08.19: Kepler’s Second Law about “sweeping out equal areas in equal time” cprj/nkyoy uxtyo- rm.( 634 x(fa2i 0wan be derived most directly from wh0o((y 64.kjmf-t/ 2 yy n uoira3wpxxrich conservation law?

  16.17:“All planets in the solar system follow elliptical orbits 6hrjzp8o2 p(s with the Sun located at one focus of the ellipse.” This statement is best sj spph(26rz 8oummarized by which one of the following choices?

  99.21: What happens to the force of 7woot1rjaz5g .xt+.0p wmde8gravitational attraction between two small objects if the mass of each object is doubled and the distance between their centerptgz .mro10x8ewjw d .oa75t+ s is doubled?

  95.09 Two spherical bodies attract each other with a gran,:t:ekl rjq 8vitational force of 4.0 N. What will be the force if the disl:qj,: ke nt8rtance between them is doubled?

  14.27: Two spherical, non-rot t9b uglww/8g/ va-px(ating planets, X andY, have the same uniform density. Planet X ha9g/uvw g(abwpl- t8x/s 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, X5bfeibn5jbuex 60; sg /tl3j g,x: -uz and Y, have the same uniform density. Planet X has twi uug05,zsj/; jx-efetxi b:gn635b blce 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 blt4:ou9tk :-1foezwci *fjqa,c/ f-ke 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 k fic:/ 1:-f4zte q-lfw,koo* jau9ctwould NOT be required in this calculation?

  99.11: Assume that the Earth attracts John Glenn with a gravitational force 6;xmosa,1yqpF at the surface of the Earth. When he made his famous second flight in orbia q1om6 ,;xpsyt, the gravitational force on John Glenn while he was in orbit was closest to which of the following?

  14.30: Considering only the Moon-Eart2 :tx/fm-(onjw;)w 3 ntwonwyh system (ignore any influence of the Sun), which wt2ot)f-(on;/n3wnwjw m:x yone of the following best expresses the magnitude of the Moon’s acceleration about the Earth?

  02.19: As a rocket blast6uvwyaju/k+h r6-t7 tq v(;6u ftg .zgs away from the earth with 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 ofhu(k.vty6qr/ug -w;j zgutft66+7a v the Earth?

  99.33: One object at the surface of the Moon experiences the same grav noa6 88*+tscww;4gkc uz;eupitational force as a4k;uo;+w zg6*p te ca8nwsuc8 second object at the surface of the Earth. Which of the following would be a reasonable conclusion?

  00.24 Consider an object tha;9hcg+ycxl 9bt 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 following would be closest to the object’s mass and weight at a distance ha9cl+b; gx9yh clfway between Moon’s center and its surface?

  96.23: A hypothetical planet has seven times the mass osjek(1) 8+ndlt, dl ndf Earth and twice the radius of Ear 8d,elk( dl) j1ndsnt+th. 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-fift *t) os)t18o(dbkq/7 zn v pf0yovwo4jh the Earth’s mass. The gravitational acceleration at the s otjn/81 ) sytq(f)d4p0kzboovvw7o *urface of the planet is most nearly

  08.38: Akg 1200 satellite orbits Planet*q3ph ( -;huhhb ).bgxmj/pzh X in a circular orbit with a constant speed of 5,000m/s. The radius of orbit g3hmhp.bh;p xh(-q/ h*)uzbjis 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 a (lcuc d q;58ffgs2j v9.bpkw9star 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 complete one orbij2l;8s(ukg qb9 9c.vdpffcw5 t?

  97.12: Two artificial satellites, 1 and 2, are put i:8wzyw /)dyvr vyq)b 4nto circular orbit at the same altitq8yr:w b)w4yy )/zvvdude 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 period of satellite 2?

  15.22 Satellite 1 makes a circular o,6d *upxuywb7pfi440 rtt2br rbit 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 jf/k4e-tm b,o to the force a scale registers. If the Earth were mbt4fek ,-oj/ to stop rotating, but not change shape,

  10.42: A comet moves in an elliptical orbit around the sun. As the comet m.6mz26w0 57w sfxq cch*0e 4apiult syoves from aphelionc5hes p4 l0wxft 7iuz6 *sy62.0qacmw (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 circular orbrzo p( c1w jt;f(1if/kits 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 mas;o( f/ 1zrj ki1fw(tcps of the binary star system?

  06.50: A rocket is in a circular orbit with speed vand orbital radius R around aau,5cfw i11kf ,n7xml mf1rh1 heavy stationary mass. An externa1fcamxr, m1wlh,15ffi u 1k7nl 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 into an elliptical orbit. In terms of R, the size of the semi-major axis a of this new elliptical orbit is