08.19: Kepler’s Second Law about “sweeping out equ8a+kqpd)sm. )( riuel)cx1 ime zt f14al areas in equal time” can be derived most directly fr( uf)lqecsm14tkp 1)ziia r.8m+xe) dom which conservation law?

  16.17:“All planets in the sol6fxw9e 3;r4 x aqa-k4+v7b oi-fjfeqmar system follow elliptical orbits with the Sun located at one focus of the ellipse.” This statemxq+r-xea kmo 7 9qj4ef 3f-i4 6v;abwfent is best summarized by which one of the following choices?

  99.21: What happens to the force(hh:o4v (az8-x otq91 guai db of gravitational attraction between two small objects if the mass of each objecto48v(hzhatug9ix1 qo - (bd a: is doubled and the distance between their centers is doubled?

  95.09 Two spherical bodies attractw(jk6,vw st t*z m,0pls )0paj each other with a gravitational force of 4.0 N. What will be the force if the w(smjs),tvazt, p600 jp* wlkdistance between them is doubled?

  14.27: Two spherical, non-rotating planets, X andaf6y b(yfe e/ci70g dz6wpf0,Y, have the same uniform density. Planewyd,izf cepf7yb0g(0 /f6e a6t 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 the same uniforgh7(c 9ctf dl;m density. Planet X has f( hcgc9;ltd 7twice 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 c jyaov),k:wlux8 m84 can be calculated if it is orbited by a small satellite by setting the gravitational force on the satellite equal to the centripet) jc:8,aw xlmkuo v48yal force on the satellite. Which of the following would NOT be required in this calculation?

  99.11: Assume that the Earth attracjt bnu.j(9:o 2 dzmvga, +b o:bdqpddq2y25b *ts 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 to which of the folloob5 b2jz+dj dp9g2:v uo*b:q .ydd,m ta(qnb2wing?

  14.30: Considering only the Moon-E;h1hqlh)wdu8wxz)x 8 s(rc/opx dg; (arth system (ignore any influence of the Sun), which one of the following best expre dhp rwlu8)dg; )xqxx osc;h(/8z 1(hwsses the magnitude of the Moon’s acceleration about the Earth?

  02.19: As a rocket blasts away from the earth with a cargo for th z;xl-ur1v ud+e international space station, which of1 z+u;dvxrl -u 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 r8 7mg5/0hct ytvhmj- Moon experiences the same gravitational force as a second object at the surface of the Earth. Which of the following would be8 5vtmgt- my07c/rjhh a reasonable conclusion?

  00.24 Consider an object that has a mass, m, and a weight, W, uh/am2m-c sbepk7k *8qkc610 y cpbk6at 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 distance halfw mkc e hp8a7*0c bqkmcu6-1pks b6/ky2ay between Moon’s center and its surface?

  96.23: A hypothetical planet has seven times the mass ofyki-.)c3p4p-qigj wg Earth and twice the radius of Earth. The magnitude of the gravitational acceleration at the surface of this planet is mo-iqgp4w- 3ypk.i )cg jst nearly:

  98.24: A planet has a radius one-half that of Earth and a mass one-fifwqdhx):t ; wbz3(b1uy8g g6afaoon*m w 9wt0+th the Earth’s mass. The gravitational acceleration at the surface by(*; f)agn t 8w0o1h6xg9 b:wwquwmzo ta +d3of the planet is most nearly

  08.38: Akg 1200 satellite orbits Planet X in a circular sx;rp tt wxgd;7a )x64orbit with a constant speed of 5,000m/s. The radius of orbit is 7,500,000 m. What is the magnitude of the gravitational force exerted on the sag7 w6pd ;xxt xas;t)r4tellite by Planet X?

  94.34: A hypothetical plgo7 x*1vbg4 ow(2uwuxanet 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 th 2xwugo71(u wvgb*xo 4e planet to complete one orbit?

  97.12: Two artificial satellites, 1 and 2, are put into circular orbit at the saoj( lectsp *gf39ttj b7vt++* me altitude above Earth’s surface. The mass of satellite 2 is twice the mass of satellite 1. If the perig3v*st* ( b7t jp+9olcj tf+teod of satellite 1 is T, what is the period of satellite 2?

  15.22 Satellite 1 makes a cir7;:u,rdh q wyccular 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 +cf.- vqe : ,zsj;e jhiz(zm; 3ku3pxra scale registers , zk(3j.z3r -jp+zq;;hmxfu i:cvs ee. If the Earth were to stop rotating, but not change shape,

  10.42: A comet moves in an elliptical orbit around the sun. As the /z qm42vlzm+r comet moves from aphelion (the point o4/+vlrmzq2m z n 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 showns9haeixh* - j1, 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 h 9x-as* 1ejhiof 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 with sfa61;z 9jcumc peed 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-major axis a of this new elliptical ormj ;u9ccz6fa1bit is