08.19: Kepler’s Second Law about “sweeping z; hulc*lsz-1 out equal areas in equal time” can be derived most directly from; c*-lzl1hu sz which conservation law?

  16.17:“All planets in the solar system follow ellipticauj5t7ix2um e m+1u4lfl orbits with the Sun located at one focus of the ellipse.” This statement is best summarized by whichum 7t1xeufm i j+l524u one of the following choices?

  99.21: What happens tftnqlip;i w5s, . d)w (e7 qbo;*jyiq+o the force of gravitational attraction between two small objects if the mass of each object is doubled and the distance between their ce(n5sj)b yl7,qq itqwi d pi+;f;*.owenters is doubled?

  95.09 Two spherical bodies li8jn sxs1 ;,wattract each other with a gravitational force of 4.0 N. What will be the force i8js;s 1n ,iwxlf the distance between them is doubled?

  14.27: Two spherical,0vix w* i2 oma1kt khgk:zos4l+2+-rt non-rotating planets, X andY, have the same uniform density. Plan2+ v:t* s-2or 1kzktkih xwgliam0o4+et 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-rotatinovyt9 fh 5 x-p2n2dce.g planets, X and Y, have the same uniform density. Planet X has twice the radius of Plane2d5x.2v ce ty o9fh-npt 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 cbv/dxz s ea jkkc9*m4xe5w::)-nj/ycan be calculated if it is orbited by a small satellite by setting the gravitational force on the satellite equal to the centripetal force on the satellite. Which of the following would NOT be required in this cxs9cd5jkm/e )xejn*bwcv ayk:4/ z: -alculation?

  99.11: Assume that the Earth attracts John Glenn with a gravitationvhc1pi3tl s4/r -ti)tal 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 t3ts4tvrp)li1 -ih /cclosest to which of the following?

  14.30: Considering only the Moon-Earth4szw:2cx9u en wt*)sd system (ignore any influence of the Sun), which one of t2wtzdxe9sc*uw)4n :she 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 the i 4 ga 03peek )lrp73o08agyvym(ltu;wnternational space station, which of the following graphs would best represent the gravitational force on the c e)t 8yuao r0agl3w;g0mvkl(4 73yppeargo versus distance from the surface of the Earth?

  99.33: One object at the surface of th82)gjjnz7ms y e Moon experiences the same gravitational force as a second object at the surface of the Earth. Which of the followinjm s8yzg n)j27g would be a reasonable conclusion?

  00.24 Consider an object that has a mass, m, and a weig)lya*j tsfln59fpjrx*w5/ x 5ht, W, at 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 halfway betwee) 5rjx5lpja/fwt**9 s5fx y lnn Moon’s center and its surface?

  96.23: A hypothetical planet has seven times the macjc4(m1 lm3c bcn*8 osss of Earth and twice the radius of Earth. The magnitude of(nb8jo4mc 3 c*1mcls c the gravitational acceleration at the surface of this planet is most nearly:

  98.24: A planet has a rz 1,pll xz61p-xy im;3 um.ijcadius one-half that of Earth and a mass one-fifth the Earth’s mass. The gravitational accelerat 1x; jm .u3xci-y1plzm,6zlip ion at the surface of the planet is most nearly

  08.38: Akg 1200 satellite orbits Planet X in a circular orbit with a + ywzwoy 6(lc0constant spez(cy 6w0yow+l ed of 5,000m/s. The radius 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 mass one-half3uya)w/aw1 d f 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 the planet to complete one orbit?a) aw3d uw1fy/

  97.12: Two artificial s ;mp7m;,2:)oejxm ty 6gnuxtbatellites, 1 and 2, are put into circular orbit at the same altitude above Earth’s surface. The mass of satellux;xm ,b7:m 6oy;j 2 mep)tgtnite 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 cire 2m3e a;*wm por81mbbcular 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 p-r ;mqbem/4sj c d--n“weight” refers to the force a scale reg/pdc emnj m;s- -b4-qristers. If the Earth were to stop rotating, but not change shape,

  10.42: A comet moves in an elliptical orbit around the sun. As th2 u6mztz+jcs;k 1hi7 ue comet moves from aphelion (the point on the orbit faus7z+u;2kztm 16ch ij rthest 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 pwfm-(2c nn 7ecuh kw3r2d wwj-6zr;o97qea9stars 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 gravitationa n2d jwehe-2wc9r( w cp7u9km6wn7;-3or zaqfl 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 o9voou,hv 2 bb)rbital 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 t ubv9)o, h2ovberms of R, the size of the semi-major axis a of this new elliptical orbit is