08.19: Kepler’s Second Law about “sweeping out equal areas in eq*9/+ kgqdw zqeual time” can be derived most directly fkqze9 g*wq d+/rom which conservation law?

  16.17:“All planets in the solar system fo(*b emd3)qqnwq2k.s o,zillmw8;* fkn* 3cj tllow elliptical orbits with the Sun located at one focus of the ellipse.” This statement is best summarized by which one of the follom l*e w3*ndqkwm o,32*lk)(.c8tbq qzfn ; sjiwing choices?

  99.21: What happens to the force of gravitational attraction betweeg mh:-qg 7 gozcue;*(bn two small objects if the mass of each object is doubled and the distance b(c g gb;:*m q-ouzh7egetween their centers is doubled?

  95.09 Two spherical bodievm :1 ao3ilka72k pb4ls attract each other with a gravitational force of 4.0 N. What will be the force if the distance between them ia ol23kvmlakbi1 7:4ps doubled?

  14.27: Two spherical, no,0 ac(v4i,xzk w s czs:cxfc8zm -mk72n-rotating planets, X andY, have the same uniform density. Planet X has mxz2:( -vz4zcck 7s8s wmak,,fixc0ctwice 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, havgxldzt4 wz pp+3m*3e y/k aq( t+oy+8buqq5 (ae the same uniform density. Planqtx3 tq4amzp( by kao/ue(q++8+d*5p zlg 3wyet 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 calculated if it is orbited by a small satelok7fnmu6r5;3qc e ta( lite by setting the gravitational force on the satellite equal to the centripetal force on the satellite. Which of the following would NOT be (7kuenqr 6co35f;mta required in this calculation?

  99.11: Assume that the Earthx2yz08yr9z x1w knnn * attracts John Glenn with a gravitational force F at the surface of the Earth. When he made his famous second flight in orbit, th*wn nk nzy1r2y8xz09 xe gravitational force on John Glenn while he was in orbit was closest to which of the following?

  14.30: Considering only the Moon-Ear tn1p+l6.eqm4mpy aq: 1uw zs4th system (ignore any influence of the Sun), which one of the following best expresses the magnitude of thw.e1pqm+6 4q1uzy m4a n plt:se Moon’s acceleration about the Earth?

  02.19: As a rocket bhvs1l-/ szo. klasts away from the earth with a cargo for the international space station, which of the following graphs would best represent the gravitational force on the cargo versus distance from the surface of theh o- 1z.lkvss/ Earth?

  99.33: One object at the surface of the Moon experoqz-x i,d5 r5viences the same gravitational force as a second object at the surface of the Earth. Which of the followingxrzi,5v5dq -o would be a reasonable conclusion?

  00.24 Consider an object that ha.v h/98 +jiup,wdim tis 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 would be closest to the object’s mass anwt8mj +,.ii dpiu9v/hd weight at a distance halfway between Moon’s center and its surface?

  96.23: A hypothetical planet has senjqt l 8g l6390mk7snnven times the mass of Earth and twice the radius of 783tjnsn06lqk9 l ngm Earth. 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 one-fifth the Eaqdefin km/5:) rth’s mass. The gravitational acf5)nk/ mdiq: eceleration at the surface of the planet is most nearly

  08.38: Akg 1200 satellite orbits /pw rsd *bc.r4Planet X in a circular orbit with a constant speed of 5,000m/s. T. /ws4cdb r*prhe 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 m on6dcgkpwel l 4g.g1p6/ 7u:lass of our sun. The planet’s orbital rgc/p l.p1 6l6d 7nl:4uwokg geadius 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 satellites, 1 and 2(zfa( /sy- 2b 3p 6gw3ktxjsei, are put 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 issszbi3p/j 6tk2g3aw - fe(y (x T, what is the period of satellite 2?

  15.22 Satellite 1 makes a circulx/3.mlt mggh5x,.cj h ar orbit 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 scalek4vsw2 k*wy8a registers. If the E*w8a vk2s yw4karth were to stop rotating, but not change shape,

  10.42: A comet moves in an elliptical orbit around the sun. As thex8b4 6*mlrq-f8 tz-e .vwimac comet moves from aphelion (the point on the orbit farthest from the sun) to pf8irmtwmexl .6- *v bz48qa -cerihelion (the point on the orbit closest to the sun), which of the following results is true?

  17.48: In the binary star system shown,nu5u*o7i2 1jv1ltt lj 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 attractvo*l71itljuun t2j 15ion. 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 wity 143oc zknxa3)qjd ,xh speed vand orbital radius R around a heavy stationary mass. An external imxjy1)na o 3,qc4d3zxkpulse 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