08.19: Kepler’s Second Law about “sweeping out equal areas in equal1wg33xnul/iy(p i 5s) 1vcc7e(jaj mx time” can be derived moi) ms3(xv/ l5ge (nja 7jyc11uciwxp3 st directly from which conservation law?

  16.17:“All planets in the solar system follow elliptical orbits with thec07 5ozkbgp/ u 26omxq Sun located at one focus of the ellipse.” This statem p6k bc5oox/2z q7ug0ment is best summarized by which one of the following choices?

  99.21: What happens to the force of gravitationwb1ugdzh8l9o ): ev9 v-zemt.al attraction between two small objects if the mass of each object is doubled and the distance bedl.wz-9g veu ovz 1m9bhe8): ttween their centers is doubled?

  95.09 Two spherical bodies ls3 ka4 49h6g amahh(fattract each other with a gravitational force of 4.0 N. What will be the force if the distance betwhk ah4s ag3 (lmfa649heen them is doubled?

  14.27: Two spherical, non-rokyuvubu(s -;-hf+ hbo rr/1z 8tating planets, X andY, have the same uniform density. Planet X has twice /1-+u;hbfy 8 su(uk rovbrh z-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 uny rw9 tj/q, d0lz;bcghss/m9.iform density. Planet X;/g/.mc hyrzsl,9qtsbw0dj9 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 :cu*pyn 2t6j tis orbited by a small satellite by setting the gravitational force on the satellite equal to the centripetal force on the 2y ct *u6jpnt:satellite. Which of the following would NOT be required in this calculation?

  99.11: Assume that the Earth attracts qfp2fp*s xuh+; x2 4bqms;ep7cs;(k eJohn Glenn with a gravitational force F at the surface ouq* 2c b;e( xx7sffq;k m+php2se ;sp4f the Earth. When he made his 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 (ignore any in h8ayge rzfsz-eo 2i4 9/gwk8b))us 1wfluence of the Sun), which one of the following best gwwo94fz /ker)ezu2i 8ss1ha8-) by gexpresses the magnitude of the Moon’s acceleration about the Earth?

  02.19: As a rocket blasts awapg diqpng6dsc; 64q0: bk/7ury from the earth with a cargo for the international space station, which of the following graphs would best represent the gravitational force on the cargo versus distance 6 c 6gkq:7g/r0sd dp4uqbnp ;ifrom the surface of the Earth?

  99.33: One object at the surface of the Mooeqxuc;lb99x+a wl eh0k sgid ,;5m3;an experiences the same gravitational force as a second object at the surface of the Earth. Which of the following would be a i;x 9me93kea;csq, g0w5alb+duhx; lreasonable conclusion?

  00.24 Consider an object that has a mass, m, and/54r*qet; p mgr )ebqo a weight, W, at the surface of the moon. If we assume the moon has a nearly uniform densibg5;r qo4r)eem/ *pqtty, 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 Earth and twice t)/ p lh 7eh2gpojx7a4ahe radius of Earth. The magnitude of thegh2h/7ajp) l 7oxp4ae gravitational acceleration at the surface of this planet is most nearly:

  98.24: A planet has a radius one-half that of Earth and a//*x (zov zi1c3rxh t5bv*ckh mass one-fifth the Earth’s mass. The gravitational15z i3kv/ crxvzobc/hh** x t( acceleration at the surface of the planet is most nearly

  08.38: Akg 1200 satellite orbits Planet X in a circular orbit with a usqso9 2) +0tmz ,4 reav *rtn9ycw2ydconstant speed of 5,000m/s. The radius otyvn r *r)2sw4ts 29o9 +qu m0acdzy,ef 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 star with mass one-half the mass of our s8ge2a rkh-wiae5u e62)s*ug/sqa) w hun. The planet’s orbital radius is the same as the Earth’s. e6qegaa 2 e*wks82 hhi)raw5ug/)- usApproximately how many Earth years does it take for the planet to complete one orbit?

  97.12: Two artificial satellites,, fkg0 w3xm8 bvq.ndu b,(riw9 1 and 2, are put into circular orbit at the same altitude above Earth’s surf,qnb(vm0 wbr guikf8, x w3.d9ace. The mass of satellite 2 is twice the mass of satellite 1. If the period of satellite 1 is T, what is the period of satellite 2?

  15.22 Satellite 1 makes a circular orbit around7j,g+vn y6 xu*fy5* j47o4 kiojlywka 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 “weight” refers to the f,+hws 1i5 ot1j2qbpezorce a scale regot iw5s e1qj,2zhb+1pisters. If the Earth were to stop rotating, but not change shape,

  10.42: A comet moves in an elliptic 1:ktyw6h es.nal orbit around the sun. As the comet moves from aphelion (the point on n1w:kt eysh6. 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 system shown, the two / ;mzxrfz m*4s,(csgy stars follow circular orbits about the system’s center of mass. zfr cms*ms/gzy 4x,(;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 speedw7w i0*g7 usmm vand orbital radius R around a heavy statwu7 wmi0g* s7mionary 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 elliptical orbit is