08.19: Kepler’s Second Law about “s 4c;vlmip(4m-pnfl7k weeping out equal areas in equal time” can be deriv fli m4mn(;-pcpkv4l7 ed most directly from which conservation law?

  16.17:“All planets in the solar system follow elliptical orbits with thek5l 3uus*i lmiq)dhpcf6;+ +u Sun located at one focus of the ellipse.” This statement iqi++u) l5fd cmulp6h 3;kiu*ss best summarized by which one of the following choices?

  99.21: What happens to the force of grav w oe 2gydfd/1fen)n.3itational attraction between two small objects if the mass eo1yf .fngw2)d3den / of each object is doubled and the distance between their centers is doubled?

  95.09 Two spherical bodies attract each other w 9gfvskzx + + 6fql-bqn81x2enith a gravitational force of 4.0 N. W9ge8b -s lf1xxqq knf 6+2v+nzhat will be the force if the distance between them is doubled?

  14.27: Two spherical, non-rotating planets, X andY0/(iken b .e;1xktwq a, have the same uniform density. Plakq ewk0x t.n(i1bae; /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 den7;zd9-txxoo d /giydl7vp qg.1h;5uq sity. Planet X has twice the radius of Planet Y. Lel ugvo9 -xh.odtiqpdg7x 1;;/d5qzy7 t $v_x$ 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 orbit02 oo, 6phrtfged by a small satellite by setting the gravitational force on the satellite equal to the centripetal force on the satellite. phrg,tf6oo20 Which of the following would NOT be required in this calculation?

  99.11: Assume that the Earth attt*c hepg8 ,tcx3rkbqp0m e/)1 racts John Glenn with a gravitational force F at the surface of the Earth. When he made his famous second flight in orbit, the gravitational force on Johxeke8 gb 0)3/1cc r,thp*tq mpn Glenn while he was in orbit was closest to which of the following?

  14.30: Considering only the Moon- imf8pv7n f,3zEarth system (ignore any influence of the Sun), which one of th7f,fmp38 nziv e 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 cargd8s we+)hnxjn9kj w .0o for the international space station, which of the following graphs would best rnwk9. sxdh j) 0wjen8+epresent the gravitational force on the cargo versus distance from the surface of the Earth?

  99.33: One object at the surface of the Moon experieny7 hrj/a o t*zv4t+*c3dp 7gvgces the same gravitational force as a sg* 43d7*/+ r7pvhgvtco j zytaecond 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, aehjz)j:i 9 mt9z+*ujond a weight, W, at the surface of the moon. If we assume the moon has a nearly uniformjt *uzojj9i:mzeh +)9 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 ofn*8jz/t .ru ds Earth and twice the radius of Earth. The magnitude of the gravitational accelerati /du*8.jr stnzon at the surface of this planet is most nearly:

  98.24: A planet has a radius one-half that of Earth and a mass one-fifth the ga44u4um9 uzal-vj 4qEarth’s mass. The gravitational a4 4u9z-uaa4mvq l4 jgucceleration at the surface of the planet is most nearly

  08.38: Akg 1200 satellite orbits Planet X in a circular orbit with a constant sp ++*lntebwpr8f: im bur5c +7oeedebi+r *ct+n:bpm r5w8luf+ 7o 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-half the mass d.ycnx s6rtm2v+ku 5y2a-vv( of our sun. The planet’s orbital radius is the same as yk.6+ u-nca(vds vx22t5m yrvthe Earth’s. Approximately how many Earth years does it take for the planet to complete one orbit?

  97.12: Two artificial satellites, 1 an./w u ,fwjgn cs;.pqc9d 2, are put into circular orbit at the same altitude above Earth’s surface. The mass of satellite 2 isnqw;gpc s.wc9/j f ,.u 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 Earth with a r,it /-zbz r3rmadius $r_1= R$. 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 the for dx)/ kl,j/ji,ez4jps,l m p5cce a scale registers. If the Earth were ecjz ,i,/xp5lljpmjs4, d /k)to stop rotating, but not change shape,

  10.42: A comet moves in an elliptical orbit-7gok utfx7 s:/ vneli,bg: *i around the sun. As the comet moves from aphelion (the point on th/gb: gnvot kf7,lux-s*: iei7 e 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, the4sbu zt y 2fhbip *v6 9q6.j+74eqwuyv two stars 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 gravitational attraction. The orbital period of the star of mass M is T. Which one of the following choices represents the total mass o9hf*uje66.7 iq ysb4 2zpy4vt+w bvqu f the binary star system?

  06.50: A rocket is in a f51c 1qp3k;em cl ug(kld.r mi; 2yt+lcircular 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 to v/2, putting the rocket inmk3lc5c2.u (+;kld;p tiqgefm 1 1rylto an elliptical orbit. In terms of R, the size of the semi-major axis a of this new elliptical orbit is