08.19: Kepler’s Second Law about “sweeping out equal areas in equal time” can ben)zw omm67zbw -k/h4 ie::nro derive:m :7m-nzw/erin)wobkz4 h6od most directly from which conservation law?

  16.17:“All planets in the solar system f7lc +,4 kk-spo5qmmw wollow elliptical orbits with the Sun located at one focus of the ellipse.” This statement is best summarized by which one of the followingmqc m7wl,k4k-pwo+s5 choices?

  99.21: What happens to the force of gravitationalw yx9*:g*ba t2nax3l p1 qyh4n attraction between two small objects if the mass of each object is doubled and the distance between tl**n pxyga 2ay4nh3w xb:9 t1qheir centers is doubled?

  95.09 Two spherical bodies attract each other with a grg,vt ,;mhgx8 pavitational force of 4.0 N. What wiph;gxm v ,,8gtll be the force if the distance between them is doubled?

  14.27: Two spherical, non-rotatin1zyxgd.zj 3f67 beun2k0b5jl g planets, X andY, have the same uniform density. Planet X has twice the rafz5y1l g237x.b juk d ezn6jb0dius 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 zra*lr2q kfttk- +0c,, X and Y, have the same uniform density. Planet X has twice t r-l,fzq0 k*+2at tcrkhe 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 calculppsei 3sok) ko4f*(r12je 1esated if it is orbited by a small satellite by setting the gravitational force on the p1)r3s4o 1s2s pk(f oi*k jeeesatellite equal 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 widzuz7p)u ledw x;at5 :o+45v kth a gravitational force F at the surface of the Earth. Whe+ 57;)tpa4zuw:oel5 d xvdkuzn 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 inm ,1uss*+,a utstfu* pfluence of the Sun), which one of the following best expresses t,us *1+t maup,ss*t fuhe magnitude of the Moon’s acceleration about the Earth?

  02.19: As a rocket blasts away from the earth with a cargo fc j1wkulr(s1xat6fq-;oj, ,tor the international space statkft,w,sq;j( r1 - jx6a ctulo1ion, 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 graviteuy+mo7g1m8q2f 7 h-6b6iap or77ozj x4v jigational force as a second object at the sujh2ie-6q74i8ay1bg pum7z ofx 6gjvoo7r 7m + rface of the Earth. Which of the following would be a reasonable conclusion?

  00.24 Consider an object that has a mass, m, and a weight, W, at the surface ofk x 5 eg591qmgxpoz5z7 the moon. If we assume the moon has a nearly uniform density, which of the foll59xx 15mz5kg zpqoge7owing 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 thx4j/5b* (znd-xjosg: 3 dyz qce mass of Earth and twice the radius of Earth. The magnitude of the gravitational acceleration at the surfaceq5 dj(o gyz/jb:34nxc*z x-sd of this planet is most nearly:

  98.24: A planet has a radius oneyckp5:be1e8m ml*ya2 -half that of Earth and a mass one-fifth the Earth’s mass. The gravitational acceleration at the surface of the planet is ayc1b *pmm2:k8 el5ey most nearly

  08.38: Akg 1200 satellite orbits ,h;xub0u seoj *8pkw)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 map*,k xhe;bu0su wj8 )ognitude of the gravitational force exerted on the satellite by Planet X?

  94.34: A hypothetica u 01u4ztv0 g2fo9vzhtl planet orbits 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 Earth years does it take for the planet to completgot1zuv t 0z hf2u04v9e one orbit?

  97.12: Two artificial satellites, 1 and 2, g66 6tmb2ahld 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 satellite 1 is T, what 6m26ba ghd6tl is the period of satellite 2?

  15.22 Satellite 1 makes a circ lth1gpw +b0-mular 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 following proaqtonvccw3a6 g+(wkc.cqu f1i1(a 95blem, the word “weight” refers to the force a scale registers. If the k(vcg6. 1 i(t3u+cwfcon qqac 19wa5aEarth were to stop rotating, but not change shape,

  10.42: A comet moves in an elliptical orbit around of o.-oz4m(-p6va 8)s;g xax2bdtaqwthe sun. As the comet moves from aphelion (the poiwgxa6o-;z8o qb x 2mapa)f(tv s4.d o-nt 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 c(6jhfm q5(bn wxt4b c+ircular 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 orbh+(wqn5t (cbfj6b4x mital 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 radius R around a zc)o ufu;73f*ppa8 qy8zf9 oj 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 elliptical orbit. In terms of R, the size of the semi-major axi o)a7 zfucj3py8o 9zpq fu8*f;s a of this new elliptical orbit is