08.19: Kepler’s Second Law about “sweeping out equal areas in equ9i,/5qwfrcyx8k xx2 g20xju p al time” can be derived most directly from which conservation law?p w/8x2kgqx0r 9 x5,uc xifyj2

  16.17:“All planets in the solar system follow elliptical orbits with the Suw uqr:fxe/ * uc3e9s-nn located at one focus of t/u ef-cxw: *nrseuq93he ellipse.” This statement is best summarized by which one of the following choices?

  99.21: What happens to the fchnu4z9-aa. wzfhr 59 z , c0e8(leutworce of gravitational attraction between two small objects if the mass of each object is doubled u4rt.e8la zhc0ww5 aeu(n hz9z- 9c,fand the distance between their centers is doubled?

  95.09 Two spherical bodies attractwdo,jej7y:22jkk9 0in)bms n each other with a gravitational force of 4.0 N. What will be the force if the distance between them is doubls b 20j9: om)ky7ekd ,ijnjw2ned?

  14.27: Two spherical, non-rotating planets, X andY, have the omq8v7nv;uz lq 8ce :6same uniform density. Planet X has twicvquqc;o6n87l:z8 em ve 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, nb9 i-u.dxw bkl+5tyw9 on-rotating planets, X and Y, have the same uniform density. Planet X hkw9wi ut-+b5.y 9lxb das 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 *,h9c4 xhut ma y:2qn2exz l,tcan be calculated if it is orbited by a small satellite by setting the gravitational force on the satellite equal to t2cz9eyq 4,*t ah,:lxux 2nhmthe centripetal force on the satellite. Which of the following would NOT be required in this calculation?

  99.11: Assume that the Earth attrace-qwcif 4h5c6b2 . qg)ykli,e ts John Glenn with a gravitational force F at the surface of the Earth. When he made his faq6wbce )hqc.2,4eikil y 5 -gfmous 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 Mo a3uar)(z ycom,7k0b bzp kz;4on-Earth system (ignore any influence of the Sun), which one of the following best expresses the magnitude of the Moon ayz),o7(kuba3b;c kpzr 4zm0’s acceleration about the Earth?

  02.19: As a rocket blasts away from the earth wio0 qd joa+bq0cwvi58+th a cargo for the international space station, which of the following graphs would best represent the gr0c0jo 8 qv+ba5wq+ doiavitational force on the cargo versus distance from the surface of the Earth?

  99.33: One object at the surface of the Moo o.,3obiko* g euu9rgl)4yi p+n experiences the same gravitational force as a second object at the surface of the Earth. Whichlpu ubii .* 4+g3r kog)ye,9oo of the following would be a reasonable conclusion?

  00.24 Consider an object that has8 r 0qrx3gath- a mass, m, and a weight, W, at the surface of the moon. If we assume the moon has a nearly uniform density, which of the following w3xa0rgh-q8r t ould be closest to the object’s mass and weight at a distance halfway between Moon’s center and its surface?

  96.23: A hypothetical plan(wh yp /scy4nz:8*eh net has seven times the mass of Earth and twice the radius of Earth. The magnitude of the gravitational accelerat pnhch:4/(zsw n *yy8eion at the surface of this planet is most nearly:

  98.24: A planet has a radw8gy 8 e1d0gm dy *jur7xi,+voius one-half that of Earth and a mass one-fifth the Earth’s mass. The gravitational acceleration at the surfac8jr, u8g +iw*d7ym0d vgyoe 1xe of the planet is most nearly

  08.38: Akg 1200 satellite orbits Planet X in a circular orbc tywx7/aghryl y vlw(;*w 9e5-mtz6,it with a constant speed of 5,000m/s. Tzc;(6,5mwytw a/* ylly- 9rv7hg xewthe 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 owxy yg2v6x85 j.v9 sta 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 does it take for the planet to complete one orb8g.9jsw y x6v5x2voytit?

  97.12: Two artificial satellites, 1 and 2, are put into circula7 qq; *ih7 .ia 8w)1gjoaz7(avgvny gnr 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 satqg izg.a1nv;y7qga* j8 7o)i(7vnwah ellite 1 is T, what is the period of satellite 2?

  15.22 Satellite 1 makes a circular orbit aroun r3we)g84 n8jxb7sryw d 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 worf )yw8jayf(5c4:yr5 ok*nk wyd “weight” refers to the force a scale registers. If tf5 wy ok:ywf58acnyy4)k( r*j he Earth were to stop rotating, but not change shape,

  10.42: A comet moves in an elliptical orbit around the sun. As the comet movl3y+ fsdu: 7gnes from aphelion (the point on the orbit farthest from the sun) to perihelion (the point on the orbit closeu f+3l:ndg sy7st to the sun), which of the following results is true?

  17.48: In the binary star system shown, the two stars follow circular a(xs 895a dp9iv:c-0jmanf rh 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 masvairmhaan- 99j(cpx0 8 : 5sfds 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 wywnw2/ v) 4 tga*a9rdqvs)jj:ith 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 the rocket into an elliptical orbit. In terms of R, the size of the semi-majoj a a)gy4)*qv2/9tnwvdr:wjs r axis a of this new elliptical orbit is