08.19: Kepler’s Second 9 v:x,gl+rhq *zk/e0y0l ikdhLaw about “sweeping out equal areas in equal time” can be dxq:0r kl0k9+/g,i lzvh*ydeh erived most directly from which conservation law?

  16.17:“All planets in the solar system follow elliptical orbits wi/ r1)73bwgahvsm mw v0w/ h7dwth the Sun locav /7w va0sw7g/hwmr 1d)mhbw3ted at one focus of the ellipse.” This statement is best summarized by which one of the following choices?

  99.21: What happens to the force of gravitational attrq, 2f*s / ooef4xu* /:szrjqozaction between two small objects if the mass of each object is doubled and s4s z/qj*,*2u oooq f:xf/zerthe distance between their centers is doubled?

  95.09 Two spherical bodies attract each other with tzr.l0b sz11.ki .hrca gravitational force of 4.0 N. What will be the force skl.zb r iz.1 r.0ht1cif the distance between them is doubled?

  14.27: Two spherical,()+c tyiz7to ej;bxtu fss .(; non-rotating planets, X andY, have the same uniform density. Planet X has twuytz s s)(i;;+(c.o j 7tetxbfice 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-rotating planetv.k a e(yzb:74lwjr i(s, X and Y, have the same uniform density. Plavy.:w ajriz(k4 (7b elnet 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 plab 1e /1*nw-pm.aqeifp( lugjg -b08odnet 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 would NOT be required in this calculati 0o lw(8-b-pifa qu*dmngpg /1.be1ejon?

  99.11: Assume that the Earth attracts John Glenn with a gravitational force F vz qf19k1) 6kir,3ie ardh5y tat the surface of the Earth. When he made hfr1,1 ev9aktizryidk )5h 3q6is famous second flight in orbit, the 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 influencs i zhe22fs)(zgs) y7ge of the Sun), which one of the following best expresses the ysg)2s fi(gzh)27zs emagnitude of the Moon’s acceleration about the Earth?

  02.19: As a rocket blasts away from the earth wit :brq0 te7n)w+forxdibi 4,xt2.ndv+h a cargo for the international space station, which of the following grqi 2b nxv0.dro i7t+b): +nwxfe, t4draphs would best represent 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 the same gravitationyihc-l( t:f pjnxl(bg:(o,3ual force cf (t:bn-:p(h liy (jxou3 lg,as a second object at the surface of the Earth. Which of the following would be a reasonable conclusion?

  00.24 Consider an object that has a mass,p ni hbed 270j3h/5ehg m, and a weight, W, at the surface of the moon. If we assume the moon has a nearly uniform density, which of the following would be 0ghee/25ip7h nd b 3jhclosest 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 time:xxi)x qf3s d1s the mass of Earth and twice the radius of Earth. The magnitude of the gravitational 3ixs):xx fqd 1acceleration at the surface of this planet is most nearly:

  98.24: A planet has a radius one-half that of Earth and a mass one-fifth the ,4klwfbmpc g bsibz)/ /r3l /.Earth’s mass. The gravitational accelewl)4bi k /fcml./z /gr,3bbspration at the surface of the planet is most nearly

  08.38: Akg 1200 satellite orbits Planet X in a cim9cv0uli f/3l/cb5 eak n/yk1p0 2 hpqrcular orbit with a constant speed of 5,000m/s. The radius of orbit is 7,500,000 m. What is the magnitude of the gravitational force exerted on the satel//lvcpni k 25/3fpykaueb0mhq0 1c 9llite by Planet X?

  94.34: A hypothetical planet orbits a star with mass one-half the mass of our sujzs nd-e lb nx/1oo,).,k5izbn. The planet’s orbital radius is the same as the Earth’s. Approximanz idzolj).n, /bs oe1b,5- xktely 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 cg.tya :s,;lv ,3hz lhrircular orbit at the same altitude above Earth’s surface. The mass of satellite 2 is twice theh,l:ylz ;ragvs3.,t h mass of satellite 1. If the period of satellite 1 is T, what is the period of satellite 2?

  15.22 Satellite 1 makes a circular orbit around the Earth with a r73j0fz.eyjbny r;gp8 adius $r_1= R$. 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 prob+3//odorl7r8oar e6dg atl (u lem, the word “weight” refers to the force a scale registers. If the Eluotodg +78r 3ar /(derol/a6arth were to stop rotating, but not change shape,

  10.42: A comet moves in an elliptical orbit around the sun. As the comet moves s,-jmx qp9li r/n--bf*avr) x from aphelion (the point on the orbit farthest from the sun) to perihelio -js,q/x-vr *p b-ra)il9xnmfn (the point on the orbit closest to the sun), which of the following results is true?

  17.48: In the binary star system shown, t(xi/r)aoq,,b .pnk*f eyu jh9s6 do*qhe two stars follow circular orbits about the system’s center of mass. The stars are separa p*j,ix)*u d,qhb6fays/n 9o orkq.e(ted 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 orbit wi 31sa+9+ nxjudc z zv0 uta+nx1ba,4bsth 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 of th +nz10+3dz, j4nxcx+vb a tsuas9ab1ue semi-major axis a of this new elliptical orbit is