08.19: Kepler’s Second Law about “sweeping out equal areas in equal timeafw276)y. hg/cv jx kly3yb4 v” can be derived most directly from which.jwya cv3x gf726bkhv y4y/l) conservation law?

  16.17:“All planets in the solar system follow elliptical orbitsof:m1;,y habf with the Sun located at one focus of the ellipse.” Thisbh1 m:f;y, afo statement is best summarized by which one of the following choices?

  99.21: What happens to the force of gravitational attraction between two small oe3wy sq6xo c+8 t;tbr/bjects if the mass of each object is dou8t os3crebt xwy+6q/ ;bled and the distance between their centers is doubled?

  95.09 Two spherical bodies attract each other with a gravitk1 qvsj6qs:6y ational force of 4.0 N. What will be the force if the distance betwe66sysqv1 :jk qen them is doubled?

  14.27: Two spherical, non-rotatij1jlmu 5*l3az ng planets, X andY, have the same uniform density. Planet X hasm*l ljua531 zj 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 uniform de9 r.q8hdrl dit-)u /tuzi7+jfnsity. iu rjiq f.r/lhd-97)8+d uttz 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 orbite*) -6sdhw4dnkbh,q wdd by a small satellite by setting the gravitational force on the satellite equal to the centripetal force on the satellite. Which dhqw b,nw4 k* 6hsdd-)of the following would NOT be required in this calculation?

  99.11: Assume that the Earth attracts John Glelghh2y) kg qgmin5b* -j8d61f nn 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 to2y8hd*5j hm-nqb k )6g1lgig f which of the following?

  14.30: Considering only the Moon-Earth system (ignore any influence of g.p-vagutm)w fg-n553h)uedi ppr 21the Sun), which one of the following best expresses th gg-vi5f na.r) -3p)ep w15pghmudtu2e magnitude of the Moon’s acceleration about the Earth?

  02.19: As a rocket blasts awa2u9qr 5b1hyti y from the 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 th i9uh 1t2yb5rqe surface of the Earth?

  99.33: One object at the surface of the Moon experiences the same gravitatiou2 9yeg bqv.-mnal force as a s- uvgqby.9m2eecond 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 a wx-g 5.rxy ughc)ypz2 5eight, 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 be)y 2.5r phgzc x-5xguytween Moon’s center and its surface?

  96.23: A hypothetical planet h yg g/rkqo8-rkl+-t-)im*za aas seven times the mass of Earth and twice the radius oflg a+-krt yg)i-am-8/*qkz r o Earth. The magnitude of the gravitational acceleration at the surface of this planet is most nearly:

  98.24: A planet has a radius one-half that of Earth and a mass one-fifth the s:oeu2,io/* h/ mtbzd t7had1q d cs/+Earth’s mass. The gravitational acceleration at the surface of theu 1h,o/it z:dbes+d d oh7csaqt2 m/*/ planet is most nearly

  08.38: Akg 1200 satellite orbits Planet X in a circular orbit with cg; oo+2zu 0ne1-tx uu k9iqv5* 8ck5np.xdhwa constant speed of 5,000m/s. Tdvn-1ko+u* k2t9c50cpx.n;i 5que8 o xug hw zhe 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 mass of odd atk/306 j2sog/wm+j d doi0ur 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 complete one orb+j/23d 6 idjsdw a0to/g k0omdit?

  97.12: Two artificial si,w* nqdwn9x3atellites, 1 and 2, are 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 satelli,3d wi*wnqx9nte 1 is T, what is the period of satellite 2?

  15.22 Satellite 1 makes a circular orbit around the Earth witht 8yr crl7i7*wlloq41 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” ik vlheh)* y zp()s*7lrefers to the force a scale regi*zpvl l)7)*(hh ieksysters. If the Earth were to stop rotating, but not change shape,

  10.42: A comet moves in an elliptical orbivh4 gson*9ui7fks3r b ts z:7d,*g.hmt around the sun. As the comet moves from aphelion (the point on the orbit farthest from the sun) to perihelion (thz: 37sg* th*7nuhd9s.iv4 kmr fbosg,e 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 orb (4( .xqqawpe8hl-gw,x y+wll its about the system’s center of mass. The stars are separated by a distance D that is large compared to theiehw lalx.,q (pqw+-y4 gw(8x lr size and are subject only to their mutual 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 ikci 7m0j, -0,p y9ws z2moz1axihw4 wqn a circular orbit with speed vand orbital radius R around a heavy stationary mass. An external impulse is qui w xs-02mwmzwza h,kp0o1i49 cj yi7,qckly 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