08.19: Kepler’s Second L / u:d/gfj )cjvj:6usaaw about “sweeping out equal areas in equal time” can be derived most directly from which cons6uj:d :gavcujf/ /s) jervation law?

  16.17:“All planets in the solar system follow elliptical orbitsos1cmz/ l9 3,qssr.gg with the Sun located at onocsqg 1 sz3g/9 rml,.se focus of the ellipse.” This statement is best summarized by which one of the following choices?

  99.21: What happens to the force of gravitationabd a*e 7xz8qdyi2s7x, l attraction between two small objects if the mass of each object is doubled and the dist7dx *d2e 8iyq7sb,ax zance between their centers is doubled?

  95.09 Two spherical bo p,+c s .3qhc2ie)sfeqdies attract each other with a gravitational force of 4.0 N. What will be the forc, h)q qse.32sicefp+ce if the distance between them is doubled?

  14.27: Two spherical, non-rotating planets, X andY, havhxp3k,jzpiyj, f; 6 .ne the same uniform density. Planet X has twice the radius of Planet Y. Letzyhp3;. ,x 6,jjpiknf $g_x$ 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 threm6o vc9ez ;w4wwf+f r7.d0 pe same uniform density. Planet X has c7.496wo;+fdf r0zpvwre we mtwice 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 khh, qv9rghy0 :a 3hga 6az7zs)k 0e-gcalculated 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 3qh0 0 7szh vay9-g eagh,hz)ka:k6grbe required in this calculation?

  99.11: Assume that the Earth attracts John Glenn with anfb s3 9 xwary2wbi (dp7o3h5+ 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 closest to which of the followf3 op(wrn yd9 2bsx waib5+73hing?

  14.30: Considering only the Moon-k k2m b22fu+zwEarth system (ignore any influence of the Sun), which one of the following best expresses the magnitude of the Mo+bf m k22wuzk2on’s acceleration about the Earth?

  02.19: As a rocket blasts away from the earth with a cargo for the internationae*cgog3*slt- v1znx b( fn8v ;l space station, whi3gbt1 n*vv;xls- (zeo f*8cngch 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 at3-sp e6/.v8 madh wctc8eez0:j5uwbl the surface of the Moon experiences the same gravitational force as a second object at the s8a: / 0hvbmdcpec8wlwe5szu6 .3 t-e jurface of the Earth. Which of the following would be a reasonable conclusion?

  00.24 Consider an object that has a m8uoiynw.blv1 ) .9ch iass, m, and a weight, W, at the surface of the moon. If we assume the moon has a nearly uniih.iv9yoc 8bwn )1lu .form 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 9 bf -l5mbtn)n)zhp/fseven times the mass of Earth and twice the radius of Earth. The magnitude of the gravitational acceleration at the surface of thin/ htmb59)b-n ) pzflfs planet is most nearly:

  98.24: A planet has a radius o3hmzy* kqsei6rb+ 2 7rne-half that of Earth and a mass one-fifth the Earth’s mass. The gravitational accerb2seiq *z+k h6rym73 leration at the surface of the planet is most nearly

  08.38: Akg 1200 satellite orbits Planet X in a circular orbit with a const 2u3t27 hgebrbant speed of 5,000m/s. The radius of orbit is 7,500,000 m. What is the magnitude of the gravitatio2g3b h r2utbe7nal force exerted on the satellite by Planet X?

  94.34: A hypothetical planet orbits a star with mass one-half the mass of oui+a )nvdw6q3w i6dm9-bgxm .pr sun. The planet’s orbital radius is the same as the Earth’s. Approximately how man) +xg-b9p.6iwdmm3 qind wav6 y Earth years does it take for the planet to complete one orbit?

  97.12: Two artificial satellites, 1 and 2, are put into circular or:6 ej od/e2)hzs due(d a0jc7aq:hk :nbit at the same altitude above 7k02ao/e(:)c haq den:js jz :ud ed6hEarth’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 satellite 2?

  15.22 Satellite 1 makes eyrm ji7,ix(tv;8b i i *j66fla 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 force a scale rlu78rmh 2mzdism:( v +osi*z9 egisters. If the Earth were to stop rotating, but not change shape lim(9s ozviu8z rmds: *h7+m2,

  10.42: A comet moves in an elliptical orbit around the sun. As the comet moves 6qydl 9e:qd g(ja z6h2d: ur+gfrom aphelion (the point on the orbit farthest from the sun) to per:jz6hye+692 g:rugdq qdl d a(ihelion (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 njnjdb6w1qk.4 lq)gqvicx95ez* , )ptwo stars follow circular orbits aboutg e9n5zpqd )knc*qlx461q j ,v)jb wi. 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 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 circu hot6b(,ddbn )a r6:gwlar orbit 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 o6(:bn 6r )dog,ahd bwtf the semi-major axis a of this new elliptical orbit is