08.19: Kepler’s Second Law about “sweeping ou i3e /mjhj:o)jt equal areas in equal time” can be derived mostji/jj3:he )om directly from which conservation law?

  16.17:“All planets in the solar system follow elliptical orbit9o4pqrr:o x4v q)k 7cvs with the Sun located arxoc4q4q:o9 v7vrpk)t one focus of the ellipse.” This statement is best summarized by which one of the following choices?

  99.21: What happens to the force of gravitational attraction between two 5 5w1 7 rylu,f tsjumvfo2s:i5small objects if the mass of each object is doubled and the distance between their ce2l ,s 5m wtfj1vyufi:uo5 5rs7nters is doubled?

  95.09 Two spherical bodies attract each oc3uuwrjmdt 4 n -d4x,0ther with a gravitational force of 4.0 N. What will be the force if the distance between them is rjd4,c-x u4t0wnmd3 udoubled?

  14.27: Two spherical, non-rotating planets, X andY, haverxny: a1)o xgk,d6sfn )e6 f*w the same uniform density. Plaf1en,sk:6arnx w*f )gdxoy)6 net 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-rotating planets, X and Y, have the same uniform g6s fb3 1ik-fudensity. Planet X has twice the radius fib3 6k fg-1usof 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 orbt)ha 5bawxb;b 25bqrw7m11nsited by a small satellite by setting the gravitational force on the satellite equal to the centripetal )wnb7b52 w mbb1;5 ash1qaxtrforce on the satellite. Which of the following would NOT be required in this calculation?

  99.11: Assume that the Earth attracts Jf( cd om ,z 70fz(2jpj7oo2wsfohn Glenn with a gravitational force F at j(( ff0z2od so2zf,77owpcj m 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 closest to which of the following?

  14.30: Considering only the Moon-Earth syste(o rbqgkr602608 o xrnsb4xxkm (ignore any influence of the Sun), which one of the following best expresses the magnitude of the Mo 6g4xr(b6xrbk 0oo0q82rs nkxon’s acceleration about the Earth?

  02.19: As a rocket blasts away from the earth witheq.kd y9tm/cn c8rj19xja re 9zo30 l( a cargo for the international space station, which of the following graphs would best represent the grknjdc(3 m tq col099z 9e8axj1/err .yavitational force on the cargo versus distance from the surface of the Earth?

  99.33: One object at the surface of t19f tlc )5vgwehe Moon experiences the same gravitational force as a second object at the surface of the Earth. Which of the following would be a reasonable conclusegw 9f )clv5t1ion?

  00.24 Consider an object that has a mass, m, aepnb7b-ao;p4f,cyo(ie yt2( nd a weight, W, at the surface of the moon. If weea,oppn yiec( 7 4;tbf-(b 2oy 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 between Moon’s center and its surface?

  96.23: A hypothetical planet has seven times the mass of ,ym9 qev20 tkaEarth and twice the radius of Earth. The magnitude of the gravitational acceleration at t,2ay km09veqthe surface of this planet is most nearly:

  98.24: A planet has a radius one-hans.ngv6f-.r.ea w n;.ivy+ hzlf that of Earth and a mass one-fifth the Earth’s mass. The gravitational acceleration at tgfh 6-v.yn .v s .wzn+;na.erihe surface of the planet is most nearly

  08.38: Akg 1200 satellite orbits Planet X in a ciryodz t e 8(o69plkl2k,cular 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 forc2lt,dzoklkeo 6py 8 (9e exerted on the satellite by Planet X?

  94.34: A hypothetical planet orbits a star with massn* h z55jukcb*tm ;2ts 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 it take for the planemu;52z5tth nbj*kcs*t to complete one orbit?

  97.12: Two artificial satellites, 1 and 2, are put into circular orbit at the jl5r ad8o7n2eg(hj. wsame altitude above Earth’s surface. The mass of satellite 2 is twice the mass of s agjo7weh dlr2.jn5 (8atellite 1. If the period of satellite 1 is T, what is the period of satellite 2?

  15.22 Satellite 1 makes a. w pcquw.vgfz/-z; x5 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 following problem, the word “weight” refers to thevw /5(fffz/de9 p/m.ewrkq4 c force a scale registers. If theff( /d f/49zc wm./r 5kepqvwe Earth were to stop rotating, but not change shape,

  10.42: A comet moves in an * p+lwi /2 j;e9qfjatyelliptical orbit around the sun. As the comet moves from aphelioy+jetf ji q*aw lp2/;9n (the 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 star system shown, the twx2exxv3 d kr.gii 0s;ki,2g q+o stars follow circular orbits about the system’s center of mass. The stars are separated by a distance D that is large compared to x2 v,ki3de+rs giiqxkg.;x 02 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 valy .a,ii :ny +pn(wow)nd orbital radius R around a heavy stationarwnipy .:(l)i+wy n, oay 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 terms of R, the size of the semi-major axis a of this new elliptical orbit is