08.19: Kepler’s Second Law about “sweeping out equal areas ig hl5 /)gakk+t kiak1 gr/4j;nck+j(mx c5hg4n equal time” can be derived most directly from whicgkl irta+g/+ 5n14m a );j4 /(hk5kxjhgcckkg h conservation law?

  16.17:“All planets in t*x .jkagsxr + 7b7gnc2he solar system follow elliptical orbits with the Sun located at one focus of the ellipsegxscb gna72k jr .x+7*.” This statement is best summarized by which one of the following choices?

  99.21: What happens to tb rtwk; 3z1 v(rlzh0+ehe force of gravitational attraction between two small obj0rvz(w t3r beh+lzk1 ;ects if the mass of each object is doubled and the distance between their centers is doubled?

  95.09 Two spherical bodies attract each other tp.kyc;b7vsvb 5ikfpsf2*y60c+-miwith a gravitational force of 4.0 N. What will be the force if the ytmfv76c20; -.yksi b +ps5k pcbvi*fdistance between them is doubled?

  14.27: Two spherical, non-rotating planets, X andY, have the same uniform dewzqh8e3l d5i, i ):tbunsity. Planet X has twice the radius of Pla3)t 5zlwi8d:b,i uehqnet 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-rotating planets, X and Y, have the same unifo16un plh t8o: byh5gv.rm density.1htyn :blh5.8v u g6op Planet X has 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 caf*d (q1wxtqbzfh 2g :7n be calculated 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 (ztwfq7bq*gd 1h: x2fof the following would NOT be required in this calculation?

  99.11: Assume that the Earth attra1)t7p qhfz-8ri esit ;cts John Glenn 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 in o )h pq8zerttif;-i7 1srbit was closest to which of the following?

  14.30: Considering only the Moon-Earth system (ignore any influence of the Sun)vp*i-buap ch-o8+ff +s)+ wzf, which one of the fo uc) hff aw -p*+i-o+s8fb+pvzllowing best expresses the magnitude of the Moon’s acceleration about the Earth?

  02.19: As a rocket blasts away from the earth with a cartyia hy4 gt 1ph)3mm, g2.pi1mgo for the international space station, which of the following graphs would best represgpmi 2 34m)pthhy g.iyatm1,1ent the gravitational force on the cargo versus distance from the surface of the Earth?

  99.33: One object at the surface of the Moon experiences *88u wyjq0 *zhvl ry3cthe same gravitational force as a second object at the surfacw yz 8*y8hlqu c3r*0jve of the Earth. Which of the following would be a reasonable conclusion?

  00.24 Consider an object that has a mass, m, and a weight, W, at the surface ofz(,eydfmj*4 u4dt d7i 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 weig,4yd7 *eu4dzmd(itf jht at a distance halfway between Moon’s center and its surface?

  96.23: A hypothetical planet has seven times the mass of Earcbhogtt 2ijq973 m:6 nth and twice the radius of Earth. The magnitude of the gravitational acceleration at the surface of this plabhmt: 3qj o29c6t nig7net is most nearly:

  98.24: A planet has a radius one-pywsa:a:i( bqhfk6 /+half that of Earth and a mass one-fifth the Earth’s mass. The gravitatiobhf: : /(pq yaaik6w+snal acceleration at the surface of the planet is most nearly

  08.38: Akg 1200 satellite orbits Planet X in a circular orbit with3l-k8jm* qaoq 6)ztr y a constant speed of 5,000m/s. The radius of orbitr)qja k*yo- l6m38 zqt 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 h(n h 9(+/r)k wp3veszoea/shmass of our sun. The pla(p9h vs3rzh(+/ewes) knhoa /net’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 satellite l0n bv2n/iyfw n+w65nq0 b6rcs, 1 and 2, are put into circular 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 the0 wbvln+ic50n2 qy6fb wn6r n/ period of satellite 2?

  15.22 Satellite 1 makes a circular orbit ar,ffxg mti6y26fo x:2 uound 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 wordu.j*4v piu0za “weight” refers to the force a scale registers. If the Epv 0a.j 4*uiuzarth were to stop rotating, but not change shape,

  10.42: A comet moves in an elliptical orbit around the sun. As ts*1zxj 6a/c1xk,a td a6t sil:he comet moves from aphelion (the point on the orbit farthest ,6ksjla1iaz* x/ax6d:s ct1t 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 fol.tanja3, z qc;f3h6l xlow circular orbits about 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 sta.3;l3z6n qfc axtja, hr system?

  06.50: A rocket is in a circular orbiv:k; w5j unmh-aqi;(nt 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 ter mn-kjw; iuh5v:;qa(nms of R, the size of the semi-major axis a of this new elliptical orbit is