08.19: Kepler’s Second Law .ugry4l:68e y ts doz;about “sweeping out equal areas in equal time” can be derived mosd t6uo; eyg8z:.sl4y rt directly from which conservation law?

  16.17:“All planets in the solar system follow elliptical orbits with the Sun loc l2c7y7days i777wgezt 3rn;zgtw5. vm *vq0uated at one focus of the ellipse.” This statement is best summarized by which one of the follo27nt w t g.w 0dsc3 yyi77m; z*gqelz7va7u5rvwing choices?

  99.21: What happens to the force of gravitational attraction between g :jj hfg3r6c7q f4oe4two small objects if the 4qh ej643frfgg7 j o:cmass of each object is doubled and the distance between their centers is doubled?

  95.09 Two spherical bodies attract eacw1necy8:sm3 gh other with a gravitational force of 4.0 N. What will be the force if the distance betweegy31e8 m nc:swn them is doubled?

  14.27: Two spherical, non-rotating planets, X andY, have the same uniform densit:we*qjk.o1/ nfo cy( ior3 lah*m;p5ty. Planet X has twice the radius of Planet Y. Lq ieclf:ha y(otp.*o 15*/ kjrm;n3woet $g_x$ 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, havd*2 rdzny 4vf,e the same uniform density. Planet X has twice the radid,4 frd2* ynvzus 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 if it is orbited by a se0df+xsa:b8b n2 tfk 5mall satellite by setting the gravitational force on the satellite equal to the centripetal force o5en:bf+b t x 0ds8fk2an the satellite. Which of the following would NOT be required in this calculation?

  99.11: Assume that the Earth attracts John Glenn with *5rih4 xrb7 bta gravitational force F at the subr4 xi* tbr75hrface 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 following?

  14.30: Considering only the Moon-Earme )edvt a r .je2:9rgkju o,qs6 61vwni8,fv7th system (ignore any influence of the Sun), which one of the following best expresses the magnitude of the Moon’s acc 69qkiwmv rg)oe 8esj,r :fa,venu jd v.27t61eleration about the Earth?

  02.19: As a rocket blasts away frommtblcmn,o / n-y-yh.7vhn5pk1( 3d mzek 4m;c the earth with a cargo for the international space station, which of the following graphs would bcp7;mke/hmy31m5 c my4n ol-nkz t(v. b-,n dhest 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 gravic+ zv5wc0g3t:8 d emnqtational force as a secg5ecw8 mq03z: tdvc +nond 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, q4cb2.r4 pu-bh(i npp,x8 tud at the surface of the moon. If we assume the moon has a nearly uniform density, which of th,8hqu c(t.dpb 44x2ri-p nbpu e 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 hypotheticats+aiw * -emrz,+i at+l planet has seven times the mass of Earth and twice the radius of Earth. The magnitude of the gravitational acceleration at the su++a -m i+ sizetawt*r,rface of this planet is most nearly:

  98.24: A planet has a v+0d,10n1xqk yu yjamradius one-half that of Earth and a mass one-fifth the Earth’s mamx y1v,0+u dqj k0ny1ass. The gravitational acceleration at the surface of the planet is most nearly

  08.38: Akg 1200 satellite orbits Planet X in a circular orbit with a constant sce*mwn*cssok2f*s y.uw z,7 ,peed of 5,000m/s. The radius of orbit is 7,500,000 m. What is the magnitude of the gravitational force exerted on the cwuz*snfc. 7okym ,w*s e,s*2 satellite by Planet X?

  94.34: A hypothetical planet orbits a star with mass one-half ths30t (odzrfd4e mass of our sun. The planet’s orbital radius is the same as the Earth’s. Approximately how many Ear0d s4tdo(r fz3th years does it take for the planet to complete one orbit?

  97.12: Two artificial satellites, 1 4 f fe85x7nfr6ufz wt+and 2, are put into circular orbit at the same altitude above Earth’s surface. The mass +7fuef fft 6nrw8zx45of 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 around the E (n.(uwh(gtzkarth 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 to8 7rad6si.--2q: b ;enasi w:tadjww s the force a scale registersdw2 -tr:-sa7qibde8ww: ; naji6as.s. If the Earth were to stop rotating, but not change shape,

  10.42: A comet moves in an e9 e k5d:win,z6 besf7xlliptical orbit around the sun. As the comet moves from aphelion (the point on the 9kb5n zxw:ei76 de ,sforbit 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 t35gydg8qkdvvnw -(y 1 wo stars follow circular orbits about the system’s center of mass. The stars are separated by aq8d vk-gg1d 5nywy 3v( 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 ca;t3 j.d,q6gdi-fygs ircular orbit with speed vand orbital radius R around a heavy stationary mass. An external impulse is quafiy q ,;dj6.sdg-g3 tickly 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