08.19: Kepler’s Second Law about “sweeping out equal areas vfqa q0j0d g9 s5v6z*win equal time” can be derived fq 6gdqvvw *a9s0j5 0zmost directly from which conservation law?

  16.17:“All planets in the solar system follow elliptical orbits with s8pib;m d94tq the Sun located at one focus of the ellip;qt 984ismpbd se.” This statement is best summarized by which one of the following choices?

  99.21: What happens to the force of gravitational attraction betwe:hewu+* qyn gv*gbc mi9 9:dc/en two small objects if the mass of each object is doubl*u9+nd :ebi /h9g ywqv*:gcmced and the distance between their centers is doubled?

  95.09 Two spherical bodies attract each otw 3,/h: nc0l ly7aoigqc7,pl qher with a gravitational force of 4.0 N. What will be the force if the distance betwee0 qnlch,/ig: 3y 7lpqw7 lco,an them is doubled?

  14.27: Two spherical, non-rotating planets, X andY, have the5rjuao9mlv3.n)7re z d8n 8vp same uniform densityvajpvru8 7) r .nl835zdme9on. Planet 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 planets, Xq5buvbep4;q 2 5qs n-m and Y, have the same uniform density. Planqpum-5bs2ebvq 4n; q5et 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 orbited by a small sa /*ybb*f(r h9gov-kdutellite by setting the gravitational force on the satellite equal to the centripetal force on the satellite. Which of /b ko*y -fur9d(*vhbgthe following would NOT be required in this calculation?

  99.11: Assume that the Earth attracts John Glenn with aflc n/qmh/k om e/;,/)k iaqx8 gravitational 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 in orbit was closeq k xa/hf/mcml8/o qnk),ei /;st to which of the following?

  14.30: Considering only thexpci qp; .n2 27 xd5ryc,7ijka Moon-Earth system (ignore any influence of the Sun), which one of the following best expre x xdyj;c27ic2pap, . rq5n7kisses the magnitude of the Moon’s acceleration about the Earth?

  02.19: As a rocket blasts away from the earth with a cargo for the intern+ua*7 eh9uaq uu *u4fcational space station, which of the following graphs would best represent the gravitational force q7uf ua hucu +*ea94u*on the cargo versus distance from the surface of the Earth?

  99.33: One object at the surface of the Moon experiences the rjbk72f 0bhu0k1*iy8rao jos) .w0,cttma3 l same gravitational force as a second objec7 urf.c )lj b0ki tr23aos0y w*,omhj0t1 8bkat at the surface of the Earth. Which of the following would be a reasonable conclusion?

  00.24 Consider an object that has a mass, t7g7 z2xyp7 qqm, and a weight, W, at the surface of the moon. If we assume the moon has a nearly uniform density, which7y zqpx 772gqt 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 sevenfrp5qqima 4qkczx /f807 ;vc, times the mass of Earth and twice the radius of Earth. The magnitude of the gravitational acceleration at th 8z ,qvf ;fc7xicpk/aq5r40 mqe surface of this planet is most nearly:

  98.24: A planet has a radius4s(zdxq mn * top rp96lyf-d(7 one-half that of Earth and a mass one-fifth the Earth’s mass. The gravitational acceleration at the surface of the planet inpxf4pzoql 7-* tdyr (s(96md s most nearly

  08.38: Akg 1200 satellite orbits Planet m,fe2/uy d8ihd z7 7krX 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 satelh7 rdez /id2,7mku8fylite by Planet X?

  94.34: A hypothetical planet orbits a star with mass one-half the mass t;ib d)* (x+mfc+ j cpu(.zdnnof our sun. The planet’s orbital radius is the same as the Earth’s. Approximately how many Earth years does it take for the planet to cd ).xi+( bdtcmfn*(n z j+cpu;omplete one orbit?

  97.12: Two artificial satellites, 1 and 2, are put into circular orbye q96- eox4kc7q6wor na q49mit at the same altitude above Earth’s surface. The mass of satellite 2 is twice the mass of satellite 1. If the p ekme94nra 697q 6 woq-o4ycqxeriod of satellite 1 is T, what is the period of satellite 2?

  15.22 Satellite 1 makes a circular o5 t rg,h)kvrl*rbit 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 “weight” refers to the forf4dek*3ooo7ag , z e;ace a scale regis oakao*e,ef 4 goz37d;ters. 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 moveku tuz8yrr26 3 x.netm)u3 .oos from aphelion (the point on the orbit farthest from the sun) to perihelion (the point on the orbit o2uu6yrrn3xztt.k8 eo3 ).m u closest to the sun), which of the following results is true?

  17.48: In the binary star system sh27dyi6+ :1wjalbtp amown, the two stars follow circular orbits about the system’s center of mass. The s1wlb i a7md:2jptay6 +tars 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 spedfit y mx;; ,1ytl()ered vand orbital radius R around a heavy stationary mass. An external impulse is quickly applied to the rocket directly oppos( ri)yf dmyt t,elx;;1ite 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