08.19: Kepler’s Secon 2o dh3ngbd)(ku;2 gpf7h;cio jrjv) -d Law about “sweeping out equal areas in equal time” can be derived most directly from which conse dh)ck;r 2u;fnhbi o) v(gdpj2g7o3j -rvation law?

  16.17:“All planets in the solar system followv4 528,b fwo4xnf oolidn3as3 elliptical orbits with the Sun located at one focus of the ellipse.” This statement is best summarized by which one of the following choicelifa 4b3x4dnvo83o nsf 52wo,s?

  99.21: What happens to the force of gravitational attraction between two small o51rio8rglv,i ,i gc :(ar+av9uvq f/xbjects if the mass of each object is doubled 9vilvarxfio aq1ig ,+ 5,u8/rc:g(rv and the distance between their centers is doubled?

  95.09 Two spherical bodies attract each other with a gravitational force of 4 oytdjd,zss :h58d18q j0a7qu.0 N. What will be the7hjq:s, 8uyasd1dzd j5t 08oq force if the distance between them is doubled?

  14.27: Two spherical, non-rotating pla+rn2* tqzjn+y4tz nf0 nets, X andY, have the same uniform densitfy zzrj++0q *nn4t 2tny. 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, no vj/5r)k0-p u vng)k6daku 4cxn-rotating planets, X and Y, have the same uniform density. Planet X has twice the radius of Planet-ukrva 6vk)ng0du) k/5xjc p4 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 planetm-m+qamut .;1m v yt n/ q)o9lgi:5pim can be calculated if it is orbited by a small satellite by setting the gravitational force on the satellite equa m.i)o :m5 +9 naqmupm;lytmiq1-gvt /l to the centripetal force on the satellite. Which of the following would NOT be required in this calculation?

  99.11: Assume that the Earth attracts John Glenn withkuxgn +j)9. pileh8 hz*jmr1 + a gravitational force F at the surface of the Earth. When he made h zl9ue++ gx*.hk 1i)jpr jnh8mis 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 bn ) orde-jl1y-58tjd .pg p,e(ignore any influence of the Sun), which one of the following best n,g )pl-.e1tjpej5d d8by-or 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 in;:.fkts .tr dtternational space station, which of the following graphs would best represent the gravitational force on the cargo versus distance from the sur.:k;. dtfts trface of the Earth?

  99.33: One object at the surface of the M4k1j88viv c48pyu ayuoon experiences the same gravitational fo8u 41yckpu4vvi 8 y8jarce 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, m, and a weight, W, at the surface ocf2r , g 3ub/9hnlg:it2 wr.mdf the moon. If we assume the moon3, nr l9g2u w:hg.ci/ftm2b dr 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 center and its surface?

  96.23: A hypothetical ;w f(b5:vicn,uw oze pa2-(z.u pcix3 planet has seven times the mass of Earth and twice the radius of Earth. The magnitude of the gravitational acceleration at2wwa; ve (io,pup-b :u3i.cczfn5z(x the surface of this planet is most nearly:

  98.24: A planet has a radiz .bd c22drok:6g/j .x*s9jq hw:hfvdus one-half that of Earth and a mass one-fifth the Earth’s mass. The gravitational acceleration at the surface of the planet is most near qjd/:9 wvhj zkcb:d26.h*rfxs g. d2oly

  08.38: Akg 1200 satellite orbits Planet X in a circular orbit with au4 ahg4r4j wyf0g*o n* constant speed of 5,000m/s. The radius of orbit is 7,500,000 m. What is the magnitude of the gravitational fo na4u*whfgor4*4g jy0rce exerted on the satellite by Planet X?

  94.34: A hypothetical plan1:n ,xml1d+e hhdcq-m atpg*;et orbits a star with mass one-half the mass of our sun. The planet’s orbital radius is the same as the Eart-dg1,+e:ntcl1ph qx amdh*m; h’s. 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 ci;a- /zyky/ pt2lvychy,h5u :a rcular orbit at the same altitude above Earth’s suly5htv:u/2,; z/ ay phkyc a-yrface. 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 satellite 2?

  15.22 Satellite 1 makes a circunxel2p18g 8*vii.qwc0 urt/r lar 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 p b j+b8g.:fv /uqlt;vmroblem, the word “weight” refers to the force a scale rg+v lf m:q;tv bu8.jb/egisters. If the Earth were to stop rotating, but not change shape,

  10.42: A comet moves in an elliptical orbit around the sun. As the comet my ;jc.n mkw+,,fclxs 8eg8jn 9oves fromfx,jk+le m9 yccnws.;j n,8g 8 aphelion (the point on the 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 a*ryhkz -7ky9 6y -a (l5pbgblqu-jp4circular 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 mutua-p- lkh y( b7ar9jga6 yk*u4z q-pby5ll 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 circult7xn7mu0t a+u 72ao dqhsq i,0ar orbit 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 slow0n2a0t i a+q7uh q 7,m7dxostued 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