08.19: Kepler’s Second Law a 6e, hcz tb0be zn 8um;ik/-s9r 3h53z*qvxhffbout “sweeping out equal areas in equal time” can be derived m; h vfi9qhbfz 6m8bzneztsx/ch -k05*,3eu r 3ost directly from which conservation law?

  16.17:“All planets in the sod xwlbj,98o o(sv *th3lar system follow elliptical orbits with the Sun located at one focus of the ellipse.” This statement is best summarized by which one of ,odhv x8 (w9l*bs to3jthe following choices?

  99.21: What happens to the force of gravitational attraction betwfv;(x)z)m ujt een two small objects if the mass of each object is doubled and the disxmj( v);tfz u)tance between their centers is doubled?

  95.09 Two spherical bodies attract each c67wr s7sa /wj)sh ;mfit16oiother with a gravitational force of 4.0 N. What will be the force if the distance6f sw6m)cas7ri/sjo 7; 1wiht between them is doubled?

  14.27: Two spherical, non-rotating planets, X andY, have the sazm c,mu2q pr0jry; 69ozq-u9q me uniform density. Planet qu99oq p z;2r ,-qmymruc6j z0X 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 samef3np1-q;g rnb uniform density. Planet X has twice the radiuspqn- r3gfb;1n 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 calculated if it is orbited by a small kmnu2g4dp sa0ir 7a84 satellite by setting the gravitational force on the satellite equal to the centripetal force onaumn02 84sk7i agrd4p the satellite. Which of the following would NOT be required in this calculation?

  99.11: Assume that the Earth attracts John Glenn with a gravita-r6m.t 7kwletny .:cb tional force F at the surface of the Earth. When he made his famous second flight in orbit, the gravitatibkl-wym n6rct7te.:. onal 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 influence of the Sun)yl8*y 5bkq(k i iam2xcemt0f e7 ,1(kx, which k(i7my5bxtxq ae, kei80(f1 *ykcm2 lone of the following best expresses the magnitude of the Moon’s acceleration about the Earth?

  02.19: As a rocket blasts away from the earth with a cargo for the internr0yw*qre; 1cna*f e/tational space station, which of the following graphs would be1ey /f*;t*nrcreq aw0st represent the gravitational force on the cargo versus distance from the surface of the Earth?

  99.33: One object at the surface of the Moo )o9vgq8 r*m t3htz.npn experiences the same gravitational force as a second object at )t*gnph 8v9m.z orq3t the surface of the Earth. Which of the following would be a reasonable conclusion?

  00.24 Consider an object that has a mass, m, and a weij-mgizwnwh7 m m-3t-8 ght, W, at the surface of the moon. If wej7n-8zm-3wi-hmtm w g 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 t 87f w;)gdfk,ui z8m+mv .pyibhe mass of Earth and twice the radius of Earth. The magnitude of the gravitational acceleration at the surface of this pf8z+m d pkmgvbw.;y8f7i i), ulanet is most nearly:

  98.24: A planet has a radius one-half that of Earth and a 3rz8fa7nc qv(3z,kt r .f5lnr92ttsimass one-fifth the Earth’s mass. The gravitational a3.r3tlzn7tar9 ,2(85 qfisz rntv kcfcceleration at the surface of the planet is most nearly

  08.38: Akg 1200 satellite orbits Planet X in a circular orbit8mnn3 ;whgt9 kl0-h ej with a constant speed of 5,000m/s. The radius of orbit is 7,50h;g j-net0n w39k 8mlh0,000 m. What is the magnitude of the gravitational force exerted on the satellite by Planet X?

  94.34: A hypothetical planet orbits a star with mass one-half the ma7o-*d -arom w.projw: ss of our sun. The planet’s orbital radius is the same as the Earth’s. Approximateo --*ood r wrw:7.jmaply how many Earth years does it take for the planet to complete one orbit?

  97.12: Two artificial satellites, 1 and 2, are put into circular orbit atpg2::mfw:)nglfn- ea the same altitude above Earth’s surface. The mass opfl:fawm2)gn : g-ne :f 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 thk t.: gr zij5 xuc813lhs/pf7qe 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 “weiglw:6hy t)3c ydht” refers to the force a scale registers. If the Earth were to stop rotating, but not chang:ly3w)h t6yd ce shape,

  10.42: A comet moves in an elliptical orbit around the sun. ylh s,j kk9zu*/0-o 78glnx jqgo*i,l As the comet moves from aphelion (the point on the orbit farthest*i*,sg9q7yo luklxz8o hkjng,0-/l j 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 shqw2hhj j4r1i;own, 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 oneq jhhj42r;i 1w of the following choices represents the total mass of the binary star system?

  06.50: A rocket is in a circular orbitgn5h gbf9 7yf/ with 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 the rocket’s speed is slowed to v/2, putting theyf 9 hgg/b57fn rocket into an elliptical orbit. In terms of R, the size of the semi-major axis a of this new elliptical orbit is