08.19: Kepler’s Second Law abzhk5xaylxmfk2 fpu/(l:11 + d out “sweeping out equal areas in equal time” can be derived most dir x2alhp1d(:f5u/ kl ky xz1m+fectly from which conservation law?

  16.17:“All planets in the solar system follow elliptical orbits with the6dyys),(sb7 wvlh bl2 Sun located at one focus of the ellipse.” This statement is best summarized by which one of the following ch b l2yd,ybh6svw (7sl)oices?

  99.21: What happens to the force of gravitational attraction between two 9 qei(f09ykpm small objects if the mass of each object is doubl9k9( m iq0feyped and the distance between their centers is doubled?

  95.09 Two spherical bodies attract eacb)v,z cf(9ijkh other with a gravitational force of 4.0 N. What will be the force i,) z bik9(fjcvf the distance between them is doubled?

  14.27: Two spherical, non-rotating planets, X andY, haucby:wc0/ t, hve the same uniform density. Planet X has twice the radius of Planet Y. Lch/u,b0 c:wty et $g_x$ 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 sbn+/t7f ,5d1 q/d)cuvz myawi5 6 jfkxame uniform density. Planet X haw f6,m+i/yadn /t )cfb1jzkvdxqu755 s 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 4p*vvtnh h 0dks+38adis orbited by a small satellite by setting the gravitational force on the satellite equal to the centripetal force on the satellite. Which of the followi8p *vkdd +sahth043nvng would NOT be required in this calculation?

  99.11: Assume that the Earth attracts John Geu b, lmpr105ylenn 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 0p1b ,eym5rl uin orbit was closest to which of the following?

  14.30: Considering only the Moon-Earth system (ignore any influence of the Sunb(tem;k4fmu ic3ybvk 5xn0tt s z329 .), which one of the following best expresses thni fksexm9v 2u(y3 mt43c bbt.5z;k0te magnitude of the Moon’s acceleration about the Earth?

  02.19: As a rocket blasts away from the earth with a cargo for the internationm 4hiw2mzv-1- lzx0b xt)ok0hal space station, which of the following graphs would best represent the gravitational xbo 0wiz)k-m0x2vmlz4ht- 1h force on the cargo versus distance from the surface of the Earth?

  99.33: One object at the surface of the Moon experieft3 (iya:;8jm tz o7bs/ksr +:gcq*nogmzf/9nces the same gravitational force as a second object at the surface of the Earth. Which of ag8m k(f: qrotc+y3n/t; i9gzj oszm/sbf:7*the following would be a reasonable conclusion?

  00.24 Consider an object that has a mass, m,7ak14l+gbmdw and a weight, 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 halflmd4g7 1awb +kway between Moon’s center and its surface?

  96.23: A hypothetical planet has seven times the mass,nl1jq/r bo;rf 0c.oj of Earth and twice the radius of Earth. The magnitude of the gravitational acceleration at the surface of this planet is most/ln 1,;oc0brojr. q fj nearly:

  98.24: A planet has a radius one-half that of Earth and a mastx q/g2d,3e wyc8zy.uox *qec 7/p 5/xvy psp.s one-fifth the Earth’s mass. The gravitational acceleration at the surface of the planet is mosgexpwcx/yq3y8e7,v 5op cd.y qtu*p/zx/s.2t nearly

  08.38: Akg 1200 satellite orbits Planet X in a circular orbit with a constanxguqz: hoh0rr46au6yqr :/zpk z:,d,t spee4od:h z0 gqk6puzyxqhur: r,6rz/a:,d 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 planet orbits a star with mass one-half the mass of our sbayhy/k;9+r27v z c liun. The planeha 9r ylc2;ziv y7/+bkt’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 putu46 3nujx :xqv into circular orbit at the same altitude above Earth’s surface. The mass of satellite 2 is twiv43:jq 6uxunx ce 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 circutj889 z8i kd ez4oli8 g8myz9slar 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” rqw,um.x/ .b qhefers to the force a scale registers. If the Earth were to stop rotating, but not changuqbwx .q/ hm,.e shape,

  10.42: A comet moves in an elliptical orbit arounqt :n (dzbr)(sd the sun. As the comet moves from aphelion (the point on the orbit farthest from the sun) (bs:(zdqntr ) 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, vdyc;;bxt tbo: (9d9v((hi m/9 eapdrthe two stars follow circular orbits about the system’s center of mass. The stars arevc(xry ttde hoabp/9 d (;(v9bd: m9i; 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 speed vand+hj *hh,)ah ki 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 axi,k*+ih )ahh jhs a of this new elliptical orbit is