08.19: Kepler’s Seconqif3t s -ihm,q+1uxf: d Law about “sweeping out equal areas in equal time” can be derived most directly from wh-hxmu,3+ ft fq 1:sqiiich conservation law?

  16.17:“All planets in the solar system follow elliptical orbits with trbf 68 .zb(c(fu 7ue4nqsjs c,ol2:ju he Sun located at one focus of the ellipse.” This statement is best summarized by which one of the following choib6c s.( fcunqef:7j,uz8ju2(brs 4ol ces?

  99.21: What happens to the force of gravitational attraction between two smal(bi(a ou4t/ fp)6ypo3 1zpsxzl objects if the opy /6(ozu 3(tsax1pizp bf4) mass of each object is doubled and the distance between their centers is doubled?

  95.09 Two spherical bodies attract each other withrdzw3x 7syu9 au.y/l5 a gravitational force of 4.0 N. What will be the force il szd u753w9axy.y/ urf the distance between them is doubled?

  14.27: Two spherical, non-rotating planets, X andY, have ts(wh; k8v(9pfki: k c:l mtx2e)idcs1he same uniform density. Planes; k (k1ifi9:vsmkht(c8wx:)cde lp 2 t 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,ot s/3mkgp)y and Y, have the same uniform density. Planet X has twice/ t3okg)mpy s, 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 v a2bpalvc5g x5 1zfvd6r:-alpo8 ,):p itdz2can 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 calculationl)g drpfz-c:225 zt 1 pva5v o8:pa,6xvbdlia?

  99.11: Assume that the Earth attracts John Glenn with a gravitational forcxc3on-k lt -yz8t v ( uxf7w*6s5yeiy:m r9k+he F at the surface of the Earth. When he made his famous second flight in orbit, the gravitational force on John Glenn whi9ix-ky5yuv6y-m 3rw en t8 l:+ t 7shfkzc*(xole he was in orbit was closest to which of the following?

  14.30: Considering only the Moon-Earth system (ignore vgczh;/h 7 8fgk-1hv3 bq2p/wqtd v2bany influence of the Sun), which one of the following best expresses37d gg8 ;hkqq2vz1//bh wh v2cb f-tpv the magnitude of the Moon’s acceleration about the Earth?

  02.19: As a rocket blau0 dtjg,n;,sgcy lee5gzj eo1+ lu/7.sts away from the earth with a cargo for the international space station, which of the following graphs would best represent the gravitational fo uzlgdous,nge+; 1, y e.jl5t0/ 7gecjrce on the cargo versus distance from the surface of the Earth?

  99.33: One object at the surface of the Moon experiex5r *3 vpps:*auz kp9pnces the same gravitational force as a second object at the surface of the Earth. Which of the follo*a53 9:xppu*szprkvpwing would be a reasonable conclusion?

  00.24 Consider an object that has a mass, gxm, l, )zjox1 g,+ hvwe15vasm, and a weight, W, at the surface of the moon. If we assume the moon has a nearly uniform density, which of hg1l sg,oe x+vz,5w vja1x,)mthe 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 seven times the mass of Earth and twice t4fd 6ue qb s1 h6bkqd5g95v0a/uoapf6he radius of Earth. The magnitude of the gravitational acceleratioupsaug 54f v60/ob19 d6kba6qf qe5dh n 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-fiyg wlr33 ebi-qopddr0+qf8 p2e ;30 edfth the Earth’s mass. The dyw2de-38 l +bip0 dfre;e3 goqqrp30 gravitational acceleration at the surface of the planet is most nearly

  08.38: Akg 1200 satellite orbits Planet X inkq63fv0. hq3 )3 cdw+ nhezq gs3u5als a circular 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 satellileq3 s.gv563sfnzqh33hku)wc0 da + qte by Planet X?

  94.34: A hypothetical planet/o+uqjg fsk*ze*o0h : orbits a star with mass one-half the mass of our sun. The planet’s orbital radius is the same as the Earth’s.f*/s+o 0qj*ue z:gkh o Approximately 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 circul ,uu41 st1t0vfs32p d v5ttdttar 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 period1vt d53tpu su 04t2tts1t ,vfd of satellite 2?

  15.22 Satellite 1 makes a circularl16 yx dpey 3(:hk:rsb p zb+,,u(klffk0/hwv 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 scaon2/8z-xqap v( ke mnta;s4l ;le registers. If the Earth were to stop rotati n4a;txpl( n 8z2;qa/kovme-s ng, but not change shape,

  10.42: A comet moves in an elliptical orbit around the:yj0f *rv 2kax 6mps,u sun. As the comet moves from aphelion (the point on the u,pv2:s fm0jxk yr6a* orbit farthest 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 follow circular orbits ab4vhkhx +iaj (wa,r8o :out 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 rewaj o +8k4(,av: hxihrpresents the total mass of the binary star system?

  06.50: A rocket is in a circular orbit with 3 ss dnyv3qv12,1giesd(e fz1speed 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 the semi-m, vdy12z qds3 fgeeis(vs 11n3ajor axis a of this new elliptical orbit is