08.19: Kepler’s Second Law about “sweeping out equal areas in equal time” caeor;ps3a-cb6pmjtf ( neg.uk:lo 2,in 7vz 6;n be derived most directly from which conservation 2 3;c -sz6akmon tie6rbgvlp.eo, fpu(7n:;jlaw?

  16.17:“All planets in the solar system follow elliptical orbits with the Su zuw7yq.., kbscvwi/7n loca sziv. qyb.k ,cu/w7w7ted at one focus of the ellipse.” This statement is best summarized by which one of the following choices?

  99.21: What happens to the force of gravitational spbd6b; 5)l1ojag8okattraction between two small objects if the mass of each object is doubled and thejpsl k;o6db 1)a8o5 bg distance between their centers is doubled?

  95.09 Two spherical bodies attract each other with a gravitational force of 4.0-l cx o.yfm7/j N. What will be the force if the di.-lcf 7/xjym ostance between them is doubled?

  14.27: Two spherical, non-rotating planets, X andY, have the same uniform densdmt cvgts1 .-9-l:cv e -qiq+y,syx*mity.l9qv -y mt-g1 qec +,vitsx-y*dm.: cs 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, non-rotating planets, X and Y, have the same ujt; q/ q)p/6,qivr kg43e ed d+vt59 hyyxs9ypniform density. Planet X has twiej +eqp9pv5)dx,g yy q3dk9/6 ;i /t4vrsqt hyce 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 aq:p92: cdbnus( gix m87flzy-pfr 0:t planet can be calculated if it is orbited by a small satellite by setting the gravitational force on the satellite equ7g::qzdp2p( :st ufcm0r -bynx8fl9ial 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 with a gravitational force Fns onz0+st7sj b+ q/;y4lf6kg at the 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 ;st qn fgs7+jo lk60sb+ y/zn4of the following?

  14.30: Considering only the Moon-Earth system (ignore ;b ,pc6vbb;kjl(b(c+fqfsf7 any influence of the Sun), which one of the6,bljqbf( kb+vfcp7 bs;(c; f following best expresses the magnitude of the Moon’s acceleration about the Earth?

  02.19: As a rocket blasts away from the earth wi( 8jzx ol 7.wg6dv/p5zjffc 2vth a cargo for the international space station, which of the following graphs would best represent the gravitational force on the cargo versus distance from the surface of the E5 wzdfj62fv 7oc( 8jzlx pvg/.arth?

  99.33: One object at the surface of the Moon experiences yltsvp /;wg)rv3 jcpo0 b+a 7p*7h5 bqthe same gravitational force as a second object at the surface of the Earth. Which of the following would be a reasonable concluap s7+l gj/o) vt;bvr7cpqhw p0y 5*3bsion?

  00.24 Consider an object that has a mass, m, and a weight, W, at gbul1 y,j1 y(hthe surface of the moon. If we assume the moon has a nearly uniform density, which of the following j gyulyh(11,b 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 k+ .pj 5/( zbey.haklawrr+0wEarth and twice the radius of Ear.h0a wkr+wb5zy lke j +r/(.apth. The magnitude of the 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--qcfr:d8pu5 fk4, ri)gfx y -ufifth the Earth’s mu, -yfr-qk5dg:icpxf 8f u4)rass. The gravitational acceleration at the surface of the planet is most nearly

  08.38: Akg 1200 satellcbi,1mj h r ya)x0q:zt r06v )igko91lite orbits Planet X in a circular orbit with a constant speed of 5,000m/s. The radius of orbit is 7,500,000 m. What is the magnitude o br,yxmtio9hk ij:ar)qz)0gv1l16c 0f the gravitational force exerted on the satellite by Planet X?

  94.34: A hypothetical planet orb sfns y5i;3sj+its a 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 it take for the planet to complet3i;s5s +nyfsj e one orbit?

  97.12: Two artificial satellites, 1 ann s(tp4*n-o4gjq. 18t vh3nbzwnsm,od 2, are put into circular orbit at the same altitude above Earth’s surface. T8s t(w4vj,n n*1s. qtg n n3bohp4-zomhe 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 circwyyhip58,hg, ular 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 scale ugb0gqhw5 79 pqu 7rcyyb273 tregisters b057qb gu9h372qrgt y7pcw uy. If the Earth were to stop rotating, but not change shape,

  10.42: A comet moves in an psn8.n+ ak5syelliptical orbit around the sun. As the comet moves from aphelion (the point on the orbit farthest from the sun) to perihelion (the point on the orbit closekn sy5+n.a8s pst to the sun), which of the following results is true?

  17.48: In the binary star system shown, the twonia ))o-zaf d:t(fnt, stars follow circular 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 of the star of mass M is T. Which one of the following choices represents the total mass of the bd tt :fa)-, if)(zanoninary star system?

  06.50: A rocket is in a circular orbit ke9ej7b.qdc; ywse08with 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 th79kd c ws;8ebyq.je0e e 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