08.19: Kepler’s Second Law about “sweepingn0uu1n f;o+ey out equal areas in equal time” can be derived most directly fru+e 1nfo0;un yom which conservation law?

  16.17:“All planets in the solar system follow elliptical orbitspojj5e mc x7hw .j* .ku8e3;dr with the Sun located at one focus of the ellipse.” Thrp.hjkdoe.;7c85wxm j 3 u*ejis statement is best summarized by which one of the following choices?

  99.21: What happens to the force of gravitational attraction between two smal9gtg6*)b6,m e yagc xnl objects if the mass of each object is doubled and the distance between their centerg 6xbtgcy6)ag * ,ne9ms is doubled?

  95.09 Two spherical bodies attract each other with xns0 hd5;23xwvf jhr8lq d+/fa gravitational force of 4.0 N. What will be the force if the distance between them is doubled? dfvsx08 x /w2qhj5 f3dn+rl;h

  14.27: Two spherical, non-rotatin*h: f (leax4zjg planets, X andY, have the same uniform density. Planet X h* al(xf 4:zhjeas 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, fh+6x:zqu/xxp3.8brd .kdd dnon-rotating planets, X and Y, have the same uniform density. Planet X has twice the radiusd6dx 8/z rk:.f+ 3dpq hb.dxxu 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 smaloyi-u(cu s2 )apqicmxc;zvhd0q/0; 4 l satellite by setting the gravitational force onc hvx(yuci/ d oas);q0m0; qp42iz uc- 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 Glenn with r6iy,zg,wyj 5a 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 cloj y,w5gi6,ryz sest to which of the following?

  14.30: Considering only the Moon-Earth system (ignore any influence ofrnn r* -c9taben+x/f8 the Sun), which one of the follocr8-bn etx9a /nfn +*rwing best expresses the magnitude of the Moon’s acceleration about the Earth?

  02.19: As a rocket blasts away hmzqughiiq86z/6 7ualg (/- sfrom 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 from the surface of the Earth/ 7ml zuzqgusgq6-h(86ia/ih?

  99.33: One object at the surface of ou9sqi8y23*bqi i8c fm k +fjkr(ts 4)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 conclq)3 f4 (bm c2 9sof8 jruis+iyqk*tk8iusion?

  00.24 Consider an object that has a mass, m, and a weight, W, at01 j6 wiro(k5yee hj/vyb(,l9v5w bvi the surface of the moon. If we assume the moon has a nearly uniform density, which of the following would be v(ei 6(ykv/e jj,lby91 b5wr05vwoih closest to the object’s mass and weight at a distance halfway between Moon’s center and its surface?

  96.23: A hypothetical planht3m1r rr+,a4golbb :et has seven times the mass of Earth and twice the radius of Earth. The magnitude of the gravh,trbl:rb4m1r+3g oa itational 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 ou3zgg/1ab.kfe30itv- (v zzpne-fifth the Earth’s mass. The gravitational acceleration at the surface of the planet is most fz 1.0/z3zpv(uevgkbg 3ati- nearly

  08.38: Akg 1200 satellit+qnjzu2a: v 1xuuctu8z *;k/pe orbits Planet X in a circular orbit with a constant speedztu*qp:k u2a+ / n1u;8zcx ujv 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 planm/n3/f cb(utba; uw 3ket orbits a star with mass one-half the mass of our sun. The planet’s orbital radius is the same as the Earth’s. Approximately how many Earth years does it 3/utc3f k ;uan( w/bbmtake for the planet to complete one orbit?

  97.12: Two artificial satellites, 1 and 2, are put into circular orpdvh*mt9d (h) bit at the same altitude above Earth’s surface. The mass of satellite 2 is twice the mass of satellite 1. If the period of sad (*h9pdv)ht mtellite 1 is T, what is the period of satellite 2?

  15.22 Satellite 1 makes a circular orbit around the Earth with a rmcs h83-8 d w/zlunvq/s0u1l uadius $r_1= R$. 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” ree3.der df6k. qfers to the force a scale registers. If the Earth were to stop rotating, b re. dqd.3k6efut not change shape,

  10.42: A comet moves in an elliptical orbit around the sun. As ti)e4ph+y w *-nwd-g1ir;s fk che 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 thw n peg);-hfi+r-4wik c s*1dye following results is true?

  17.48: In the binary star system shown, the two stars follow circular orbits wa- 6encw-dd iv9/6vmabout 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 md9wdi-66n cwv-me v/ autual 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 speed vand orbital radius R arotgki3zn b)2clqqvu:b- -dybf 77hv0/ und 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 qf3h/nvtcbl bi20dkqg: u) v 7y7bz-- R, the size of the semi-major axis a of this new elliptical orbit is