w(k /qg-ps statement is best summarized by which one of the following choices?

  99.21: What happens to oldjcvwwq8 s7, 3djt3tl+ot3r7 iz7 )the force of gravitational attraction between two small objects if the mass of each object is dow8+ lq7ojlo , wvt733r3 7i d)ttjzdscubled and the distance between their centers is doubled?

  95.09 Two spherical bodrj ee((jpssoa, ipk,a+ b;( o9ies attract each other with a gravitational force of 4.0 N. What will be the force if the distance between taj; e(iop+s jr obsp ,ae9(k,(hem is doubled?

  14.27: Two spherical, non-rotan,d ijjxupbgo )/ 3x-cos2i11ting planets, X andY, have the same uniform densit npi 2j-ic,joxxu1/)o bgd1s3y. 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, ha1 efof. vr n*emewpjj;52;8qh ve the same uniform density. Planet X has twice the radius of Planet Y.j52 mvejfe n.o;18*;pqher w f 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 6dh f 03scyd7( a,jdoaif it is orbited by a small satellite by setting the gravitational force on the satellite equal to the centripetal fors 7dd f3j,y6(a0ah ocdce on the satellite. Which of the following would NOT be required in this calculation?

  99.11: Assume that the Earth attracts John Glenn with a gravitation,:lv ukg7ol/ hal force F at the surface of the Earth. When he made his famous second flight in orbit, the gravitationa:,l kgo /vu7hll force on John Glenn while he was in orbit was closest to which of the following?

  14.30: Considering only the Moon-v)i*89c1odp gc qgswwa )y-/ kEarth system (ignore any influence of the Sun), which one of the following best expresses the m )g*-scc i w8gapv/ wd)q1koy9agnitude of the Moon’s acceleration about the Earth?

  02.19: As a rocket blasts away from the earth , y;)0jpwdn) qh(zetswith a cargo for the international space station,)t(jws z; qe hpy,0)nd 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 experie v)8( la g4ulx,x*uiiyevv21w k0 o9dgnces the same gravitational force as a seconivl2k uiv,8) lgwaxx0ogu41(*ye vd9d object at the surface of the Earth. Which of the following would be a reasonable conclusion?

  00.24 Consider an object that has a mass, qbj pe50na0 x2m, 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 between Moon’s center and its s q0n5epa20jbxurface?

  96.23: A hypothetical planet has se+ yudm3ssj1)1fgqw.k1 n u/qeven times the mass of Earth and twice the radius of Earth. The magnitude of the gravitational acceleration adeq1.mwsy+n/uj1 gq)u ks31 ft the surface of this planet is most nearly:

  98.24: A planet has a radius one-half that of Earth and(7de js6lb1t0 oj s(pk a mass one-fifth the Earth’s mass. The gravitational acceleration at the surface of the planebpj 7 edo(jskt6ls0 (1t is most nearly

  08.38: Akg 1200 satellite orbits Planet X in a circu vuq78i12 0.u2nt xu2yuczhq qlar 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 e c2 . 8uqqxyut 0z7nu12h2iuvqxerted on the satellite by Planet X?

  94.34: A hypothetical planet orbrz9g -ty19t bqcu+h9 yits a star with mass one-half the mass of our sun. The planet’s orbital radius is the same as the Earth’s. Approximately how many Eart guhryc -b9qt+1z t9y9h years does it take for the planet to complete one orbit?

  97.12: Two artificial satellites, 1 and 2, are put into circular 303igit) ktaqbeq 0 7eorbit at the same altitude above Earth’s7a eitt00b kgq)ei3q 3 surface. The mass of satellite 2 is twice the mass of satellite 1. If the period of satellite 1 is T, what is the period of satellite 2?

  15.22 Satellite 1 makes ;fk b6/klf1grmpv1b/bt z; c(km49 cea circular orbit 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 followingewo,.8u t (a ,yrdlx v4ao0s8g problem, the word “weight” refers to the force a scale registers. If the Earth were to stoy,(gva8eadou4,8 .xw0slotrp rotating, but not change shape,

  10.42: A comet moves in an elliptical orbit around the sun. As the comx s m9h-4ed;edet moves from aphelion (the point onxehsm9 ;4-d de 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, theyc9loa8, vd w8 two stars follow circular 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 mutual gravitational attrac,9ya vc8ldo 8wtion. 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 speed vand orbital radfj25-:do p)b uoqo9y jius R around a heavy stationary mass. An external impulse is quickly applied to the rocket directly opposite to the velocity and the r 9 :yfjopquo5j-2bod)ocket’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