08.19: Kepler’s Second Law about “sweeping out equal areas in equal)t23sgdkopjx5: -bhh4kn4j ; j9pnvd d7hk-z time” can be derived most directly from which consekh 2dkh -74s:4dnp5v nz3db ;ph9xtjj) k-jog rvation law?

  16.17:“All planets in the solar system follow egxqq :j xb.8j:bw2; williptical orbits with the Sun located at one focus of the ellipse.” This statement is best summarized bxxqbjwji q;w:8:2. gby which one of the following choices?

  99.21: What happens to the force of gravitational attraction between two small oti s +pu:3sut(bjects if t (u+s s3uptit:he 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 of 4. gqdrwc18t ht f*d49/)qf(y ci0 N. What will be the force if the distanc)iy( *qf8ccd trwg d49 /t1qhfe between them is doubled?

  14.27: Two spherical, non-rotating planets, X 3m(v 3l /-kmb: 9alby)jbq ndqandY, have the same uniform density. Planet X has twice the radiub l(kvl 9:q 3-bq ybm)3ndjam/s 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, havg/ nfhjekrc-mtp.6w3j2 ,rjhz z 54*we the same uniform density. Planet X has twice the radius of jfgw6re n wm4pj- h*5chzr2k.z, j/3 tPlanet 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 orbqwr sndq -, fgk*x357bited by a small satellite by setting the gravitational force on the satellite equal to the centripetal force on the bks rx, 7dqgnq*3f-5wsatellite. Which of the following would NOT be required in this calculation?

  99.11: Assume that the Earth attracts John Glenn with a gra11e0 trhegf )dvitational force F at the surface of the Earth. When he made his famous second flight in orbit, the gravitational force onhedetf 1g)r1 0 John Glenn while he was in orbit was closest to which of the following?

  14.30: Considering only the Moon2q7*d8 eo n b 0h;7ftjcsupd;2sj/ yei-Earth system (ignore any influence of the Sun), which one of the following best expresses the magnitude of the Moon’s acceleration about the Earth*08u;oj7njp2sd c bde tf q;/yh7e2is?

  02.19: As a rocket blasts away fzo.l0s dy6 qkl;p.*gz rom the earth with a cargo for the international space station, which of the following graphs would best represent the gravitational forploz.g *ls60z qdy;.kce on the cargo versus distance from the surface of the Earth?

  99.33: One object at the surface of the Moon experiences th*nkmwj0e6*b :f .xcgy7 rqy9ce same gravitational force as a second object at the surface of the Earth. Which of the following would be a reasonable conclusion? *m9cyyg .nxcr b:6*ewq07kfj

  00.24 Consider an objec1ongj,):74q2hg)copf ;b.s r wompbct that 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 2))b 4mc, 7 f ng.osh:ocbqjgw1por;pobject’s mass and weight at a distance halfway between Moon’s center and its surface?

  96.23: A hypothetical pl m1sc2,o wqv)ianet has seven times the mass of Earth and twice the radius of Earth. The magnitude of the gravitational acceleration at the surface of to2,svwc)1mq i his planet is most nearly:

  98.24: A planet has a radius one-half that of Earth and a mass on8(x e)df c4xtdbzvvtl1i30t* e-fifth the Earth’s masvfz)ti3 (* blx8x4d t0d ectv1s. The gravitational acceleration at the surface of the planet is most nearly

  08.38: Akg 1200 satellite orbits Planet X in a circular or6x yg3)-gtbj (d.yr02mv ncdwbit with a constant speed of 5,000m/s. The radius of orbit is 7,500ndr.36t b)0v 2ydc (-mjggywx,000 m. What is the magnitude of the gravitational force exerted on the satellite by Planet X?

  94.34: A hypothetical planet orbits a sc5ddk :e )tmg3d69sq:z vrk5 pr,k2 ictar with mass one-half the mass of our sun. The plan52k35 q6m gvst,ci dz)rdd9kcp k:e:ret’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 circuley8gj+dqe y*mt2x n)3 ar orbit at the same altitude above Earth’s surface. The mass of satellite 2 is twice the mass of satellite 1. If t )gt8m2dee jq +yy*n3xhe period of satellite 1 is T, what is the period of satellite 2?

  15.22 Satellite 1 makes fz+p zuk-g2 pgfhc4;q78h l4ea 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 woex1y 7ox+bh)f rd “weight” refers to the force a scale registers. If the Eyh+xb)e o17 xfarth were to stop rotating, but not change shape,

  10.42: A comet moves in an elliptical 8eapwi)hu2 *g orbit around the sun. As the comet moves from aphelion (the point on thwa e2)i8u*g hpe 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 system shown, the two stars folve lv:w1-9w)muuu8 v ulow 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 8v v-1wuulmu): 9 evuwthe following choices represents the total mass of the binary star system?

  06.50: A rocket is in albs2 +s u4l*rc circular orbit 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 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 erls 2cu*sl4 +blliptical orbit is