08.19: Kepler’s Second Law about “sweeping out equal areas in s6/ku , ijo6/rkgmpy8equal time” can be derived mo u /mjoi/yprs6k,8k6g st directly from which conservation law?

  16.17:“All planets in the solar system fol, rp fkkx3n5 c:fp*9dgt* fef/low elliptical orbits with the Sun located ap e*xk/*3f 5f:kgfc9f,tnd rpt 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 attraction between two small ca4 ny/+unobkyd;j+u3m i5 *gdn6.m* hn+nooobjects if the mass of eacyo + i*nu dcy6amo+hn.gb n+onju*n /5 m4dk;3h object is doubled and the distance between their centers is doubled?

  95.09 Two spherical bodies attract each other with a gravi 5*hzpkcuhx)ty j9 v/q:0uo.wtational force of 4.0 N. What will be the force if the distance between them is doubled?0/ypk)o*j xw9. hc huuqzvt :5

  14.27: Two spherical, non-rotating planets, X andY, have the same unifntt o/ct(f )q6oms/xm b75 ;oaorm density.oantttcfm5qx(o7/ bo )/s ;6m Planet X 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-rotating planets, X and Y, have the6 ivljkle d)2 i x2:i)ln 5ev/1ngs7sn same uniform density. Planet X has twice the ra/ x1jl:sdv6el)) iesv2 nnln5 ki72igdius 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 ppfb./x mhaj,4 tb+p6be calculated if it is orbited by a small satellite by setting the gravitational fo/pj4xht bpf b,a.6+mp rce 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 je(oq lceur lzp2qn 3,3iq-s76 :z3gzEarth attracts John Glenn with a gravitational force F at the surface of the Earth. When he made his famous second fligl e:qqs3 u3zlrg jqz ,ocnip- z3672(eht 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 influence of todrco: )vlb6v 5d. 9czhe Sun), whv r)9d5ccvl z .bdo:o6ich one of the following best expresses the magnitude of the Moon’s acceleration about the Earth?

  02.19: As a rocket blafy59c bz2, if*rdh4hq1ix) nbsts away from the earth with a cargo for the international space station, which of the following graphs would best represent the gravitational force on td2b5nb*4 r qzih9yfh ,c)x i1fhe cargo versus distance from the surface of the Earth?

  99.33: One object at the surface of the Moon exp:b odod+)v9z n:e y,)cgb/ pqsux2ha8eriences the same gravitational force as a second object at the surface of the Earth. Which of the following would be a reaso 2bq)vszo8dp:c/+ 9xa, od):hybgeu nnable conclusion?

  00.24 Consider an object that has a mass, m,xu +h cjti:1ers9a:p * 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 closest to the object’s mass and weight at a distance halfway between Moon’s center9 jsui* x1 :ha+e:rcpt and its surface?

  96.23: A hypothetical planet has seven tiu cbw *) euyco-j;9w,uwq 5,hjmes the mass of Earth and twice the radius of Earth. The magnitude of the gravitational acceleration at the surface of wjbco,jw -qu*,e)uyc h5;9 uw this planet is most nearly:

  98.24: A planet has a radius one-half that of Earth 3 ,pyvtb 3e;i4pxc+p93w ezxzand a mass one-fifth the Earth’s mass. The gravitaz p3 ;xce+t3wb,43 ixz9yev pptional acceleration at the surface of the planet is most nearly

  08.38: Akg 1200 satellite orbits Planet X in a circular orbit wia4cqr :reg h6 g9gt0*bth a constant speed of 5,000m/s. The radius of orbit is 7,500,000 m. What is the ma6 9c g0r*rge:tg4hqabgnitude of the gravitational force exerted on the satellite by Planet X?

  94.34: A hypothetical planet orbits a star with mass one d5y;+2 1lexq: whxiue-half the mass of our sun. The planet’sx;ex+hw2e5 dlq iu1:y 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, apw6atxt 4a-vls.5 /bwre put into circular orbit at the same altitude above Earth’s surface. The mass of satellite 2 is twice the mass of sate5wtx a/-vl.6 sbt4w pallite 1. If the period of satellite 1 is T, what is the period of satellite 2?

  15.22 Satellite 1 makes 9/l 63orqd+vdqk ahpzj3xh7oe12 m1w a 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 f, /wh 0nfnqp ,9r t7drf4vsyd*orce a scale regis r9f,*y pwqr,n4v s0dd7h /tnfters. If the Earth were to stop rotating, but not change shape,

  10.42: A comet movesdjj/6v3fp3av,ibcl o 1 i -e5st)c2ve in an elliptical orbit around the sun. As the comet moves from aphelion (the point on the orbit farthest from the sun) to p/1je cvj - f st2iic3ov5)e,dlapv63berihelion (the point on the orbit closest to the sun), which of the following results is true?

  17.48: In the binary star system showlr0o v) :3rnzsk1rbb9n, the two stars follow 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 gravitatbrn9bs3 )vzlkrr0 1o :ional 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 vtisyctjo6b *89.tu 7s xi-q+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 tcv x * tq8uo-6 .i9sbt7jyst+ierms of R, the size of the semi-major axis a of this new elliptical orbit is