08.19: Kepler’s Second Law about “sweeping out eqe;4 j;z:jegllql 5g4 (0vbctv ual areas in equal time” can be derived most directly from which co zvbgl;l;t5je0e j 4qlvg: c(4nservation law?

  16.17:“All planets in the solar system fox. i; 5b5/thctfi26otm-e cd v 7uyot4llow elliptical orbits with the Sun located at one focus of the ellipse.” This statement is best umf5yoo t.ex/ bvci5dt t4i 6 t7hc-2;summarized by which one of the following choices?

  99.21: What happens to the force of gravitational attracti82;)l ya oqtz9 mufw-qon between two small objects if the mq lu 92waq-);8zo tyfmass of each object is doubled and the distance between their centers is doubled?

  95.09 Two spherical bodies attract eachn /h2nfq qrmlrk7,9*u other with a gravitational force of 4.0 N. What will be the force if the distance between theqhq r k,fm27l9/u* rnnm is doubled?

  14.27: Two spherical, non-rotating planets, X andY, have theh jn8by mf*ums/ 7,+dh same uniform density. Planet X has twice the radius of Planet Y. Let,dhh*m7/nb+ufs m 8yj $g_x$ 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 t2dmg68k95ffl*sw ka and Y, have the same uniform density. Planet X has twkg8sfw *tl2a km56f9d ice 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 calcu:za -hpur3ht kxq(a9x+hr5h +lated if it is orbited by a small satellite by setting the gravitational force on the satellite equal to the centripetal force on the satellite. Which of the following would NOT be required in t xpz+r+:5h(-ahxur3q9th kh ahis calculation?

  99.11: Assume that the Earth attracts John oij3dn-+-soyc nw,a5Glenn with a gravitational force F at the surface of the Earth. When he made his famous second flight in orbit, the grav,-nayij woo- c n3sd5+itational force on John Glenn while he was in orbit was closest to which of the following?

  14.30: Considering only the Moon-Earth systeyieic 5;-l-geu 6e pn 8py3iz7m (ignore any influence of the Sun), which one of t378ipiygyezce- u i5n l;p6e-he following best expresses the magnitude of the Moon’s acceleration about the Earth?

  02.19: As a rocket blasts away from the earth with a vh-9d lln6be 5 .2qslocargo for the international space station, which of the following graphs would best represent the gravitational forcenv9e-q. sblhl25l do6 on the cargo versus distance from the surface of the Earth?

  99.33: One object at the surface of the Moon experieno uo6jij .6x7gmi lz/e7sea:0b +yf:uces the same gravitational force as a second object at the surface of the Earth. Which of as jmg 76: 6uzy0iufe 7+loe:jib/ox. the following would be a reasonable conclusion?

  00.24 Consider an object that has a mass, m, and a weight, W, at the surf 7cq ku-nc/8b,z;pekx ace 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 centq7 c /uk8n-k bx,zepc;er and its surface?

  96.23: A hypothetical pl1 .;zxj0zr*szwlft vuo j.q3 v7w.y(fanet has seven times the mass of Earth and twice the radius of Earth. The magnitude of the gravitational acceleration at the surface of twf0.t. zz jswouy.3lvx1jrq;(7 z v*fhis planet is most nearly:

  98.24: A planet has a radius one-half that of Earth and l6hrgc 8 uc2:ia mass one-fifth the Earth’s mass. The gravitational acceleration at the surfaceh2r8lu gci6c: of the planet is most nearly

  08.38: Akg 1200 satellite orbits Planet X in a c6.arzlyi )m3 nircular orbit with a constant speed of 5,000m/s. The radius of orbit is 7,)myz3la6 rn.i 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 ofp( vshol03uw. our sun. Th.u3h p(o0wsvl e 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 circulw,8eye )3z7b- z v2jxdr-5wu ntpdnt:ar orbit at the same altitude above Earth’s surface. The mass of satellite 2 is twice the mass of satellite 1. If tz:xb yu- w,wj- vtn )p7tzddnr8235eehe period of satellite 1 is T, what is the period of satellite 2?

  15.22 Satellite 1 makes a circular orbit around t 5u5/w 7i 8rrhzjvquy u6do6g.he 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 thetpww s+89aozmau4f* 3 force a scale registers. If the Earth were to stop rotating, but not chaauto94z8fw*wm 3a+s p nge shape,

  10.42: A comet moves in an elliptical orbiue*udrx ;fk;r)hbrxa/ 7g:( ut 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 clos x(;u*a/ drergukbr) : xfhu;7est to the sun), which of the following results is true?

  17.48: In the binary star system shown, the two starl8e*pxibp r5/ s follow circular orbits about the system’s center of mass. The sx8ie lpp */5rbtars 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 or ;pg fr4/fz,erbit 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, t g/z;,prfre f4he size of the semi-major axis a of this new elliptical orbit is