08.19: Kepler’s Second Law about “sweeping out equal ah fz /xlb+pc +p60tm9-xxezt 4reas in equal time” can be derived most directly from which conservation lawxp9-h4t+b60xmx/ c l+ feptz z?

  16.17:“All planets in the solar systtdc ;k:3* dukg io4yq+em follow elliptical orbits with the Sun located at one focus of the ellipse.” This statement is best summarized by which one of the following co* :qguiy +kckd t;3d4hoices?

  99.21: What happens to the force of gravitational attrxbi8,km-*webcr 0/obu g 3u/m action between two small objects if the mass of each object is doubled and the distance between their centers is doublmm*cw/be 0r8ug,-/bbk iu 3 xoed?

  95.09 Two spherical bodies attract each other with a gravitational force ()xt/n4qm lnc).qqf g of 4.0 N. What will be the fq fqq))nm 4lg .c(/txnorce if the distance between them is doubled?

  14.27: Two spherical, non-rotating planets, X andY, have the same un+oap,j;7*wo:np s*mtg9 jwcdiform density. Planet Xjs9 n;:d *oa,p*+7 tg wmpcowj 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-n, zl gc9m3mj3rotating planets, X and Y, have the same uniform density. Planet X has twice the radius of Planet Y. Let lng3j,3m 9czm $v_x$ 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 i /rkm rdfn:0u5f it is orbited by a small satellite by setting the rnu0mkf: d5r/ 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 Glenn with a g 9nluw+ az *:cyuqeg/b:(z ym5ravitational force F at the surface of the Earth. When he made his famous second flight in orbit, tb yu:w5ulg */zz +ynaqcme9(:he gravitational force on John Glenn while he was in orbit was closest to which of the following?

  14.30: Considering only the Moon-Earth system (ignore any inf954lbgjohbey;ko zd /8q u0i fgr65h 6luence of the Sun), which one of the followir5doehugy5 4o86bjbqhi6/z lg ;f 0k9ng best expresses the magnitude of the Moon’s acceleration about the Earth?

  02.19: As a rocket blasts away f 5abaj.-s c li+np7fu5rom 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 Earthc-pf5bn s lja.5au7i+?

  99.33: One object at the surface of the Moon e c/ rdd8l-s:zuxperiences the same gravitational force as a second object at the surface of the Earth. Which of the following would be a rd:-zd 8 culs/reasonable conclusion?

  00.24 Consider an object that has a mass, m, and a weight, W, atigs8mpoz 7jj,nz419 e* z1i xt the surface of the moon. If we assume*z ,mzi nz9ji 81 4pjos7tg1xe 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 surface?

  96.23: A hypothetical planet has seven times the mass of Earth and twice the ra5roz;8hd(w bha3f up 8dius of Earth. The magnitude of the gravitational acceoz(aw h83p85;rbdufh leration at the surface of this planet is most nearly:

  98.24: A planet has a radi)ev/+ou 6qo kvus one-half that of Earth and a mass one-fifth the Earth’s mass. The grvoovuq /k+6)eavitational acceleration at the surface of the planet is most nearly

  08.38: Akg 1200 satellite orbits Planet X in a circulaj(7k kpwhgvi mzok 4e3/h/+:qm p l+z-r orbit with a constant speed of 5,000m/s. The radius of orbit is 7,500,000 m. What is th l4jkkgio/-/ +m(hve m:+p3 wzhqkp7 ze magnitude of the gravitational force exerted on the satellite by Planet X?

  94.34: A hypothetical planet orbits vfn:i/ znm+dprj1odd0( l: +ra star with mass one-half the mass of our sun. The pla:j/n d:lo pnzv +(0i 1dfrmd+rnet’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 iid+ v+,s5x+bb j7h qe7e 2djscircular orbit at the 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 of satellbi7+bjq e ,+h did+7xj25vsesite 2?

  15.22 Satellite 1 makes a circular orbit around the Earth with a radi - wcv68 nfezl/d0rwy)us $r_1= R$. 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 i,j6 76lakewppw 4oykvwo*85o x4yj( the force a scale registers. If the Earth were to stop rotatingejk4o(kl8 w4pw,* 6y 6i voow5 py7jxa, but not change shape,

  10.42: A comet moves in an elliptical orbit around the sun. As the comet moves 9rm u25kydvo 0/ujr9kfrom aphelion (the point on the orbitdo5/k9jyu rk v290mru farthest from the sun) 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, the two stars follow circular orbits a/3cfomla57+tz :t gtn nct5k8bout the system’s center of mass. The stars are separated by a distanceo:nmk8fatz3 nc/gt ltt55 +7c 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 orbital raditm04e6y wc5ymb ye9-m us R around a heavy stationary mass. An external impulse is quickly applied 94ye5yy -m06em tbm cwto 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 elliptical orbit is