08.19: Kepler’s Second Law about “sweeping out equal areas in cen :w6l3 m9dtequal time” can be derived most directly from whi t nmlec6d39w:ch conservation law?

  16.17:“All planets in the solar system follow ellipti*t egx qh/ mhj)-/2jpgcal orbits with the Sun located at one focus of the ellipse.” This statement is best summarizh2/-g*qxje )hgjm/t ped by which one of the following choices?

  99.21: What happens to the force of gravitational attraction bs n4w oirrd311jd .,voetween two small objects if the mass of each object is doubled and the distanw1d34r1nido., vj sr oce between their centers is doubled?

  95.09 Two spherical bodies attract eacjm.sr ,-ug kx5h other with a gravitational force of 4.0 N. What will b5sug,krj.- x me the force if the distance between them is doubled?

  14.27: Two spherical, non-rotating planets, X andY, have thsgm ma+cnq, ,pv 0)w+ cby:bo1e same uniform density. Planet X has twice the radius of Planet Y. v:spm,a n,b+ocg +mb)wy01q c 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 ai2 qewas57x(dqbw/ / ynd Y, have the same uniform density. Planet X has twice the radius of Pla27 bwisydqe(qxw5// anet 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 z4q6lc.*rg/umr l.epi )us9(1wn m rris orbited by a small satellite by setting the gravitational force os1)lmrp e/ l4*z( nq6.ruwg9c ru.irmn the satellite 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 attractcju*5ix-ros( d6nu 2l )cf :cjs John Glenn with a gravitational force F at the sur -fc) un62r*5d ilcoxj(:ucsjface 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 following?

  14.30: Considering only the Moon-Earth system (ignore any influe0 esohv, ;oij.3wl sc)nce of the Sun), which one of the following best expresses the magnitude of t .; evcljhos iw3os)0,he Moon’s acceleration about the Earth?

  02.19: As a rocket blasts away from t/kumfm fy(fq30 m3zd2 he earth with a cargo for the international space sta 0f yf(32m/kuf3mdmq ztion, which 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 experi0 czlh:at) zm 7e-pp0bences the same gravitational force as a setz:l-0mce7bp)hp z a0cond 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 the +4nc* jy),uhow1imb rsurface of the moon. If wj,hiyn bwc1)uo4mr+ *e 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 planehc3g; ;wmfrm k1o l8+ jizt e-z(;fh7dt has seven times the mass of Earth and twice the radius of Earth. The magnitude of the gravitational acceleration at the surface of this planet is most n hj+zf-zc ;f; t8dm7 ko1;m wl(gieh3rearly:

  98.24: A planet has a zjy-c0 l jvxco(4cu49radius one-half that of Earth and a mass one-fifth the Earth’s mass. The gravitational acceleration atzy(v04c 9jjul4 co xc- the surface of the planet is most nearly

  08.38: Akg 1200 satellite orbits Planet X in a cir; * w4wew6kgmk0vv n8ry+ 0ikpcular orbit with a constant speed of 5, 0ge4kin0;rv ykw*w+p mv8wk 6000m/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 orbits a star with mass one-half the mass of our suoc jfm. ,wy4c.qfi4a 6fi-5dg n. The planet’s orbital radius is the same as the Earfafm- q,c4. i6dyojifwg54. cth’s. Approximately how many Earth years does it take for the planet to complete one orbit?

  97.12: Two artificial satellites, 1 and 2, are put+r0.kunh5bzx ln*vm -z0 a4x h into circular orbit at the same altitude 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 5-nlh00ak.x hxrzz +4nvub*m is the period of satellite 2?

  15.22 Satellite 1 makes a circular 6h(t .zf;ko1 68k f e0yuqvkp1qwdr/ zorbit 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 to the force a scalet*s :qbt (b/lw registers. If the Earth were to stop rotating, but not: /lq wsbt(*bt change shape,

  10.42: A comet moves in an elliptical orbit around the sun. Asfhp.((wpgl+/9 9n k7p skiwem the comet moves from aphelion (the point on the orbit farthest from the sun) to perihelion (the point on the orbit closest t79/(pgw wm(9 en hls+fkki.pp o the sun), which of the following results is true?

  17.48: In the binary star yhqgmd u9-yb3o; (rpe+;ev -bsystem shown, 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 ipru- d-h b+q9g 3y;(yv;m obees 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 orbin2ve+8oi;v dg f8rs8 dtal radius R around a heavy stationary mass. An external impulero828vvfi+d;sdng 8se 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