08.19: Kepler’s Second Law about “sweeping 58vln sajzdedx()dfj;r8 7-oout equal areas in equal time” can be derv fj -8a (5jo7ne8d;ld xsdz)rived most directly from which conservation law?

  16.17:“All planets in titri1(u2k h1bofpz v.)th ,;w:bsf+ ihe solar system follow elliptical orbits with the Sun located at one focus of the ellipse.” This statement is best sumh s,w.fi)to 1i2;k +b(br pvuzf1ht:imarized by which one of the following choices?

  99.21: What happens to the force of gravitational attraction between two smallfe,99- q-aj nf5bysi04x k,4qh m heya objects if the mass of each object is doubled and the distance betwf 5-a i4- am9k49x,yq sh 0hefjeyq,nbeen their centers is doubled?

  95.09 Two spherical bodies attract each other with a gravitatio4jmk/.hle uoi/3f *jxnal force of 4.0 N. What will be the force if the distance between themmxhfu*43 jk/i .e/o lj is doubled?

  14.27: Two spherical, non-rotating planets, X andY, have the same uniform de . d fmli(6gtut )oq 5j25nsyqlu9/p2hxk2v8rnsity. Planet X has twice the radius of Planet Y. Let u (jqs2/6r )hn.uv q mk28lpxi9ytl d5f2og5t$g_x$ 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,ru 5r(2w/qz0zy hb6mzho6(7cgnl )qb have the same uniform density. Planet X has twice the radius of Planet Y. Letc(/ zgw6bz 6(ozbhumqql7n2r hr0)5y $v_x$ 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 bevg;0qo 5 r/b5t h(dsby a small satellite by setting the gravitational foo5gb;0 e/ rdvt(q h5bsrce on the satellite 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 with abux1 7 ;yrrf :qsw.ql. gravitational force F at the surface of the Earth. When he made his famous second flight in orbit, the guq qr 7xsy;.:r1 lfwb.ravitational 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 su q3yzn)3 o5dof the Sun), which one of the following best expresses the magniu3n) qz5y 3odstude of the Moon’s acceleration about the Earth?

  02.19: As a rocket blasts away from the earth with a cag r4e1bmom ,; a-/wowsrgo for the international space station, which of the following graphs ww1gs m/,ow m4;o-eb raould best represent the gravitational force on the cargo versus distance from the surface of the Earth?

  99.33: One object at the spz,k-j:uw s- dtmunj+(u/o5 surface of the Moon experiences the same gravitational force as a second object at the surface of the Earth. Which of the following would/p st-jowuz5k ,j :m-uns+u(d be a reasonable conclusion?

  00.24 Consider an object that has a mass, m, and a weight, Wttjzy+.le ms + 1rt k-ga*1w3 xdz5z:f, at the surface of the moon. If we assdst.y+w+5*za3x 1rfzm1 ez lkgt jt:-ume 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 surface?

  96.23: A hypothetical planet has seven times the mask ( 79v 1 hbsbahkps-:iyonu6+s of Earth and twice the radius of Earth. The magnitude of the gravitational:as(6+hhpy79 u b 1skk-n oibv 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 .pxo:/ zdfn .fthe Earth’:zxp.fdo . /nfs mass. The gravitational acceleration at the surface of the planet is most nearly

  08.38: Akg 1200 satellite orbits Planet X in(voj;d6akh)*mb uh05 k 3vkgu a circular orbit with a constant sp ak*0k5uhv;vj )6du oh(km3 bgeed 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 o)e( 2x*/fz3g(yr a* cpeg vpcwrbits a star with mass one-half the mass of our sun. The plc2e(*w) pgzf rp*xc 3ega y(/vanet’s orbital radius is the same as the Earth’s. Approximately 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 cir1 .s: rk5.66acu65wg ralfzwp0w oaae cular 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 ifco6e a:u165rg s w.pwaalrza0wk. 5 6s T, what is the period of satellite 2?

  15.22 Satellite 1 makesf 3v . thpth5b45f+(ji xudics6p(cq;*gc i p3 a 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 following problem, the word “weight” refers to the force a scalfvmwd)n +9zn3 qt4l ,-3k oghde registers. If the Earth were to stop rotating, but not change shape+n 9mnf -hd ,g3ow3kvdq4) zlt,

  10.42: A comet moves in an elliptical orbit around the sun. As the co:hqf1g 6l y zyvw2,ae;met moves from aphelion (the point on the orbit 6wh aqv ey2,;l:z f1gyfarthest 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 5j83ottb jrjp7zg)1s system shown, the two stars follow circular orbits about the system’s center of mass. The stj r1j75osp tz8b3g j)tars 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 one of the following choices represents the total mass of the binary star system?

  06.50: A rocket is in a circular orbit with sje5ko;6ed1zi 1y+ x yipeed vand orbital radius 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 rockeiyyk 5+e6 ed;ozx11jit into an elliptical orbit. In terms of R, the size of the semi-major axis a of this new elliptical orbit is