08.19: Kepler’s Second Law about “sweeping out equal areas in equal time” can bebhc9l i fjlty*zaxzt 8i* dbe6.u +80; derived most directly fxle + 0h.zydlctu88bb*ij*6zt9;fai rom which conservation law?

  16.17:“All planets in the solar system follow elliptical orbits with the Su.cmv-t.; gerqn located at one focus of the ellipse.” This statement is best summarizegcr; -q..tmev d by which one of the following choices?

  99.21: What happens to the force ouhh y((3u. 9 n v/kyo73gyzsypf gravitational attraction between two small objects if thezuohh 9 s7yky(3vg/uy.p3 ( yn mass of each object is doubled and the distance between their centers is doubled?

  95.09 Two spherical bodies att; .0e+ek zgsqjract each other with a gravitational force of 4.0 N. What will be the force if thgej .zske+q;0e distance between them is doubled?

  14.27: Two spherical, non-rotating planets, X andY, have the same uniformg )rryz.ja2 o3 density.2az 3.rg jyo)r 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-rotatinyfs ;d)ed0zw/ g planets, X and Y, have the same uniform density. Planet X has twice the radius of Planet Y. Le ;wy/z)edds0ft $v_x$ 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 plan etg;cg y6)mj,et can be calculated if it is orbited by a small satellite by setting the gravitational force on the satellite equal to the centripetal force on the satellite.m6gc )ej;gt y, Which of the following would NOT be required in this calculation?

  99.11: Assume that the Eaehsu4sp (x/ rj,cs 3tfgw 112rrth attracts John Glenn with a 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 closest to which of thj r1,u(1 cxt ss2r/4 efswh3pge following?

  14.30: Considering only the Motqq 8pscd kr;aj:4qy/a v 3;q*on-Earth system (ignore any influence of the Sun), which one of the following best expresses the magnitude of the Moon’s acceleration about c q/3q8q;:vqra*d s;yt4 kajpthe Earth?

  02.19: As a rocket blasts awayobi22wa 0 4ugg-l)f.zpy 2 x7nqp;lyv 4ruy2d from the earth with a cargo for the international space station, wh2-za0;fbpnl )y4gg yr oqxw 422p uu.l 27dviyich of the following graphs would best represent the gravitational force on the cargo versus distance from the surface of the Earth?

  99.33: One object at s/wrm *d-vjq7 the surface of the Moon experiences the same gravitational force as a second object at the surface of the Earth. Which of the following would besjw/*vd -mqr7 a reasonable conclusion?

  00.24 Consider an object that has a mass, m, and a weight, W, at the fprbh9q*2;og5lz l-i;:ubzp r5 ov-jsurface of the moon. If we assume the moon has a nearly uniform density, which of the follor5uh-l z;9q5ro fpvzl ;- gi *:jpb2obwing 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 seve xh aps,cit6x, (c*w+ig)i9 aun times the mass of Earth and twice the radius of Earth. The magnitude of ti,+iw(ixx),c96g cs aaph*u the gravitational acceleration at the surface of this planet is most nearly:

  98.24: A planet has a radius one-mmz56c; 3gwqc8o +doz half that of Earth and a mass one-fifth the Earth’s mass. The gravitational acceleration at the surface o5 d ozcoz;mq68w+cg3mf the planet is most nearly

  08.38: Akg 1200 satellite orbits Planet X in a circular orbit with a con qr-a7(rpbm0 wstant 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 satellite by Planet bp0-q( m awr7rX?

  94.34: A hypothetical planet oxa jfcf)k(d8 mn7 j1*erbits a star with mass one-half the mass of our sun.me1j(fn *xf)d8k7 j ca The planet’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 circular orioua/ g,rw;nu(v9s 2 bbit at the same altitude above E,i/9us og; (v 2wunrabarth’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 period of satellite 2?

  15.22 Satellite 1 makes a circular orbit around the Earth with a radiwvcbs0 :v*4o;y eez/ +ugty6dus $r_1= R$. 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 wordrnr u fkt0b zp74g,3+ubuk:o fw67,zx “weight” refers to the force a scale register:kf 37u6 0wpx7br 4foknuu ,rgz+bt,zs. If the Earth were to stop rotating, but not change shape,

  10.42: A comet moves in an elliptical orbts 5az2 oe9qt2it around the sun. As the comet moves from 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 result qt5 eas2z29ots is true?

  17.48: In the binary star s 8s5amjr+j 7y5czn 8rwystem 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 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 them7jw8zy5 ac sjrn8 5r+ binary star system?

  06.50: A rocket is in a cirtkx3,+)r f sjmcular orbit with speed vand orbital radius R around a heavy stationary mass. An external impulse is quickly applied to the rocket directly opposite xf 3jmk,)trs+ 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