08.19: Kepler’s Second Law about “sweeping out equal areas in equal time” can belumq8q,ky d(0 derived most directly from which conseruy, 0mqd( 8lkqvation law?

  16.17:“All planets in the solar system followie/u;v jt2t ,s elliptical orbits with the Sun located at one focus of the ellipse.” This statemts/;euij2 vt ,ent is best summarized by which one of the following choices?

  99.21: What happens to the force of gravitational atubx48mp vqcn1 z63q5btraction between two small objects if the mass of each object is doubled and the distance between their cen6b8mv ub43qqnc z5x 1pters is doubled?

  95.09 Two spherical bodies attract each other with a gravitatiopk) 7 jy)u8szhnal force of 4.0 N. What will be the force if the distance between them is doubps)uzhy j78)k led?

  14.27: Two spherical, non-rotating plan0a) m*wv0bb nfdkua xl.) p,ei;o3-kwets, X andY, have the same uniform density. Pbi)d*,am.l x )a ;3k0p 0owbkunvwef-lanet X has twice 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 planv+ 5lqticwbm-* +0h0 1d lbsdzets, X and Y, have the same uniform density. Pland* vlbb+-0 imd s5+0wctq zh1let 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 calc)u iu6qyqrb frjl- 0*h,ot)1rj pg,z 1ulated if it is orbited by a small satellite by setting the gravitational force on the satellitej0yu,lt )*pqi1bo1)j grrf - qur,6z h equal to the centripetal force on the satellite. Which of the following would NOT be required in this calculation?

  99.11: Assume that the Earth attracts John Glenn with a gravitational forcxi2lo qim4d7 2e F at the surface of the Earth. When he made his famous second flight in orbit, the gravitational2io7m4idq x2 l force on John Glenn while he was in orbit was closest to which of the following?

  14.30: Considering only the Moon-Earth system (ignore any 5ba qdmw9x- ai g:tr/.influence of the Sun), whi /qm:a.b 9di5-tg rwaxch 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 catjmkpa5-o(q. h1 t6e trgo for the international space station, which of the followingqt1.t j-m 6ae 5po(hkt graphs would best represent the gravitational force on the cargo versus distance from the surface of the Earth?

  99.33: One object at the lc2a*7q:27kina xm/qvm;g au surface of the Moon experiences the same gravitational force as a second object at the surface of the Earth. Which of the following would be a reasonable conci*;/mm2 : a 7qvxc7agqakn2ullusion?

  00.24 Consider an object that has a mass, m, and a weight, W, at the surfx rps )rqh0j, ,sti/g(cf-;ut ace of the moon. If we assume the moon has a nearly uniform density, which of the following wouldcjr hqr;,f pi0u ,st t)/xg-(s 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 twich fjb3 i+btr85e the radius of Earth. The magnitude of the gravitational acceleration at the surface of this b5tbi3r8f+ hjplanet is most nearly:

  98.24: A planet has a radius one-half that of 5;drya * gq* bhnr3w+vEarth and a mass one-fifth the Earth’s mass. The gravitational acceleratiohrn+qg yawrb;v* 53*dn at the surface of the planet is most nearly

  08.38: Akg 1200 satellite orbits Planej/- 86vz +fzxl3zb ; cdntdoc9t X in a circular orbit with a constant speec;bd zftxjoc3n/8d l z9z +v6-d 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?

  94.34: A hypothetical planet orbits a strmf1m8-chh5gxyxz3 6 ar with mass one-half the mass of our sun. The planet’s orbital radius is the smm h y5c- h1gr3zf68xxame 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 jwceljeb* b m9rkuq8j;0 i8;;ys m(a;circular orbit at the same 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 the period9lmjjuw;b;c b8;ie (qa*jmky; r8e0s of satellite 2?

  15.22 Satellite 1 makes a circular orbit around the*;4x x/wnhbnp;cgds:/b fxp 9 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 “weight” refers ts5fc h(9mieou; 3+yufo the force a scale regiufys9c+i fm3( oh5 ;uesters. If the Earth were to stop rotating, but not change shape,

  10.42: A comet moves in an elliptical orbit around the sun. As the comet moves f 4 k* p+2(.qbfwtosphcob3 ;3vw :ioogrom 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 resultstp 2wqk.b33 cp*o (io+gwv4 o:fhsbo; is true?

  17.48: In the binary star system shown, the two stars follow i2) s j9)md c8sge))whcfi-pr circular orbits about the system’s center of mass. The stars are separated by a distance D that is large compared c)sci 8d9fmpsje))w -)r2 gihto 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 circuli aj16)q7h kv,5*svz3shpzon ar 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 axisp zojk)sisv*13nhqh,6v a 75z a of this new elliptical orbit is