08.19: Kepler’s Second Law about “sweeping ou1sigfl8jt *:+ keiqr 9t equal areas in equal time” can be derie*i :8t+k9 fqjgrs1ilved most directly from which conservation law?

  16.17:“All planets in the solar system follow elliptical eb2pm(3xjwwg/,a a.kc7r+ gsoy/ we9 orbits with the Sun located at one focus of the ellipaewe 73a m( w b/.g/,ky+wcgx 29srjopse.” This statement is best summarized by which one of the following choices?

  99.21: What happens to the force of gravitational attraction betweeni4sj9 of4vgl 3 two small objects if the mass of each ogio vl js3494fbject is doubled and the distance between their centers is doubled?

  95.09 Two spherical bodies attract each other with a gravita:mx)x/ t4 yt s )ut hrx44fw41(7bp;qixpwicptional force of 4.0 N. What will be t)ycp:ix4;7m4w4f upxs txh)px w(tt/ bqir1 4he force if the distance between them is doubled?

  14.27: Two spherical, non-rotating planetp ok )z+hx :cz21pd81a5wwxisol+: r os, X andY, have the same uniform density. Planet X has twice the radius of Planet Y. Let )pz1or5 k2dcww 8s xo lxh:1izoap+:+$g_x$ 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, nobinjt*veyf8 ; chykm7:/1 r,mn-rotating planets, X and Y, have the same uniform density. Plany8r1 n /m,im7vj:*y; ckhbtef et 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 calcubxgg3 ju0;r)qlated if it is orbited by a small satellite by setting u0 )3j;xg bgqrthe gravitational force on the satellite 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 82j dl,p g ge*5b4d6.mnx pw0e5axoiu 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 cl 6x.,u80ldge5wpid *e axjmpn25g4ob osest to which of the following?

  14.30: Considering oi0p/maftis( +rwp(jn4n4 v.(bo7 qhmnly the Moon-Earth system (ignore any influence of the Sun), which one of the followiq+n potjwm vihm ba(s( 404(7r/f ipn.ng best expresses the magnitude of the Moon’s acceleration about the Earth?

  02.19: As a rocket blasts away from qk m z p.pwkbc3k+6 .ck7vp7i3the earth with a cargo for the international space 7kc3pv3bp7 .qwkk6m kc p.+zi station, which 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 the surface of t x/s:)-gzc 0 bg2g9s hapibub5ad3o 5ehe Moon experiences the same gravitational force as a second obja: gegsb5x s/ z5od) 0gcu3b2baih9 p-ect at the surface of the Earth. Which of the following would be a reasonable conclusion?

  00.24 Consider an object that has a mass, m, and a 02uny hqg-sa .grr6*xweight, 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 object’s mass and weight at a distance halfway between Moon’s center and its surfa62sn. 0a gu*r-hgxryqce?

  96.23: A hypothetical planet has seven times the mass of Earth aa1rvdvral / q*+(- .0fe viybznd twice the radius of Earth. The magnitude of the gravit. -lqf0(z ye1dvir*+bv /varaational acceleration at the surface of this planet is most nearly:

  98.24: A planet has a radius one-half that of Earth and a mass one-fifth the 5hvy2lrb*m/ v(ehxl.i*h j *,2vdmjvEarth’s mass. il/l*h.j*jvd2*hm( mb vhe 5 vyvr,2xThe gravitational acceleration at the surface of the planet is most nearly

  08.38: Akg 1200 satellite orbits Planet X in a circular orbit with a constant 1j zxt3rl3 h+mspeed of 5,000m/s. The radius of orbit is 7,500,000 m. What is rxm13lj3zth +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 fg3jkzhy54g5 the mass of our sun. The planet’s orbital radius is the same as the Earth’s. Approximately how many Earth yearskgyj5f4zgh 5 3 does it take for the planet to complete one orbit?

  97.12: Two artificial satellites, 1 and 2, are put into circular orbit at the x4sk7 jq;pn:s7m nep )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 period n snjp:7q;x7)k m4pesof satellite 2?

  15.22 Satellite 1 makxguu:4tu ijjv+*jb 17es a 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 word “weight” refers to the f1jik+irgvcj v 6 j;0j-orce a scale registers. If the Earth were to stop rotating, bj+ic ; jrv-ijk1v6j0g ut not change shape,

  10.42: A comet moves in an elliptical orbit around the sun. As the comet movem28n 8hjjj1xm s from aphelion (the point on the orbit farthest from the sun) to pemxjhj88 mj2n 1rihelion (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 follow ciddf7x +2wux/-.*ylgto:nlj2 wj 8 xxwrcular orbits about the system’s center of mass. The stars are separated by a distance D that is large compared to the7j: l-xjxxl22/.8 u w+f *gtnw xoyddwir 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 oxwdh s/t*f7(y; fvq q.rbit 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 elliptiq;hwtfy q7/(xfv * ds.cal orbit is