08.19: Kepler’s Second Law about “x8h/v2 ;l5cl cu pnf.bsweeping out equal areas in equal time” can be derived most directlyvb/ 8.25un p hcfl;xlc from which conservation law?

  16.17:“All planets in the solar system follow elliptical orbits with the S. aox acm(8y -nxa: c9jpn*oo8un located at one focus of the ellipse.” This stateme* a8o.cncaym(o:n- x pojax 98nt is best summarized by which one of the following choices?

  99.21: What happens to the fo j3sl7w3dfo9frce of gravitational attraction between two small owj f7sl3odf39bjects if the mass of each object is doubled and the distance between their centers is doubled?

  95.09 Two spherical bodies attract each other with a gravitatio)*bc7-wj n urbnal force of 4.0 N. njuw-r *)7 bcbWhat will be the force if the distance between them is doubled?

  14.27: Two spherical, non-rotating planets, X andY, have the same uniform densit.wvsw +mbk. b 3c3vrsn6mj v85dw 4*gfy. Planet X has twf6.vrb3mm8v5.k b+vg*cs4wdnw sj3 wice 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 plqevpxol5 ,f6r6q(h.mpgjz( 33xjx1u anets, X and Y, have the same uniform density. Planet X has twice the radiujup6xqx1l5.3 3h z(fgoemv jr 6x, (pqs 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 calculaba 1(1e-2nlmpig t1 dited if it is orbited by a small satellite by setting the gravitational force on the satellite equal to the centripetal force on the satellite. Which of11pa d (1 gebin-itlm2 the following would NOT be required in this calculation?

  99.11: Assume that twvm2;,xcj3zi1:qvdh7*od2 tu / holwhe Earth attracts John Glenn 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 closv3;71wodih2,:wvjoz/c lxm 2ut hdq *est to which of the following?

  14.30: Considering only the Moon-Earth snq mi9)jgyn ;: c+nt:lystem (ignore any influence of the Sun), which one of the following best expresses the magnitude of the Moon’s acceleration about the Ea+tnn )i: c:gm9 nqy;jlrth?

  02.19: As a rocket blasts away from the earth with a cargo for the in -bi947cfmuu uternational space station, which of the following graphs would best represent the gravitational force on the cargo versus distance from the surface of tu-i 7ubfu cm94he Earth?

  99.33: One object at the surface of the Moon experiences the same gra uv0:;t3gxv pl/muyau*7 tvb -vitational force as a second object at the surface of the Earth. Which of the fgu/mt- p v:v*lyau7t;03vbx u ollowing would be a reasonable conclusion?

  00.24 Consider an object that has a mass, m49 9m3y*jg*qlss;oue: h e hzm, and a weight, W, at the surface of the moon. If we assume the moon has a nearm9;ey9 3qhu z os:j*m4lhs*e gly 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 mass of Earth and twice the6w w l)doi(de8noq9 -1ypk i)y radius o qyiw 1i )ld98(6kewn o-yod)pf 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 ttvl g1-/f4(k1*hv +pcm bkh wio*zw)k hat of Earth and a mass one-fifth the Earth’s mass. The gravitational a v-kvkwh(/if4 c*p1bh+ mwk)ogzl*1t cceleration at the surface of the planet is most nearly

  08.38: Akg 1200 satellitj23p 6y.tooj-iwkmbqqo( 1+ ge orbits Planet X in a circular orbit with a constant speed of 5,000m/s. The radius of orbit og2 qqj+wojm6oib1t.ky3-( p 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 ouyb3wit ,n+7wp7ipi 0 ne-half the mass of our sun. The p70ywwpi i3,n7iput +b lanet’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 circular orbit a acwyos.) emsv +h789qt the same altitude above Earth’s surface. The mass of satellite 2 is twice the mass of satellite 1. If eovqhs7ysc)9ma.+ 8wthe period of satellite 1 is T, what is the period of satellite 2?

  15.22 Satellite 1 makes a circular orbit around the Ean6q3aodni -: drth 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 k sfxp0p 1nvaf;;lf95force a scale registers. If the Earth were f;s0n v 51a lk9;ppfxfto stop rotating, but not change shape,

  10.42: A comet moves in an elkd)) kwrmm0otrp:e l2x *c 9b8liptical orbit around the sun. As the comet moves from aphelion (the point on the orbit farthest from mmdpk lec*rr8k0x:wt9)2bo) 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 sy-yu h;ewb8t8k h 85wsp. cehi8stem shown, the two 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 one of the following choices represents the total masswyeph8eu- wi c. h8hkb58ts 8; of the binary star system?

  06.50: A rocket is in a circular orbit with speed van+r:(t:ggv(9.g yc; u trxkgnjd 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 rocket into an elliptical orbit. In terms of R, the size of the semi-major axis a of this new elnkr v+.g tc9ugr(xg :;g(tj:yliptical orbit is