08.19: Kepler’s Second Law absj8uo1+w ; 6kwcniw5oz ghd 8.8wokq6out “sweeping out equal areas in equal time” can be derived most directly from which conservati; qiwo wsk+gz wo8od8.j61w5hk 8nuc 6on law?

  16.17:“All planets in the solar nc1e8e3rk 4naoon-xpn+b /8x system follow elliptical orbits with the Sun located at one focus of the ellipse.” This statement is best summarized by which one of the following choic np+xn-bokr e/13x88nce aon4es?

  99.21: What happens to t -it 4kx) awjr0:iz,tthe force of gravitational attraction between two small objects if th:t) k0j tarw,4itxiz -e mass of each object is doubled and the distance between their centers is doubled?

  95.09 Two spherical bodies attract each other with a gravitational force of 4.01e hw:dc)v *ye N. What will be the yvw)e1: cedh*force if the distance between them is doubled?

  14.27: Two spherical, non-rotating planets, X andY, have the same uniformrg1n0cl+03yh pu3 0.rcu8s m:ldjkk y densitg1:3+p0c l8.kjm3krh00yu d rn yulsc y. 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 planetssje25 lzfr4 y j2z3ke8, X and Y, have the same uniform density. Planet X has twice the radius of Planet Y. L22zlez54j j8ye3skr fet $v_x$ 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 mam la1 ;-ddw8is orbited by a small satellite by setting the gravitational force on the satellite equal to the centripetal force on the satellite. 1mada8; md-wl Which of the following would NOT be required in this calculation?

  99.11: Assume that the Earth attracts John Glenn with a g8*+d jctt( 54tufrsoaravitational force F at the surface of the Earth. When he made his famous second flight in orbit, the gravitationatf*8 ot4dsj cu5r+(ta l force on John Glenn while he was in orbit was closest to which of the following?

  14.30: Considering only the Moon-Earth sys h;(j dac7me6dtem (ignore any influence of the Sun), which one of the following best expresses the magnitude o cd;a6he7m(jdf the Moon’s acceleration about the Earth?

  02.19: As a rocket blasts away from the earth with a cargo for the ik4e u+crr:yb /nternational space station, which of the following graphs would best represent the gravitational force on the cargo versus distance fro c4y+rb/ku re:m the surface of the Earth?

  99.33: One object at the surface of the Moon experiences the same0.q 6e vf*uk vk4n)sxe gravitational force as a second object at the surface of the Earth. Which of the following would be a reasonable conclusiox64) qe vf*.neksku0vn?

  00.24 Consider an object that has a mass, m, and z1ggc7)iq v7lwk, wz fi9fc-//rnol0 a weight, W, at the surface of the moon. If we assume the moon has a nearly unifor7lic n7grkz-i/f,qv1g f0l cw9) /wz om 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 timesy 6,n4 umtxyix)e1dxd p17wan24pr) a the mass of Earth and twice the radiusd1 n ar2t7i)6p,4m x1wa) dpyn4xy exu of Earth. 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-fifd +x7glnvk18 , z(k4qzjy acv-th the Earth’s mass. The gravitational acceleration at the surface of the planet is most ne+4 jqkky7(davx1z c zl8-gvn ,arly

  08.38: Akg 1200 satellite orbits Planet X in a circuxrwaqhcb47no2)e 3wf) 4z 2 zblar orbit with a constant speed of 5,000m/s. The radius of orbit is 7,500,000 m. What is the magnitude of the gravitational force exerted onnz 243xbz)w o4rc2hq7)fbe w a the satellite by Planet X?

  94.34: A hypothetical planet orbits a star with massmegaxkr06rj ) bd:2 )a one-half the mass of our sun. The planet’s orbital radius is the same as the Earth)0 rm):ab2jkrx6eg da’s. Approximately how many Earth years does it take for the planet to complete one orbit?

  97.12: Two artificial satellites, 1 and 2,(e3kw/ 5ppn+qr o th4):k gsife vg67p are put into circular orbit at the same altitude above Earth’s surface. The mass of satellite 2 is twice the m (e/skie43prh ng5 gkpq: 76)vo +ftpwass 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 the Earth with a radiuszdk1z ef f41 +4bbx+vb $r_1= R$. 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 :)gi9r(vvok, dwqbln + :,1;jlaz egta scale registers. If the Earth vn1:q w,kb:rogllj v,9ti z;ge( a d)+were to stop rotating, but not change shape,

  10.42: A comet moves in an elliptical orbit around the sun. As the ce1:o1 cvlpqux801v bn yxhz1 /omet moves from aphelion (the point on the orbit farthest from the sun) to perihelion (the point on the orbit closest to the sun), whi0ouc1n ezp:/lhxxv1b8 qyv1 1ch of the following results is true?

  17.48: In the binary star system i(tdf912a4 rcpijuf)9n *x ofshown, 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 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 syste9ai dpjf)4c1t(fr *i9nxouf2 m?

  06.50: A rocket is in a circular orbit with speed vai :)qi:kzc.xf44wanly23ry /,sij c dnd orbital radius R around a heavy stationary mass. An external impulse is quickly applied to ckyqzw.4 f y3i:la:s24xijc /n id )r,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