08.19: Kepler’s Second Law about “sweeping out equal areas in equal tiressv z38nm;dy- f6g4 me” can be derived mos s;63mne z8gvrf-d4yst directly from which conservation law?

  16.17:“All planets in the solar system folr6q v:nwqf4 c3low elliptical orbits with the Sun located at one focus of the elrf:q36vq w4n clipse.” 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 o z7tyw +xnf-ep2, nj19wm3y ztbjects if the mass of each object is doubled and the distance betwee7x+nwj2f-z1 et,z3tnwy9mp yn their centers is doubled?

  95.09 Two spherical bodies attract each other with a gravitwsse *m h)c7(/iyme9cational force of 4.0 N. What will be the force if the distance between them is doub*mweh)csm 7 eyisc/(9led?

  14.27: Two spherical22: (hsgv acxxy8akqt60 ky,t, non-rotating planets, X andY, have the same uniform density. Planet X has twice the radius of Playykxts t2qgvx8( k:a6ah2, c0net 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,89w(vv4gixxyw5 m ;hb X and Y, have the same uniform density. Planet X has twice the radius of Planet Y v 5x;wyxvb(98ihmgw4. 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 bc vh+( 3z2unhi+r mvx8e 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 calculatiu hh ++vx2ri(c z8vnm3on?

  99.11: Assume that the Earth attracts John Glenn with a gravitational forc20m/w k2fpfofe F at the surface of the Earth. When he made his famous second of/ 2pfw0 2mkfflight 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 infgd;gdz6 yd u45x-hf d:5n:kmqluence of the Sun), which one of the following bestd; fkyh:q5-d ggd 4 ndumxz65: expresses the magnitude of the Moon’s acceleration about the Earth?

  02.19: As a rocket byxhy2hu8 +sp (sob 3s,lasts away from the earth with a cargo for the international space st soy(s28x ybhsp3 ,+uhation, which of the following graphs would best represent the gravitational force on the cargo versus distance from the surface of the Earth?

  99.33: One object at the surface of the Moon experiqzfon ;ug x,ssa5z.asx-08/q ences the same gravitational force as a zn8a.q-xfz;50gs q,xssaou /second object at the surface of the Earth. Which of the following would be a reasonable conclusion?

  00.24 Consider an ob chl7y5vyc3fe1 asur22ac+ +m,wajs ;ject that has a mass, m, and a weight, W, at the surface of thu+2 +jvlh7a c,y1f 2earw;s sc35cyma e 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 center and its surface?

  96.23: A hypothetical planet has seven times the mass of Earth and twice thetq)ajh: n uh u* l juww,-;syp7f5:l(w radius of Earth. The magnitude of the gravitational acceleration at the surface of this planeu)au(- q:jh:hj l5pu,*swnl fww;y 7tt is most nearly:

  98.24: A planet has a radius one-half that g5 tzl/zt1v9w/ 7f baoof Earth and a mass one-fifth the Earth’s mass. The gravitational acceleration at the sub/ lawt7z o/f1vzg 95trface of the planet is most nearly

  08.38: Akg 1200 satellite orbits Planet X in a circular orbit with a constant w*)7sw- ry jt erdv/5bnwm:pn3* hxv( 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 satellite by Planet )xvy msw j 3tb*h5 wvr/rwdpn :e7*-n(X?

  94.34: A hypothetical planet orbits a star with mass one-half the mass l4e53 fmt4u8psil( mz of our sun. The planet’s orbital radius is the same as the Earth’s. Approximately how many Earth years does it take for the planet to complete m3tfe uls5l i44pzm8(one orbit?

  97.12: Two artificial satellites, 1 and 2, are put into circular orbit at the sab4oxn.f ,hhps )ay 3u)me altitude above Earth’s surfacefhx.aph)s n3ob,4y u ). 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 circular orbit around tiojc8m .0a.o;ith 5h mhe 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 /jn)d;y jhc :7fxq;wl force a scale registj:dyx q w ;/);nlh7fjcers. 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 c ru:n: 7ey fq*hdrw-5*y2mqsvomet moves from 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 w q fu2:dhemyv 7**r5syn:q-r results is true?

  17.48: In the binary star system shob7y)rl 3yy*s4 wj n(buwn, 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 3y sr(w7 y 4*unlbjb)yto 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 raditg4pa )av.p f; n9oqi5wtt* ,ius 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 i,9i* 4t a.vpg5qfio tptnw a);nto an elliptical orbit. In terms of R, the size of the semi-major axis a of this new elliptical orbit is