08.19: Kepler’s Second Law about “swe q00+fgavl x.*lzkdyr1 p*sp5eping out equal areas in equal time” can be derived most directly from which conservation lapfrg.1y *p00+ 5ak*ql sdxlvzw?

  16.17:“All planets in the solar system follow lhvzh9vwz-w(e: j, f*elliptical orbits with the Sun located at one focus of the ellipse.” This statement is bes9 jzhhwvwze ,fv(-l:*t summarized by which one of the following choices?

  99.21: What happens to the force of gravitational ck4 vzq*5q r) t/kxi-o.ru0k/adsn0 :/br zkzattraction between two small objects if the mass of each object is doubled and the distance between their c vr0*rkd4/ruz/i /c5q0a.ozqs-:nb k k)xtkz enters is doubled?

  95.09 Two spherical bodies attract each other with a gravitational force o+ky x-f qojnb a,f4l,0fy8*jnf 4.0 N. What will be the force ajo, 0fn 8kx, fyf+l4j-ny*qbif the distance between them is doubled?

  14.27: Two spherical, non-rotating planetsr 8mtvq pg)j1,8jjum6, X andY, have the same uniform density. Plaj)p8 vjqgt6 , umm81rjnet X has twice 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, have v, w/uu7hr:umthe same uniform density. Planet X has twice the radius of Planetv/ r hwmu7u,:u 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 orbitee jyem ,v 3vh:s+p7 nv4gmeq/-d by a small satellite by setting the gravitational force on the satellite equal to the centripetal force on the satellite. Which of the following,nqp/s:4+m7gyee mh j ev3vv- would NOT be required in this calculation?

  99.11: Assume that th( / og5ztoaa/ne Earth attracts John Glenn with a gravitational force 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 ton/tao /(agzo 5 which of the following?

  14.30: Considering only the Moon-Earth system (ignore any influuu. 9b 33rmwcsfuxvdb:;m +s8ence of the Sun), which one of wx.f m:s 8v;uus 3ucmbr3 +9bdthe following best expresses the magnitude of the Moon’s acceleration about the Earth?

  02.19: As a rocket blasts away from thmiv48 p2ck6kte earth with a cargo for the international space station, which of the folmv4 tki k268cplowing graphs would best represent the gravitational force on the cargo versus distance from the surface of the Earth?

  99.33: One object ats)d7v b8 kt0fuo3j ov+9;k qy3oz 6kmf the surface of the Moon experiences the same gravitational fo ojvkm9+ 3k)svf6d7 zk ;0otf83uqyborce as 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 the surfic r8e wdn:de3(g *bey.0n +ayace 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 distance halfway between Moon’s center and it*3ncie( +d:yg0ybea8. w enrd s surface?

  96.23: A hypothetical l,her+qcxlj8:rz5g n436khs planet has seven times the mass of Earth and twice the radius6:4grl, jxhzs+ 5recqlh 38 kn of 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 Ear 7r4 6+tja 4eovkkwc;uyd7 *xsth’s mass. The gravitational accelera6ky7cx ;o j*dewr7 avst4+ ku4tion at the surface of the planet is most nearly

  08.38: Akg 1200 satellite orbits gm9ss0 vb6n l5o7gdvmrp16 h9Planet X in a circular orbit with a constant speed of 5,000m/s. The radius of orbit is 7,500,000 m. Whabdl msgph0g9v rs6179n5m ov6t is the magnitude of the gravitational force exerted on the satellite by Planet X?

  94.34: A hypothetical plana v)-gaoydq8 /et orbits a 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 orbitag8/ qd vyao)-?

  97.12: Two artificial satellites,zgyzhlq mbbp3./-gpcp/k/ mo 3+- j 5f 1 and 2, are put into circular orbit at the same altitude above Earth’s surface. The mass 3p/bjcf /hp3z-5ky+bz .m-og pl/mgqof 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 ciw0umr5i tvc +n1h,wuccel.:8rcular 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 scale rjwz12cdo9xkklim 1.:+b kj 9iegisters. If the Earth were to stop rotating, but m 9z il2:bik+19jo1ckxj.wdknot change shape,

  10.42: A comet moves in an elliptical orbit around the sun. As the comet mov y dszd:6,m, 8gaua,tves from aphelion (the point on the orbit farthest from the sun) to perihelion (the point on the o,sgd,8 v ,uazty6d:marbit closest to the sun), which of the following results is true?

  17.48: In the binary star system shown, the two stars follow circular orbit rxj6(xc r9.wis 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 attractioj(9c6wr.ri xxn. 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 wvb/7ik8,fd . r6 lyeapith speed vand orbital radius R around a heavy stationary mass. An external impulse is quickly applied to the rocket directly opposite torev8bf ka,i/ 7ylpd 6. 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