08.19: Kepler’s Second Law about “sweeping out equal areas in eqjj:z3*kt0r.kp oz:az.r,vm p ual time” can be derived most directly fro:jz z pz3v: *tkpo.,.k0rrmaj m which conservation law?

  16.17:“All planets in the solar system fz(+e ,txdh xvt3122ev1sy ipz ollow elliptical orbits with the Sun located at o di3,1zt1+szetxv( 22epxvhyne focus of the ellipse.” This statement is best summarized by which one of the following choices?

  99.21: What happens to the force of gravitationiztjk c(lk 5m7ok*- n)al attraction between two small objects if the mass of each object is doubled and the distance between their centers is doubledn t( l7 micj*)kzo5-kk?

  95.09 Two spherical bodies attrazr u5lp4,jnl6 ct each other with a gravitational force of 4.0 N. What will be the force if the distance between them is doubl zlunr4 j6,pl5ed?

  14.27: Two spherical, non-rotativ-xm : 6.i3ff1gc jjn 37vdnbrio1+s - tbc;afng planets, X andY, have the same uniform density. Planet X has twice the radius ;33 bbs716jr1df c --tfmvogia. vn+j: xn cfiof 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 the same uniform densn*u .. n, g1.d9ukiksjjcwc .jity. Planet X hasj u9juw1k .cd..kn.nis j*,g c 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 planet can be calculated if it is 8 j 4nkh*c7zr ht*itnz( l/xr9orbited by a small satellite by settinr489hxi*h nr*z7 jztc/k nt(lg the gravitational force 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 thexwlq ivj08o-- Earth attracts John Glenn with a gravitational force F at the 0w joq8l-i-vx surface of the Earth. When he made his 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 tu0uc; we:j2lt g;rtf, 3f;u fux4vq nl1a ,ol-he Moon-Earth system (ignore any influence of the Sun), which one of the following best expresses the magnitude of the Moon’s acceleration about:efl;;ju ,f uv; c ,uo-4w0gq 1a2x3rln tulft the Earth?

  02.19: As a rocket blasts away from the earth with a cargo for m/2 sb b,x ,o(g+hgctodjc 7z pi,x3n1the international space station, which of the following graphs would best represent the gravitational force on the cargo versus distance fro+s,ni x p21(b/c g7ghtc ob,mo3,zjdxm the surface of the Earth?

  99.33: One object at the surface of t7* pfxqt7od7s04cuu d8;tggdgr( ey . he Moon experiences the same gravitational force as a second object at the surface of the Earth. Which of the fo g4 x77 stcp*0gfqu8yu;edgd ro( .t7dllowing would be a reasonable conclusion?

  00.24 Consider an object that has a mass, m, and a weight, W,sk.ycsz7 5q75 wtdz0d at the surface of the moon. If we assume the moon has a nearly uniform density, which of the followin5 dq zkd77zws0.y5 cstg 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 sevenecpoi) :f je23t: od/a times the mass of Earth and twice the radius of Earth. The magnitude of the2ea3i:tpd )/ ec:oj of gravitational acceleration 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 1hekvk4 wqmn*5kbx n*nj; 1/h:qn f6lp* kt 6sthe Earth’s mass. The gravitationa/psqjh1k **v *xkl qbhn6e:n k1k w6nf4n;5tml acceleration at the surface of the planet is most nearly

  08.38: Akg 1200 satellite orbits Planet X in a circular orbit with a bygg*8ptmm/7t s+ *t qconstant speed of 5,000m/s. The radius of orbit is 7,500,000 m. What is the magnitude of the gravitational force exerted g *ps+tbt8m gy*mtq 7/on the satellite by Planet X?

  94.34: A hypothetical planet orbinz,o,zjzj( q9ovsnorke5vnu*. 1h)l k5-e: hts a star with mass one-half the mass of our sun. The plan 5 juoq:j9.k-hevo,z 1z, r*nv5kzoh)sne(lnet’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 sately3j3,2 - xtpdek1xa ;c unth,llites, 1 and 2, are put into circular orbit at the same altitude ;a-u kp1 cyenx xtjl,3h 3,2dtabove 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 satellite 2?

  15.22 Satellite 1 make nz(o6pnt9r(*t3 i qtkl2do,g s 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 follow*kmxb0zu sl)uhl(5 -ring problem, the word “weight” refers to the force a scale registers. If the Earth were to stop rota)zh0u s5(- l xrbm*lkuting, but not change shape,

  10.42: A comet moves in an elliptical orbit around the sun. As l2vswou;d y 5fo/ *zf6the comet moves from aphelion (the point on the orbit farthest from the sun) to perihelion (the point on thdslz fw2f6o o*y ;/vu5e orbit closest to the sun), which of the following results is true?

  17.48: In the binarytmlc1;x6pp c7ulk/lb-y fc4/ star system shown, the two stars follow circular orbits about the system;l/yc16 c kf7b lcut -xlpm/p4’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 represents the total mass of the binary star system?

  06.50: A rocket is in a circular orbit with speed vand orbital radius R around sgwl nq30k/2f a heavy stationary mass. An external impulse is quickly f3s2q/ ng0wklapplied 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