08.19: Kepler’s Second Law about “sweeping outiqpf*o 9+ bzjz1s;pi; a b*d1a equal areas in equal time” can be derived most directly from whicq;d1 jzabb i z9*io1a* s+pf;ph conservation law?

  16.17:“All planets in the solar system follow ellipticale7x-nxsq25 ) upu60ar hkavl 7 orbits with the Sun located at one focus of the ellipse.” This statement is best summarized by w k-p vqu2s r)7lux0ah7a6enx5hich one of the following choices?

  99.21: What happens tx/*yi,o5 bfl n*4,. xpowzowao the force of gravitational attraction between two small objects if the mass of each object is doubled ,**.w,l oxzb o p5f 4anixy/woand the distance between their centers is doubled?

  95.09 Two spherical bodies attract each othei2 *slcd-.m bsr with a gravitational force of 4.0 lbs- .dc smi*2N. What will be the force if the distance between them is doubled?

  14.27: Two spherical, non-rotating planets, X andY, ba bn3tf9*y3ra/sba :hxbn)( have the same uniform density. Planet X has twice the radsbb3)bf: a t3b*r(ha n anxy9/ius 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 uniform dq*j-1 yd*aga .cqgshiy 5r/zj)g p,r(ensity. Planet X has twicaz5s.dgjq -iq gh)ry1(/prc * j y*,gae 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 calculated if it is orbited by a smj m6oebr/2x/ yall satellite by setting the gravitational force on the satelm/ yje2ox 6/rblite equal 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;l7w v6a wk9 -uq mlxl;s2*bh*(jj/ oyc8 dtrt F 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 of the follo6ll7;k(ry *28chd;/w xm tls9* tv -qoujwbjawing?

  14.30: Considering only the Moon(:c5-w x6ofro ebpd b2-Earth system (ignore any influence of the Sun), which one of the following best expresses the magnitude of the Moon’s accel wb -:6o2expcf 5bdo(reration about the Earth?

  02.19: As a rocket blast4l2cckhc33g+ j (gtiys away from the earth with a cargo for the international space station, hljc2tgc iy k3g(+3c4which of the following graphs would best represent the gravitational force on the cargo versus distance from the surface of the Earth?

  99.33: One object at the surface of the Moon experiences the same gravitational cusw6/ :tyeg z6 ej*q6force a 6sc*eew6j y6q/g t:uzs a second object at 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 weight, W, at tjwewr52/k 4r.ntdii 0he surface of the moon. If we assume the moor4i2t wwk 0in/r j5e.dn 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:.jj m 8 (n)e-nde3d:zhmaahn9 dys:b times the mass of Earth and twice the radius of Eardjnn s8j:3mhd ydz- ae:m baeh.n)9(: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 onwr32u9f3jbo9i ue 2n ae-fifth the Earth’s mass. The gravitational acceleration at the surface of the planet is most nearlfb9 rj3i92wo2u3naue y

  08.38: Akg 1200 satellite orbits Planet X in a circulpv- jr+u36wmwq z6v/aar orbit with a constant speed of 5,000m/s. The radius of orbit is 7,500,000 m. What is the ma6+j3 rzupqvw vm /6a-wgnitude of the gravitational force exerted on the satellite by Planet X?

  94.34: A hypothetical planet orbits a star with mass one-half the mass of our su5:- c ,sqkboxm rx0,waud+m;a n. The planet’s ok:wq5 mbx+dr,ox,c 0-a am;surbital radius is the same as the Earth’s. Approximately how many Earth years does it take for the planet to complete one orbit?

  97.12: Two artificial satellit 8:jzshmpk- ffx4t+kvrp .. d,es, 1 and 2, are put into circular orbit at the same alti -mx4fsk:p d,hpj zr.+kt8.vftude 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 orbit around the Earth qb7 s+m(7urs47vbo xbwith 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 “weig6unyyz2ap3- ght” refers to the force a scale registers. Iu 6gynz2-3 ypaf the Earth were to stop rotating, but not change shape,

  10.42: A comet moves in an elliptical orbit around t(iom9+1zxjni 36 unc mhe sun. As the comet moves from aphelion (the point on the orbit fani9z36 mim (xnc j+o1urthest 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,zv ;wrg,mw4/ g the two stars follow circular orbits about the system’s center of mass. The star; gw/vg 4rzwm,s 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 system?

  06.50: A rocket is in a circular orbit with speed vand orbital radius R0u,1,6 +royx xqovbkr around a heavy stationary mass. An external impulse is quickly applied to the rocket directly opubq6+y01voxrr ,kx o ,posite 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