08.19: Kepler’s Second Law about “sweeping out equal/bgg v zm,430v. oz ml6 )mvnm8rghv wst8fm(5 areas in equal time” can be derived most directly vt)vw mv8vmgfgm , og (zb/s.m8h6n 35 z0l4mrfrom which conservation law?

  16.17:“All planets in the solar system follow elliptical orbits with the0nnzheeymyp7 et. n09c;z8g cd/ oq7; Sun located at one focus of the ellipse.” This statement is best summarized by which n.m;7zc getc z/ny;h ee08n p70d oqy9one of the following choices?

  99.21: What happens to then)0ubatlz300k j h zh. force of gravitational attraction between two small objects if the mass of ea0z.hkb)0u3z j lh ta0nch object is doubled and the distance between their centers is doubled?

  95.09 Two spherical bodies attract eyd5qqxeqar1n 3 t,;i: ach other with a gravitational force of 4.0 N. What will be the force if the distance betdrqy,1 eq5; n i:xt3qaween them is doubled?

  14.27: Two spherical, non-rotating planets, X andY, have th -t xd3lpg8w h2;qx5-z5jtcuve same uniform density. Planet X hasuxw vdqt ctpg82- l55-3;jxzh 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-rot,j; epj6 frlyc b;7kt,y3m* xtating planets, X and Y, have the same uniform density;prxe*,cjk ym ; 6,ybfj 3t7tl. 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 otca-4. bmavmp 2b6b 7nrbited by a small satellite by setting the gravitational force on the satellite equal to the centripetal force on the satellite. Whic46vb7c ma2b.pt nb- mah of the following would NOT be required in this calculation?

  99.11: Assume that the Earth attracts John Glennhuld8zo;o;mp zxa n 1p4yg653 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 to which of the pzmog ; 5;uny64x3do 81lpahzfollowing?

  14.30: Considering only the Moon-Earth system (ignore any influence of tf d: 1iou oqboe//5k9che Sun), which one of the following best expresses the magnituddo/:1ofqbi9 eo5/u k ce of the Moon’s acceleration about the Earth?

  02.19: As a rocket blasts away from the earth with a cargo for ttrpk*(kt;wh(m 1wu db2pjq) 9.g5jyrhe international space station, which of the fo.jr 9p (2p)uw5 kq yjrw(tkhg1;*bt mdllowing 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 s;f uei z3f.,xnn4bu() c xx/zsame gravitational force as a second object u;( x )ef,/zbicz. n fuxsx34nat the surface of the Earth. Which of the following would be a reasonable conclusion?

  00.24 Consider an objs7 dq0,; o -*.acdmmr 9luohwdect that has a mass, m, and a weight, W, at the surface of the moon. If we assume the moon has a nearly unifouals d.*hc qwd97,m -;or0modrm 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 maszix)*8kosf dw/s 1 xk(/ywq6zs of Earth and twice the radius of Earth. The magnitude of the gravitational acceleration at the surface of this plqd8ks/ k of1/xzyw sxw *)6(zianet is most nearly:

  98.24: A planet has a radius one-half that of Earth and a maqoh48t9dl, ,nb.bsw kbx*u2 bss one-fifth the Earth’s masstnd4l*xk,bb.oshqb, w8b u 29. The gravitational acceleration at the surface of the planet is most nearly

  08.38: Akg 1200 satellite orbits Planet X in a circular orbit with a consta elekmz5v :0+vnt speed of 5,000m/s. The radius of orbit is 7,500,000 m. What is the magnitude of the gravitational fvvm+5ze 0 k:leorce exerted on the satellite by Planet X?

  94.34: A hypothetical planet orbits a starn-k9d zr;,3ffkj f7n,j r.l xh*l;txu 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 funkl3 ,k9, x . ;*j -drrjf;fnxlh7tzyears does it take for the planet to complete one orbit?

  97.12: Two artificial satellites, 1 and 2, are put into circular orbit at the sah ivg6 doutf )2.c.l1jme altitude above Earth’s surface. The mass of satellite 2 is twice the mass of satelljc1u v2o)6.gt .f dilhite 1. If the period of satellite 1 is T, what is the period of satellite 2?

  15.22 Satellite 1 makes a circular or2s vim3;dl b8it7 ush+o c9kj8bit 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 wou h9u 8a0d 65v;l6 bsmise3zlrrd “weight” refers to the force a scale registerssb3 z muh 80d5 r6iusl6a;l9ve. If the Earth were to stop rotating, but not change shape,

  10.42: A comet moves in an elliptical orbit around the sun. As thu4 4z; haoyko4rg/x(zvpc+0ae comet moves from aphelion (the point on the orbit farthest from the sun) to perihelion (the point on the orbit closest to the sun), which of the following rep o xgukao40y crvh4z;4a/ z(+sults is true?

  17.48: In the binary star system shown, the two stars follow c0imh *d 5;(l*pk0seb,gc jijtircular 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 bk c(j iigdl0t;,*msj50hp*e 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 s rp48gk4l + 9zht+a8fivywu 7epeed vand orbital radius R around a heavy station z4w8fhy vilrg+89euk4 +7tap ary 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 axis a of this new elliptical orbit is