08.19: Kepler’s Second Law about “sweeping oo.ccti1 8 a)nput equal areas in equal time” can be derived most directly from whiticn o)a p1.8cch conservation law?

  16.17:“All planets in the solar system follow elliptical orbits with the S xcwwt*: lzg9)dehuu7(4lh ax )vs(7w un located at one focus of the ellipse.” This swh9 w)l x7hdwg (u (7vt:leu)xsca *4ztatement is best summarized by which one of the following choices?

  99.21: What happens to the force of gravitatiz tk5 zlz+.;9ht g;c4bj 4bhwyonal attraction between two small objl5zhty b.+4 hj b4 tw9zkz;g;cects if the mass of each object is doubled and the distance between their centers is doubled?

  95.09 Two spherical bodies attract jes/ zv( b5 f9(m* yiib:t*biseach other with a gravitational force of 4.0 N. What will be the force if (i* sfbebz9*5 ivsyj/m:t(b i the distance between them is doubled?

  14.27: Two spherical, non-rotating planets, X andY, have the sai;izt8cm9zcsd wx/5j r7a 0: zme uniform density. Planetczm8az5 9:w0j dzt7i; ri /sxc 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-rot1 mjyh+k z+jm2-zi iu q*rb1f2ating planets, X and Y, have the same uniform density. Planet X has twice the radius of Planet ijjfz r-zub+2m1 qk1 hm* +i2yY. 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 s2cd1l:pt (bnc: w pv sgj6uxk+k g68f,atellite by setting the gravitational force on the satellite equal to the centripetal force on the sakf b,2:px +:8v (s61 lgpknwd cjcu6gttellite. Which of the following would NOT be required in this calculation?

  99.11: Assume that the 3u-k q6dx ny;vEarth 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 -u ;yx3qnv6kd in orbit was closest to which of the following?

  14.30: Considering only the Moon-Earth system (ignore any spfmbx;0 m6 rcb(-q1 tinfluence of the Sun), which one ofmxsqc0( b ;rm-6pfb 1t the following best expresses the magnitude of the Moon’s acceleration about the Earth?

  02.19: As a rocket blasts away from the earth with a cargo for therc ab -90r9mhr g7/vfi international space station, which of the following graphs would b vm0c birf/9rha9g-r 7est represent the gravitational force on the cargo versus distance from the surface of the Earth?

  99.33: One object at the surface of the Moon experiences the same gravitationalohb+5w *-ioc n force as a second object at the surface of the Earth. Which of the following would be a reasonable concln oi+bhc5w*o- usion?

  00.24 Consider an object that has a mass, m, and a weight, W, at the surface o0 5k oldnurr,,f the moon. If we assume the moon has a nearly uniform density, whicru5 k,d ol,rn0h of the following would be closest to the object’s mass and weight at a distance halfway between Moon’s center and its surface?

  96.23: A hypothetical planet has seven t o-q)rn01mkjs+ :nwluimes the mass of Earth and twice the radius of Earth. The magnitude of the gravitational acceleration at the surface ofwn +uro:lnk)-s0mj1 q this planet is most nearly:

  98.24: A planet has a radius one-half that of Earth and a mass one-lmi6edqh7xc).u f t7 -fifth the Earth’s mass. The gravitational acceleration at the6u7d fq 7lx)ti-e.h cm surface of the planet is most nearly

  08.38: Akg 1200 satellite orbits Planet X in a circular orbit witq b rl58-naruufn; 02xh a constant speed of 5,000m/s. The radius of orbit is a ;rnlqxr5f82-0uubn 7,500,000 m. What is the magnitude of the gravitational force exerted on the satellite by Planet X?

  94.34: A hypothetica +.-wq4ox3 1* vpleyxalwem*tcqgz67l planet orbits a star with mass one-half the mass of our sun. The planet’s orbi36ce1l+ lxva 4qq-*ozwpxm*eg 7. tyw tal radius 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, are pqo*af6mv gi: 6ut 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 is T, whatq:6 i *fvaogm6 is the period of satellite 2?

  15.22 Satellite 1 makes a circular orbit around the3.3pu+hm owq s 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 followi5yt qr,fu u,8e 0lmv p1ar)y/nng problem, the word “weight” refers to the force a scale registers. If the Earth were to stop rotating, but not change sha0 8,yl 5yf,tu nvuam1/r e)rpqpe,

  10.42: A comet moves in an ellipticalni33+cb ybg n:(eahu8 orbit around the sun. As the comet moves from aphelion (the point on the orbit farthest from the sun) to perihelion (the point on the orbit closest to the sun), which of the following reby+ nu3a e8hin (c:3bgsults is true?

  17.48: In the binary star sz5cnbt 5mlsq b8u4 8s6ystem shown, the two stars follow circular orbits about the system’s center of mass. The stars are separated by a distance D that is large compare n tqszb8b6sm5 5lu48cd to their size and are subject only to their mutual gravitational attraction. 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 with speed vand orbital r q7iuvzoo /9o1adius R around a heavy stationary mass. 1zuoiooq/9v7 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 orbit is