08.19: Kepler’s Second Law about “sweeping out equal area2if 6kvcdrl ,9s in equal time” can be derived most directly from whc v f,6l9r2kdiich conservation law?

  16.17:“All planets in the solar system follow elliptical orbits wi+ /go;5ekavzu. uz l0qth the Sun located at one focus of the ellipse.” This statement is best summarized by which one ofa/o.zzevl 0 q+ug ;5uk the following choices?

  99.21: What happens to the force of g gik+q9z drn00ravitational attraction between two small objects if the mass of each object is doubled and the distance rd0g+k 9zqi0n between their centers is doubled?

  95.09 Two spherical bodies attract each other with a gravitati x ntyijb:, (lo,s z,kn6;fk27shy.rlonal force of 4.0 N. What will be the force if the distance y. yh6sl,ifj xbo 7(kt:r nz,,2n;slkbetween them is doubled?

  14.27: Two spherical .i((.imz8ec b *kuyo,ip ssej4*(nyx, non-rotating planets, X andY, have the same uniform density. Planet X has twice*zik sy*(yeiiu m.o. p(x8bc4 (,njes 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 plfxd8ar9e w8+ 5 zhogz*anets, X and Y, have the same uniform density. Planet X has twice the radius of Planet Yz 88 r5 wgo*xaehz9+fd. 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 orbited bnfe1w .+ :n)sh(jle wsy a small satellite by setting the gravitational force on the satellite equal to t+lns: 1e( w.n wsfe)jhhe centripetal force on the satellite. Which of the following would NOT be required in this calculation?

  99.11: Assume that the Earth attracts Jrn mgt*p -5y2fohn Glenn with a gravitational force F at the surface of the Earth. When he made his famous second flight in orbit, the gravitational force on Johngr2tf5 np -y*m Glenn while he was in orbit was closest to which of the following?

  14.30: Considering only the Moon-Earth system (igt 8ln;fro7(mr m-l,cf nore any influence of the Sun), which one of the following best expressesr7 nmc ol(rt,f;m8fl- 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 internff /fs;(ak gk(ational space station, which of the following graphs would bestf ;faf(/ kgks( represent the gravitational force on the cargo versus distance from the surface of the Earth?

  99.33: One object at the surface of the Mof:cxa.nv+3 r vp9typ) 0nz5ng coco;,on experiences the same gravitational force as a second object at the surface of the Earth. Which of the following would be a reasonable cof xyo ct:cr+ap. 5v)np,3ong0 9zn v;cnclusion?

  00.24 Consider an objectpj *jb h-h,(wtvz c+ rd9*txkmta*d(7 that has a mass, m, and a weight, W, at the surface of the moon. If we assume the moon has a nearly uniform density, which of the followingt9zx( *kc7h **mrpja+w,jh(vd d -ttb 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 timesnmtc5vv:. b8 r the mass of Earth and twice the radius of Earth. The magnitude of the gravitational acceleration at tbvm5r:8c v.n 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 Ea co.t91jalbiw f0 *g (vmze:o3rth’s mass. The gravitational acceleratwjo m3vzt. ioal: *01(bgf9ec ion at the surface of the planet is most nearly

  08.38: Akg 1200 satelli*okknzx7wo8m5kig :k;-6r gite orbits Planet X in a circular orbit with a constant spe6 k *mg57w8 ok nx-zrgoi;:kkied of 5,000m/s. The radius of orbit is 7,500,000 m. What is the magnitude of the gravitational force exerted on the satellite by Planet X?

  94.34: A hypothetical planet orbits i:htn7ha3- s 2m7shurf5vl c4/lvx9ba star with mass one-half the mass of our sun. The planet’s orbital radius is the same as the Earth’s. Approximately how many Earth years does its7v5vnf92i /h st7l- h4curxa3 :mlhb take for the planet to complete one orbit?

  97.12: Two artificial satellites, 1 and 2, ryb k3sx:.6orare put into circular 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 peryr. srkbxo:63iod of satellite 2?

  15.22 Satellite 1 makes a circular orbit around the Earth with gtk ch78ws 73d0r8er ca 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 sy9y:z;c lqk qfos/7hb+ e;ji 8cale registers. If the Earth were to stop rotatinzle8q9;;fo/hc+ ksbji: q yy 7g, but not change shape,

  10.42: A comet moves in an yvva6nl;1y2i9kc9s gelliptical orbit around the sun. As the comet moves from aphelion (the point on the orbit farthest from the suny lvkay91cvg;sin2 96) 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 circult d j5:qc)r;auar 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 gravitational attraction. The orbital period rj5;dqc) tau: 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 w k nhst - kx3ssbl;f+k:us.f3s/ prk:(rpd;u8 ith speed vand orbital radius R around a heavy stationary mass. An external impulse is quickly applied to the r b:kskk:;kr. / s ;npl xr-(8ush3d3st+ffup socket 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