08.19: Kepler’s Second Law about “sweeping out equalymf3g;evqa n( u6 0x:o areas in equal time” can be derived y fnvmx3eq;06: og u(amost directly from which conservation law?

  16.17:“All planets in the solar system fol49gxm4 ab/ ytqlow elliptical orbits with the Sun located at one focus of the ellipse.” Thimx/ga t y944bqs statement is best summarized by which one of the following choices?

  99.21: What happens to the force of gravitatio8l ky ;5+ess nfxj)ii(2zw;l onal attraction between two small objects if the mass of each object is doubled and tikj2f olw;;s( ziel 8ny)sx5+he distance between their centers is doubled?

  95.09 Two spherical bodies attract each othtnvkvf)3t9 /t al5; ewer with a gravitational force of 4.0 N. What will be 9etn5;v/3 tval w)tkf the force if the distance between them is doubled?

  14.27: Two spherical, non-rotating planets, X andY, have t-+tj mfxir6w0uoq t2;he same uniform density. Planet X has twice th i+2;6tmutor0f j qw-xe 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 pmg 8p i5patw7;wp3 6vthe same uniform density. Planet X has twice thi;w76tmppwp38 5avg p e 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 calculated h a)bigul8cq9iq2b42if it is orbited by a small satellite by setting the gravitational force on the satellite equal to the centripetal force on the satellite. Which2i8qhgb9 a )2il4cbqu of the following would NOT be required in this calculation?

  99.11: Assume that the Earth attracts John Glenn with a gravitational sshn7 o* .x4 o4cfqf3 nj8s 7kkly//miforce F at the surface of the Earth. When he made his fak/m 7nfslcx7j /8yo n43.hqsfiko *s4mous second 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 influeae+4jlz/ 3q) xh5odjo-cbjf. nce of the Sun), which one of the following best expresses the magnitude of the Moo5. 3)4fol+dxq/cjo z -jaebhjn’s acceleration about the Earth?

  02.19: As a rocket blasts away from thef,1xy9 biu+ 4za zb 8l*,dloxhyo*z5r earth with a cargo for the international space station, which of the following graphs would best represent the gravil xz49b*l, oryuxd*5yfhb i, 1+azzo8 tational 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 gravitatio)s 9vuw1rx+nt nal force as axs9)t r n+1uvw second object at the surface of the Earth. Which of the following would be a reasonable conclusion?

  00.24 Consider an obqi 9sax6 p2de srxk p4cgixui:a8 ):xl z0;5l-ject that has a mass, m, and a weight, W, at the surface of the moon. If we assume the moon has a nearly uniform density, which of th)a:siaskqu;g4-pi:60z 5x lp d9x iex2 crl x8e 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 times the mass of Earth and t+/c gz /js8c9v7lzf qhwice the radius of Earth. The magnitud/9 8z/gj 7+qsc fhzcvle 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 anj 8m(hlj,g 5z:;r apxwd a mass one-fifth the Earth’s mass. The gravitational acceleration at the surface of the lm8r zh( ;,wxp5jj:gaplanet is most nearly

  08.38: Akg 1200 satellite orbits Planet X in a circular orbit *8cb 39)hm 6pk lhjvwewith a constant speed of 5,000m/s. The radk3m9 elph 8 chvjb)6*wius of orbit is 7,500,000 m. What is the magnitude of the gravitational force exerted on the satellite by Planet X?

  94.34: A hypothetical planet orbits a star with mam 7sx7vqx+l7lf c6gp5qqc37hss 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 i 6sq7l5hl gc m +x3q7fxvq7pc7t take for the planet to complete one orbit?

  97.12: Two artificial satellites, 1 and 2, are put into circulsmm*gd.,. zbuyfumcl7(5 /e iar 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 satel7f(emb slicy./ . d5*uzmum g,lite 1 is T, what is the period of satellite 2?

  15.22 Satellite 1 makesqv* tw3iuc8p.c xy(:s a circular 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 followi3tnn8+9e fk xlng problem, the word “weight” refers to the force a scale registers. If the Earth were to stop rotating, but not c e+k9xlt8fnn3 hange shape,

  10.42: A comet moves in an elliptical or b/o(nd*v;skd1c/io;eb p. zbbit around the sun. As the comet moves from aphelion (thzickb ;son/d. ;/bb(1od e*vpe 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 fib)(j7y jfjn-.t25 ezuy4mlstar system shown, the two stars follow circular orbits about the system’s center of manyeb 4t zjj.-y75mf)l 2i(fjuss. 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 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 cinq *fe- *qm7kzrcular 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 and the rocket’s speed is slowed toemq f-*qnz k*7 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