08.19: Kepler’s Second Law about “sweeping out equal areas in equaly 4xz sjbmlkr(u rp+9.n.0* al time” can be derived most directly from which ry.+nj4lsrbp(ma0 u*l.9 zx kconservation law?

  16.17:“All planets in the, *ockc/tty6x solar system follow elliptical orbits with the Sun located at one focus of kcc*t6to/x,y the ellipse.” This statement is best summarized by which one of the following choices?

  99.21: What happens to the force of gravitational attraction b8;(- snp mtnr )6 xj/ ;dvfqq-qm9sqxyetween two small objects if the 9nfq8 n/t ( ; rv)sqmjqxd-6mqpy;-sx mass of each object is doubled and the distance between their centers is doubled?

  95.09 Two spherical bodies attract each other with ijf4 d+;b: czta gravitational force of 4.0 N. What will be the fo:t fcbj4+zd;i rce if the distance between them is doubled?

  14.27: Two spherical, non-roby0 1y-rvtp69ap( ohz)*b.zp wz hou7tating planets, X andY, have the same uniform density. Planet X has twice the radius of Planet Y. z o9(bhh.avzzr1p yp*p- y67)uwtob0 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 unifovsyx/h* div0dq54 yr3rm density. /5i3y dqs4vxyr*0 v dhPlanet 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 orbitt+nd(kgn4l2x,lu4wz qfx l-:ed 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 required in this cal+2dg f4q w(t xlklx4lun-z:,nculation?

  99.11: Assume that the Earth attracts John Glenn with a gravitatiox yrbe qdm.d *(lu*7 :ir4w eo6rq2-bwnal 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 rme 2-exrb4w*(rb :* lqiudqy7.wod6in orbit was closest to which of the following?

  14.30: Considering only the Moon-Earth system (ignore any influzn av6vlm/ v(9ence of the Sun), which one of the following best expresses the magnitude of the Moon’s acc/(vlvnva6z m9 eleration about the Earth?

  02.19: As a rocket blasts away from t yb+qtxgpjaux*)u7 )52fxlhqvr+l 26he earth with a cargo for the international space station, which of the gl22h)rxq7) *vq lt a 6p+ubxujyf+5xfollowing 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 sjmqkv.q 9,f 3(k9lvd iame gravitational force as a second object at the surface of the Earth. Which of the following would be a reasonable concluqld.39v ikmv jq9k f,(sion?

  00.24 Consider an object that has a mass, m, and a weigh +(a8wpd/cy rzt, 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 wei8(p+zcdyra w/ ght at a distance halfway between Moon’s center and its surface?

  96.23: A hypothetical planet has s *e10txjz)hyeautj-/i * 8 caieven times the mass of Earth and twice the radius of Earth. The magnitude of the gravitational acceleration at the surface of this planet is most nearly:tja*t iye u1aji0eh cx *)-8z/

  98.24: A planet has a radius one-half that of Eartdocb1j2s;;u8 aub1g 1 rd3m fkh and a mass one-fifth the Earth’s mass. The gravitationalur gjb12a8o;;k d1uf dc1bm3s acceleration at the surface of the planet is most nearly

  08.38: Akg 1200 satellite orb mj*ztmxi9nph3wvhh,tael(;4g4 l :i y0xc;+its 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 magn+cy;30z94awnpjxhgi e*xlv,hl tt;4 (hm :imitude of the gravitational force exerted on the satellite by Planet X?

  94.34: A hypothetical planet orbits a star 0xz vbpw eaw(2wlb 1hs:t)51 zwith mass one-half the mass of our sun. The planet’s orbital radius is the same as the Earth’s. Approximately how many Earth years does 1zet pwh:5vxwb)(wb 1as2l z 0it take for the planet to complete one orbit?

  97.12: Two artificial satellites, 1 and 2, are put into circulohpko90obvgus: zcrk) p4 3ja7s:0t-ar orbit at the same altitude above Earth’s surface. The mass of satellite 2 is twice the mass of satellite 1. If a:k3:-v9 op4zh0 pt boc7 s0kgosj)urthe period of satellite 1 is T, what is the period of satellite 2?

  15.22 Satellite 1 makesp ywb 7x(052 lkpr+jg u16ddis 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 nq y10nzb abar(y:89i “weight” refers to the force a scale registers. If the Earth were to stop ro bq(1yrz9a0nb8 :yinatating, but not change shape,

  10.42: A comet moves in an elliptical orbit a1 t8 3vncegiv-round the sun. As the comet moves frenv1v i3 tg-c8om 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 results is true?

  17.48: In the binary star sypb fafh9xp p43z ;r)3xstem 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 afap xh34bp;) z9 r3xfpre 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 owt/3)g *:vhxp we;ron rbit with speed 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 in);3hvpxr: w* egotw /s 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