08.19: Kepler’s Second Law about “sweeping out equal areas in equal time” canwnntr5 (oa/ vgk/90b o be derived most directly from which conservatrg( no av0/b/wt9 5nkoion law?

  16.17:“All planets in the solar systexsmjpc z -o:.t1qat 4zh,,/wjm follow elliptical orbits with the Sun located at one focus of the ellipse.” This statement is best summarized by which one zs jaht.1 ,,cp/z-:q4wmt xjo of the following choices?

  99.21: What happens to the force of gravitational attraction between two (kpak 4kvuvjq tug:s4(1*i a*small objects if the mass of each object is kak jqa *usgk4it4 v(v:p1u *(doubled and the distance between their centers is doubled?

  95.09 Two spherical bodies attract each other with a gravitathxm )-y1 wed(saij1c* ional force of 4.0 N. What will be the force if the distance between them isj se- *aydwxi()cm h11 doubled?

  14.27: Two spherical, non-rotating planets, X andY, have the same unifo f xfwsoy;qs pyn2/824zct;g 4rm density. Planet X;z 8g nscfwypx;sot 4 4yq22/f 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, no,vfrdulm60ds(gv 5-jsa9 smr mc3, f3 n-rotating planets, X and Y, have the same uniform density. Planet X has twice sjcf05u r(rl 3,,6 mma-v9svg fddsm3the 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 gv, tgll+g4gg9ls+ +o planet can 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 of the following woultlgo9gg+gls + 4gv +,ld NOT be required in this calculation?

  99.11: Assume that the Earth attracts Jo6waiigu(r,o63 *wj op hn Glenn with a gravitational force F at the surface of the Earth. When he made his famous second flight in orbit, the gravitaaou o(3*r pg,iw 66ijwtional force on John Glenn while he was in orbit was closest to which of the following?

  14.30: Considering only the Moon-E, s, /eyi+-ffcbfw 1szarth system (ignore any influence of the Sun), which i1,, wzcy+ b-sfffe /sone of the 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 cargo for the internati :q;p+runf smze9 svn5:.lkz8onal space station, which of the following graphs would best represent the gravitational force on the cargo versus distance from the surface ofs:e.s uk+p; fnq9 r5 nlvmz8:z the Earth?

  99.33: One object at the surface of the Moon experiences th enn: /,s*,ma)aiywuze same gravitational force as a second object at the surface of the Earth. Which of the following would be an)n, i aysaw/,* u:mze reasonable conclusion?

  00.24 Consider an object that has a moyfv-y:5( o)ajc 6vk fass, m, and a weight, W, at the surface of the moon. If we assume the moon has a nearly uniform density, which of) o-foyvkav6 (f5yc:j 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 hn4) ocgv,yq+ planet has seven times the mass of Earth and twice the radius of Earth. The magnitude of the gravitational acceleration at the surface of this planet is most v4,oy)+c hnq gnearly:

  98.24: A planet has a radius one-half thaags* r) qe91zlt of Earth and a mass one-fifth the Earth’s mass. The gravitaq1rg )s9z a*eltional acceleration at the surface of the planet is most nearly

  08.38: Akg 1200 satellite orbits Planet X in a circular orbit with a constant u*r 24lrbavjcfo2m 3o)qn .f9 speed of 5,000m/s. The radius of orbit is 7,500,000 m. What is the ma ujc.onvf)fbq394 al 2*or2rmgnitude of the gravitational force exerted on the satellite by Planet X?

  94.34: A hypothetical planet orbits a star with mass one-half ;f:y 2yn9(6 cvqcssjwthe mass of our sunsvqcjwn :c2fy ;y69(s. The 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*8 : efsitzzc 4r*hxja v(5up1, 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 the period of r4vfjxtu1a 8:esz hzic*5(*psatellite 2?

  15.22 Satellite 1 makes a circular orbit around the +1p mk j :, 1wi*pxe)q0uscvloEarth 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 c yb9s gf)1k v/6e5os07xp-0 yrgpd skregisters. If the Earth were to stop rotatcvg xp)yebr 70s9/sod5fk6p g-1s0k ying, but not change shape,

  10.42: A comet moves in an elliptical orbit around the sun. As rtv/,ny0tv6w /tcp: z the comet moves from aphelion (the point on the orbit farthest from the sun) to perihelion (the point on the orbit closest to the sun), whizw:/yv/0ptt rvtnc, 6 ch of the following results is true?

  17.48: In the binary star system shown, the two stars follow circular orbits a4f+ot)mior xs /1w o qo3n-iv1bout the system’s center of mass. The stars are separated by a distance D that is large compared to the woq1i4vt+3onm/xf)o1roi - sir 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 h86scwpm o1i8 with speed vand orbital radius R around a heavy st8 c psom1wih86ationary 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 axis a of this new elliptical orbit is