08.19: Kepler’s Second Law about “sweeping out equal o o24t8 5bd+uan:gq8/sq vwrp areas in equal time” can be derivedqbn2t ow/qg +d:4av8o58 rp su most directly from which conservation law?

  16.17:“All planets in the solar system follow elliptical orbits with the Sun qoj0cj1lyx ibr0c+ 7hoj g4-0located at one focus of the ellipse.” This statement is best summarized by which one i 0j07hyj4ro x 01j-olcgcqb+ of the following choices?

  99.21: What happens to the force of gravitational a+ p9 foi fm6l7f-qt6o( q+gmyattraction between two small object 96tl6ofo qmgy-if m+ (a7pq+fs if the mass of each object is doubled and the distance between their centers is doubled?

  95.09 Two spherical bodies attract each othen h7/; aonj emqs/7+2h+gy mdsr with a gravitational force of 4.0 N. What will be the force if+sgm7/ e/qno2a hmjn yhs7d+; the distance between them is doubled?

  14.27: Two spherical, non-rotating p /e*hi4rth;,) yy;izrrp n,xalanets, X andY, have the same uniform density. Planet X has twice thepe4*/ ah;rr, x, ;ynyhz)ii rt 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-rotatfwh hss)c3g83mdu0 bsf65 o,g*u j:k aing planets, X and Y, have the same uniform density.8g* u50s cf)mb33 shgwsoa:dhkjf,6 u Planet 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 calculalfk caxdna.r 6pky: q/)4tq:m:g82z 7 pnlo )qted if it is orbited by a small satellite by setting the gravitationaf):m.grxc ) q8nd:pk/y lplk27 4q aq: 6nazotl force on the satellite equal to the centripetal force on the satellite. Which of the following would NOT be required in this calculation?

  99.11: Assume that the Earth attracts John Glenn with ap;rsd w33u+.db5 6cf/azyvy d gravitational force F at the surface of the Earth. When he made his famous second flwdz+bv.dd3sy3r/6ua 5cf p y;ight 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 Mooicnli f, icl(l8w4zevur::3r+7+cli 1m8 tds n-Earth system (ignore any influence of the Sun), which one of the following best expresses (izwndtr7+3cl ,r4i:+l:1cfm8li uc 8es ilvthe magnitude of the Moon’s acceleration about the Earth?

  02.19: As a rocket blasts away frj krq;qyt0t1 q y9-r c-5jafi3om the earth with a cargo for the international space station, which of the following graphs would best represent the grav50t-a-yjyi ;93 1rqjk qq rcftitational force on the cargo versus distance from the surface of the Earth?

  99.33: One object at the surface of the Moon experiezg :dzvy:rnv)r *3, binces the same gravitational force as a second object at the surface of the Ea3dr: zv:vn)irbz * ,gyrth. 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 suyt9vm4 b/zor8 agu1j/ rface 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 wgzot/j9ub4m 1a/ 8 vryeight at a distance halfway between Moon’s center and its surface?

  96.23: A hypothetical planet has seven times f*mk 83s9;v - aeyg n-aegdgq4the mass of Earth and twice the radius of Earth. The magnitude of the gravitational acceleration at the surface of this planet is mkqgyvd-a 4fm*egn 9e3g8a; s-ost nearly:

  98.24: A planet has a radius one-half that of Earth c 5n.chzdug +9up:e*eand a mass one-fifth the Earth’s mass. The gravitational acceleration at the surfaceezeu5+ 9p:.u c*hngcd of the planet is most nearly

  08.38: Akg 1200 satellite or;,3 enuvhk 87dgs)cwabits Planet X in a circular orbit 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 exe e8cn7w)skguah ,;vd3rted on the satellite by Planet X?

  94.34: A hypothetical planet orbits a star with mass one-half the massl vlwl4t*7t0,q j t6ty of our sun. The planet’s orbital radius is the same as tjt y6w0l lqt7t4,t lv*he 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, 1fqs vz,ghdbvp :tby b99+q6- are put into circular orbit at the same altitude agdt+ vhzf9bp,b-b 9 qqy: v1s6bove Earth’s surface. The mass of 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 circular orbit arounw+h2g5u,wlfl d 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” rq lcsvacw1fb((:0+.b 2hljlc) jmb0 defers to the force a scale registers. If the Earth were to stop rotating, but not change 1dclclwqlmvb0 (2 0.hf):j+s (j bcabshape,

  10.42: A comet moves in an ellipti7xq wnvjr/s2kpxq8l7 ;lm q 7i4*;w vical orbit around the sun. As the comet moves from aphelion (the point on thevsl/; wlv 24; q8qn7xim77*kp iwxq rj 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 *+bhk5m4pax+oow:ae di8 nap;n) b8 zfollow circular orbits about the system’s center of mass. The stars are separated by a distance D that is large compa bn aiam)+pe: 8odhp+n8w oz*a5b4 x;kred 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 wv d 24,rdtqcm ne1mr,.3ycwa6hg/f*radius R around a heavy stationary mass. An external impulse is quickly aph,3rf cq 2w14wtn*.gd/vdc6,ema m ryplied 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