08.19: Kepler’s Second Law about “sweeping out equal areasv 6jm-kuq4 ,bqdd f)r :pv+1kr in equal time” can be derived most directly from whichm1rqfk,q:r v+)dj4 6v kud -bp conservation law?

  16.17:“All planets in theayrg1fovs36d7 z.i2u 9 v xag; solar system follow elliptical orbits with the Sun located at one focus of the ellipse.” This statement is best summarized by which one of thg dvufa2a;gs xz73oi y1 .vr69e following choices?

  99.21: What happens to the force of gravitational attraction between two1eek(g qs7u2q small objects if the mass of each object is doubled and the distance between ekeqsu72( g 1qtheir centers is doubled?

  95.09 Two spherical bodies attract each other with a gravi )bsqv50ck:ku tational force of 4.0 N. What will be the force if the distance between them is 0 cb5)sqv u:kkdoubled?

  14.27: Two spherical, non-roth edd(f84d ky(t((*x) wjzw rtating planets, X andY, have the same uniform density. Planet X has twice the radius of Pljkdw *(ftd)zdex y 8tr4w( ((hanet 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 uniform ec):d- szg.jm density. Planet X has twice the radius of Pla:.se )gdjzcm-net 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 satel/cexqc--ev axi ;vm6o zs6v (;lite by setting the gravitational force on the satellite equalvv; -q- ;(som zx i6vccae/6xe to the centripetal force 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 gravitational force em2/;3 zxu xqwF 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 wae/xz x;umw3q2 s closest to which of the following?

  14.30: Considering only*;34vidv deafy4b dm w(:1t pq the Moon-Earth system (ignore any influence of the Sun), which ob3(1ym:pi4* 4dtae; d vdv wqfne of the following best expresses the magnitude of the Moon’s acceleration about the Earth?

  02.19: As a rocket blasts away from the earth wi oir 5slhn9: )fi;xne;th a cargo for the international space station, which of the 9sn ;xo)lirf:in 5e;hfollowing 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 eh:qic u(1w 6u 1u;rkg( rmbc-vxperiences the same gravitational foruci1: ru(c16q(rvb-mk;gu whce as a second 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, m, and k f(06er9t7w2gyo6nu lu g6nga weight, W, at the surface of the moon. If we assume the mog(ulu oy nr96g0 t6wfeg6nk72on 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 surface?

  96.23: A hypothetical planet rivv; nvi77bug 4(m:whas seven times the mass of Earth and twice the radius of Earth. The magnitude of the gravitational acceleration at the surface n bv; (wm47viug7:vr iof this planet is most nearly:

  98.24: A planet has a radius one-half that of Earth andeb oh0./pdg p657 j(tx1 nvdme a mass one-fifth the Earth’s mass. The mbjt5.d1x do0 6env7hp (e pg/gravitational acceleration at the surface of the planet is most nearly

  08.38: Akg 1200 satellite or vex,b5rk8si+.9o+l 4ut cnhcbits Planet X in a circular orbit with a constant speedolcet9.c54 nb, v+h+u s8rkix of 5,000m/s. The radius of orbit is 7,500,000 m. What is the magnitude of the gravitational force exerted on the satellite by Planet X?

  94.34: A hypothetical planet orbits a star with mass one-half the mam 1jry3 b)nuj-ss of our sun. The planet’s orbital radius is the same as the Earth’s. Appro)bm-j1 nyju3 rximately how many Earth years does it take for the planet to complete one orbit?

  97.12: Two artificial satellites, 1 and 2, are put into ciunfw5g /fj7f. rcular orbit at the same altitude above Earth’s surface. The mass of satellite 2 is twice the mass of satellite 1. If t/n7w u5gfj .ffhe period of satellite 1 is T, what is the period of satellite 2?

  15.22 Satellite 1 makes a circular orbit around the Earth with a c jyc.53quy:w 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 worv,7fp7fo,ybh -1qeua-5 ose b 5jid e.d “weight” refers to the force a scale registers. If the Earth were to stop feah5.e1sf -j 7ood,ev7pq uby -5i b,rotating, but not change shape,

  10.42: A comet moves in an elliptical orbit aro d ptj9o,h)ek7*7k.*ynhpn x uund the sun. As the comet moves from aphelion (the point on the orbit farthest from the sun) to perihelion (the point on the orbit closest to the sun 9h*nn7 kkd,eohyjupx7p . t*)), which of the following results is true?

  17.48: In the binary star system shown, the d z)3d-kw-8 xj5eakddtwo 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 attraction. The orbital period of the star of mass M is T. Which o dzkaj-e8x kd3d)5 wd-ne 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 radiuyblrxq ig; x 7t5asdeolu0bwf (:* :4+s R around a heavy stationary mass. An external impulse 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 elliptic4aoliedgbsb* xw5 lr:7yf xt0 +;q(u:al orbit. In terms of R, the size of the semi-major axis a of this new elliptical orbit is