08.19: Kepler’s Second Law about “sweeping out equal areas in equal time” qp (o: ho6sl u6ljpa+x-03uj0h0bpo f can be delh0 bl:qjj6-ooopappu0fh(u0x s3+6rived most directly from which conservation law?

  16.17:“All planets in the solar system follow elliptical orbits with to(k3- 2 jxcwwbhe Sun located at onexjkc-o b(23 ww focus of the ellipse.” This statement is best summarized by which one of the following choices?

  99.21: What happens to the force of gravitational attraction bet1wc+gbc :pd+gym0h.web6nkhjc a 3)8ween two small objects if the mass of each object is doublea :p dmy0h3 b6+b w 1cnkj)wc.gc+geh8d and the distance between their centers is doubled?

  95.09 Two spherical bodies attract each other with awglm:g *ima 12 gravitational force of 4.0 N. What will be the force if the distance between them i12la*gi gm:wms doubled?

  14.27: Two spherical, non-rotating planets, X andY, hvn 8ebb; *xjb2ave the same uniform density. Planet X has twice the radbxn 8b;vbej* 2ius 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-roxy7yz;g85l de tating planets, X and Y, have the same uniform density. Planet X has twice the radius of Ped7 8yzgyl5 x;lanet 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 b5bz,5h;t 1h)jcmx h9qxxx0p v:1 k neyy a small satellite by setting the gravitational force on the satellite equal to the centripetal force on the satellite. Which of the following would NOT be required in this calculation? 0zj,qc;1t kxxpm59h x)n 1by h:5evxh

  99.11: Assume that the Earth ,ei1fw cj;a:qattracts John Glenn with a gravitational force F at the surface of the Earth. When he made his famous i ;qc,ef:aj w1second 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 influencsk rzi r(e*,x2f3*ksdi(r fh0uh4uu 8e of the Sun),e zsri (u ,23dih8 fu0fhxkr*r(k* 4us which one of the following best expresses the magnitude of the Moon’s acceleration about the Earth?

  02.19: As a rocket blasts away from the eart :l)iuwgh. s5r+e6nu+fnz y p1h 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+)i6nu:w5+g hpl feuz srny.1 surface of the Earth?

  99.33: One object at the surface of ok5wzd4 eloyn+t259a the Moon experiences the same gravitational force as a second object at the9 a25tlo yoe4 k5zdwn+ 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,x cl6vj/yc,v ; 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 and weight at a dcjc 6 vyx,v/;listance halfway between Moon’s center and its surface?

  96.23: A hypothetical planee r)bvi/.;f ipwy3y .ot 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 3wfiipr ey;.)v ./oybearly:

  98.24: A planet has a radius one-half that of Earth and a mass one-fifth e 9)pzqv9lmbmg 7.7 zgthe Earth’s mass. The gravitational acceleration at the surfac79v)qzg9 m.p z 7gmblee of the planet is most nearly

  08.38: Akg 1200 satellite orbits Planet X in a cirbcsmm9k9/p.p, z 2 xzqeqxj/:cular orbit with a constant speed of 5,000m/s. The radius of orbit is 7,500,000 m. What is the magnitu2 /ezm9bc9/sx:j . mpqqzpx k,de 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 i e+0 b*w 0wmmw),mjeyof our sun. The planet’s orbital radius is the same as the Earth’s. Approximately how mane wbji,w *wm+y0e)m m0y Earth years does it take for the planet to complete one orbit?

  97.12: Two artificial satellitc.8s h-bcwz kcmy 9/4hvveu5; es, 1 and 2, are put into circular orbit at the same altitude above Earth’s surface. The mass of satellite 2 is twice the mass of sa/zwchh8 vce 49ukv;m-s ybc.5tellite 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 with a ;d9ofwd 6j3xd 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 “wwsx +yr1wra84g4v, v peight” refers to the force a scale registers. If the Earth were to stop rotating, b1rr 8 pswvw,gx44vya +ut not change shape,

  10.42: A comet moves in an elliptical orbit around the sun. As the comet +uk (ln-;je) p z6 zcb espe-asoj890jmoves from aphelion (the (jpol -ej zjc0 9zeen+s6 k-s)au8pb ;point on the orbit farthest 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, the two stars 1dp01kcdv- qlgz-f x( 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 -dvzpk (q-d11f0x cl gM is T. Which one of the following choices represents the total mass of the binary star system?

  06.50: A rocket is in a ciwcd *ux8n-e.n rcular orbit 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 a n8w *cx-en.dund 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