08.19: Kepler’s Secoy6qf* jkxd.wxk2(b0p 2i jr5,ho6rp qnd Law about “sweeping out equal areas in equal time” can be derived most directly f2fw o, jj62 6dhqbxp kxr*( py0.qki5rrom which conservation law?

  16.17:“All planets in the solar system follow elliptic;. vl) se,w(kv7e xv58idth qzal orbits with the Sun located at one fo5)7vq8.e w,kxvvi tezh(;d slcus of the ellipse.” This statement is best summarized by which one of the following choices?

  99.21: What happens to the force of gravitational attraction between two zrqm;2u+lca 6 -fc3igg ;p pf3small objects if the mass of;gcla6mqp-ip3 +fzcuf;g 3 r2 each object is doubled and the distance between their centers is doubled?

  95.09 Two spherical bodies attract each otherqlm1+dtswa5p.sru d04 kz(-r with a gravitational force of 4.0 N. What will be the force if the dista slwk0u-( 4mtq5d rpr.s+dz1a nce between them is doubled?

  14.27: Two spherical, non-rotating planets, g p;t46fv8cyavsg.md) u5 rxj9 7j+gu X andY, have the same uniform density. Planet X has twice the radius.cusp9vav 47); rjxjfug6g5 d8gy t+m 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 anj,ereo,-h+b z d Y, have the same uniform density. Planet X has twice tjeb-+ ro z,,hehe 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 orbiy2mc +gpducj2:l zd bdo23q/3ted by a small satellite by setting the gravitational force on the satellite equal to the centripetal force on the satellite. Which of the following would NOT be requlp d3z+g3u c/2dy 2qmodb2j c:ired in this calculation?

  99.11: Assume that the Earth attracts John Glenn with a gravit+ jaz7aq )nfv1ational force F at the surface of the Earth. When he made his7)fv a a1+qnzj 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 . x tefn2qxg8s+eop(, (ignore any influence of the Sun), w( xto,neq8.pex+s f 2ghich one of the following best expresses the magnitude of the Moon’s acceleration about the Earth?

  02.19: As a rocket blasts away from the earth with a cargo for the ik/uro4r;)z k/2tpy sui b bu -8izc3d+nternational space station, which of the following graphs would best represent the gravit ki/r2; uzkzrytp c384d bi+u)osu/b -ational force on the cargo versus distance from the surface of the Earth?

  99.33: One object at the surface of the Moh0 xyq3-rarz 5on experiences the same gravitational force asxh35rr0zq -y a a second object at the surface of the Earth. Which of the following would be a reasonable conclusion?

  00.24 Consider an objeaufc)r 7q mzr5q )1c+mct that has a mass, m, and a weight, W, at the surface of the 5)1+ mcmacrqqfz7 ru)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 between Moon’s center and its surface?

  96.23: A hypothetical planet has seven times the mass of Eaqga6wn(.j; kn rth and twice the radius of Earth. The magnitude of the gravita jnk;g6w(n qa.tional 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 Eartv+*0i o rhim60gh4irth’s mass. The gravitational acceleration at the surface of the planet io i0 60t4rvm+*ihhgi rs most nearly

  08.38: Akg 1200 satellite orbits Planet X zxw/6b:zgwai6(em ft7:k3ud.c f.m lin a circular orbit with a constant speed of 5,000m/s. The radius of ./ (ub c:kmdt3e:m 7ww z6i.zaf6gx florbit 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 masvd6aaj pqv5nh 4n(.u1x8y; nt s of our sun. The pl apvd u h.nva61jxnn;( tq5y48anet’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 at the kg00ymhs(z fxs*1np 9same 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 is nk zyg*1 sm90pf(h0xs the period of satellite 2?

  15.22 Satellite 1 makes a circular orbit around the Earx1u ,be*:fi s: ugqyb9th 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, t qq0ltrh5o(1kp: gt1n83uo hqhe word “weight” refers to the force a scale rhgn :u( hpqor15ok l 183qtq0tegisters. If the Earth were to stop rotating, but not change shape,

  10.42: A comet moves in an elliptical orbit around the sun. 6q,4r 9-hdmdum7by-ttt n1 l oAs the 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 ofmh64qu -o tlm,d9-7 b1y ttrdn the following results is true?

  17.48: In the binary star system shown, the two stars follow 9smkc3ie5/kbx/g 3dj je(nu 6 circular orbits about the system’ ej3gum(c 39idn kxs/b /6ej5ks 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 mass of the binary star system?

  06.50: A rocket is in a circular orbit with speed vand orb zgu+ 7z.,db-rftu a th *8 zalt-8z3equknu.1ital 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 8qt uzuzta t d 3 fa+8-.k,r7ul.1h buz*gne-zthis new elliptical orbit is