08.19: Kepler’s Second Law about “sweeping out equal arep9twxp3 c/a:kq wqm ;0as in equal time” can be derived most d 0cm/ p;q:3 p9waqktxwirectly from which conservation law?

  16.17:“All planets in the solar system follow elliptical orb1y;/74um:v x b dvi-kflik(ns its with the Sun locvsdb:m-/(l kn4 vu7i iy;f k1xated 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 attraction between two small dmmuyy5 iq6 ux-(xg5q *z(zk7objects if the mass of each object is doubled and the (yx*7yzmm6 k55-qx( uiqdu gzdistance between their centers is doubled?

  95.09 Two spherical bodies attract each other with a gravitationa1g+2(nyqzt s hl force of 4.0 N. What will be the force if the d1hgqz(+n2y ts istance between them is doubled?

  14.27: Two spherical, non-rotatingw wujq+m ;4jp)o(s( af.3wtuj planets, X andY, have the same uniform density. Planet X has twice the radius ow3a( suwjqf)jotmp;4u(jw +.f 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 uniform dems ie9(*ws) usnsity. Plan)m u*i w(9sseset X has twice 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 be c)lq:dd-ty1 wj;iq c;d alculated if it is orbited by a small satellite by setting the gravitational force on the satellite equal to the centripetal force on the d)cl ;1qdqdy:;j t-iwsatellite. Which of the following would NOT be required in this calculation?

  99.11: Assume that the Earth attracts John Glenn. t9q6lmr6 sqv with a gravitational force F at the surface of the Earth. When he made his famous second flight in orbit, the gravitational force on Jo.6s 69ltrqvmqhn Glenn while he was in orbit was closest to which of the following?

  14.30: Considering only the Moon-Earth system (ignore any influence of the hl/f2 v. v61w huru(,i4yd qnuk( jd;iSun), which one of the following best expresses the magnitude of the Moon’s acceler h jlhv r.fu 1n;2v4/,d6u(ywdiu( iqkation about the Earth?

  02.19: As a rocket blasts away from the earth with a cargo for the interna dvduzy;a/ 5b(tional space station, which of the following graphs would best represent the gravitational force on the cargo versus distance from the surfac /ay;dvd uz(5be of the Earth?

  99.33: One object at i./ecb1 tuwuel-x e-,nm* i0 fthe surface of the Moon experiences the same gravitational force as a second object at the surface of the Earth. Wh*lfu.- bu/ iixe-we n,t1cme0ich of the following would be a reasonable conclusion?

  00.24 Consider an object that has a mass, m, and a weight, W, at the surface oo,2*pjkp :4wwxwh e.ef 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 w, ep4h2.j*k:epox ww 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 the e*7wy 3 e yz(1jkqpnt8 zg-m:66vvlpkradius of Earth. The magnitude of the gravvzjlenmypk*7p8v -: w 66gqt3k( 1yz eitational acceleration at the surface of this planet is most nearly:

  98.24: A planet has a radius one-half that of Earth and a masorp2futk21n s*8(u qxu0os 5us one-fifth the Earth’s mass. The gravitational acceleration at the surface ofu2su(k8 tu fxuqos n20o *15rp the planet is most nearly

  08.38: Akg 1200 satellite o(zreucqg9iwf cxu* r(8;6k2krbits Planet X in a circular orbit with a constant speed of 5,000mzuwc kf*ir c62kq8;(xu9 e(g r/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 orbitrg2+d*:p9 eyhx +mxebs 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++h:y*edr x epx mg92b does it take for the planet to complete one orbit?

  97.12: Two artificial satellites, 1 and rvi 27mt,+vv t2, are put into circular orbit at the same altitude above Earth’s surface. The mass of satellite 2 is twice the mass of satell,t m t+vriv2v7ite 1. If the period of satellite 1 is T, what is the period of satellite 2?

  15.22 Satellite 1 makes a circular orbix6u ,ut9+uluo se qe/8t 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” refe1)w wl y- o:v95tfdxogrs to the force a scale registers. If the Earth were to stop rotating, but not chanyt) 5o9 xo:1dw-gfwvlge shape,

  10.42: A comet moves/y.v 0v2y5kti .(dbm xp(r7xvec2er v in an elliptical orbit around the sun. As the comet moves from aphelion (the point on the ovy yevxkt dx2rc 0 .(v/2i mpr5b.ev(7rbit 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 sta2 .ah* zu6wgt2tcba 5frs 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 h2z52gtfcbaa6 tu w.*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 radius R ars rb:qa3 y xgeoq2.ke8-f9wf7 ound 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 into-fwskxrae oq b:e.q g39y 827f an elliptical orbit. In terms of R, the size of the semi-major axis a of this new elliptical orbit is