08.19: Kepler’s Second Law about “sweeping out equal areas nfy7d2.b vx. oin equal time” can be derived most diredvny7f. bx.2 octly from which conservation law?

  16.17:“All planets in the solar system follow elliptical orbits with the69vvtws-9v s46eppry e.l pbed.9u9l Sun located at one focus of the ellipse.” This statement is best summaribvl9 v evew9p ypu.pe64-s9.s l9t6drzed by which one of the following choices?

  99.21: What happens to the force of gravitational attraction betcg: v.ecx i:xjewrv*v7(f4 d7ween two small obje x4(7 v.edc:c gv:i w7jefx*rvcts 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 gravitational force 0 omcmn2-;j8s rmt j-kof 4.0 N. What will be the force if the distance betwe2t o0m- jnmjscm8; kr-en them is doubled?

  14.27: Two spherical, non-rotating planets, s ug-z: 747(+keat8btvjlr mgX andY, have the same uniform density. Planet X has twic-tr g8 v+4 la(bjut7e:s zgkm7e 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 planets, X and Y, have the same unacnaj m 4/*1tudrog3, iform density.d *4c,j/tu ma3 n1orga 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 calculatedp;3e aqv:,qkz if it is orbited by a small satellite by setting the gravitational force on the sataz:ke;vpq 3q, ellite equal to the centripetal force on the satellite. Which of the following would NOT be required in this calculation?

  99.11: Assume that the Earthrfh - y:k/ erguve e2k(y0i9u5 attracts John Glenn with a gravitational force F at the surface of the Earth. When he made his famoueery:h ( -2 uvkyeg/9uf0r5iks 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 onlzrn 0w;v 5mrls2an:a5y the Moon-Earth system (ignore any influence of the Sun), which nla5 0 ra2wvn:5;smzr 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.kpz29 m5(pfzo lo, iw cargo for the international space station, which of the following grak5w zm.pilo2z,f9po(phs 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 experience mobeor(0pz .5s the same gravitational force as a second object at the surface of the Earth. Which of the following would bpr(b0z5 mo oe.e a reasonable conclusion?

  00.24 Consider an object thatq6n x,ms ww;z1 has a mass, m, and a weight, W, at the surface of the 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 Moos; ,n qw6zxw1mn’s center and its surface?

  96.23: A hypothetical planet has sevfv,8 vag uks z;228yihen times the mass of Earth and twice the radius of Earth. Tvv2si82khy;gu, a fz8he magnitude of the gravitational acceleration at the surface of this planet is most nearly:

  98.24: A planet has a radius one-half that of Earthp.9oynxbm 8u y,e:3m,f - qtle and a mass one-fifth the Earth’s mass. The gravitationa em, ybmef:83opu9x.,qtn y-ll acceleration at the surface of the planet is most nearly

  08.38: Akg 1200 satek9 *60pt kgs2l.,xnfppi zf ,zllite orbits 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 magnitude of the gravitational force exerted on the satellite by Planet X?ffzk 6 ip*nps,g02 ,tpxlk9z.

  94.34: A hypothetical planet orbits a star with mass oye+wgg4hfl9 ev; 1;xj ne-half the mass of our sun. The planet’s ee;l+jx 1 g4fv9hyw;g 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 a5)6qd *k; gqojteu*l vnd 2, are put into circular orbit at the same altitude above Earth’s surface. The mass of satellite 2 is twice the mass of satelll*qkt*v5go;d6)e jq uite 1. If the period of satellite 1 is T, what is the period of satellite 2?

  15.22 Satellite 1 makeimo .o j49bs*59(pbkun isgp: s 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 word6 bj:q fym4h10pcoz 6s “weight” refers to the force a scale registers. If the Earth were to stop rotating, but not change 6p fz01bscomy j4qh:6 shape,

  10.42: A comet moves in an elliptical o o fcrpn.3,/r-l)oy ( ns;p/-akjkrrzrbit around the sun. As the comet moves from aphelion (the point on the orbit farthest from the sun).; lsorp- nr-) r/ap3(kcykz,or /jfn 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 foqb2-w79khyk(o9w; +rd4wn n6wwivvbllow circular orbits about the system’s center of mass. The stars are separated by a di vindb+o;rkww(n69ww 7-9y2 k w4 bhvqstance 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 b-dj m0j4q;moz/s:bfspeed vand orbital radius R around a heavy stationary mass. An external impulse is quickly applied to the rocket directly opposite to :fm d-qbo j/4m0jzbs; 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