08.19: Kepler’s Second L6f*in aq zp/:+;agc uoaw about “sweeping out equal areas in equal time” can be derived most direc:+agi uoqp6*c; n fza/tly from which conservation law?

  16.17:“All planets in the solar system follow ; ag3.eylfe bv0+q) 0sau-fmyelliptical orbits with the Sun located at one focus of the ellipse.” -y03 vseffb)+;yl.gqma0uea This statement is best summarized by which one of the following choices?

  99.21: What happens to the fb m(zp uot v iq:z+7dn3/4j4szorce of gravitational attraction between two small objects if the mass of each object is doub/mv44puo7 z ti j sn3(zz:+qdbled and the distance between their centers is doubled?

  95.09 Two spherical bodies attract each other with p*vz + pwdpi )e-)w.qxa gravitational force of 4.0 N. What will be the forv. *)- pwzewpd+)ipx qce if the distance between them is doubled?

  14.27: Two spherical, non-rotating planets, X andY, have the sadq bg:j o pl96cz+ 0sr)8l*fyk2 zj:awme uniform density. Planet X has twifok 6jz+ cyp)l8:* r:jlqs0 29dbwg zace 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-rotatz9;3cheqz*5zj t8 ck king planets, X and Y, have the same uniform density. Planet X has twice the radius of P chq*z8 z3z5jck;e k9tlanet 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 orbite p*o) amaq3 1v;*bdkrid 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 requiredq1d*p*3iv omaa)bk ;r in this calculation?

  99.11: Assume that the wkigb) qim63soy0h.+ Earth attracts 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 John Glenn while he was in orbit was closest to which of the followigq 36 os0h .iwb)ik+myng?

  14.30: Considering only the Moon-Earth system (ig5q)g7df6pmne eq: nv0nore any influence of the Sun), which one of the following best expresses th 0q:n 6dp5n7)fmevegqe magnitude of the Moon’s acceleration about the Earth?

  02.19: As a rocket blasts away from th7s6ki n ;uxj s eo0xxp/30xr8pe earth with a cargo for the international space station, which of the following graphs would best represent the gravitational force on the cargo versus dii8 ;n3xk jx s/07roepx xups06stance from the surface of the Earth?

  99.33: One object at the surface r ix9wvk6 0zjc1ad5y+a2nsl 2 of the Moon experiences the same gravitational force as a se r 02 dwix5+n69 2lv1kcajyzsacond 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, aw7 orjz,lh.d*x;h xx: nd a weight, 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 between Moon’s center and its surface*: w,ho7d.j r;zxhxl x?

  96.23: A hypothetical planet has seven times thetb g29b +z(y,mk szl*n mass of Earth and twice the radius of Earth. The magnitude of the gravitational acceleration at the surface of this planet is most nearly:,*ktlbnz 2bmg y+9(zs

  98.24: A planet has a radius one-halflh92yy vs0 eb+ that of Earth and a mass one-fifth the Earth’s ma yhyev+9sb 2l0ss. The gravitational acceleration at the surface of the planet is most nearly

  08.38: Akg 1200 satellite orbits Plane5plo1 st7 nv1.gez*w ht X in a circular orbit with a constant speed of 5,000m/s. The radius of orbit is 7vnw15sz1hl.pegot 7 *,500,000 m. What is the magnitude of the gravitational force exerted on the satellite by Planet X?

  94.34: A hypothetical planet or),grvwko aw*euza93 (bits a star with mass 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 thewag9z,ve ()wo * 3urak planet to complete one orbit?

  97.12: Two artificial satellites, 1*p.fvmk u. gd, and 2, are put into circular orbit at the same altitude above Earth’s surface. T.v, *mp.ug fdkhe mass of 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 mak);hw ms68lcje es 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 following problem, the word “weight” refers8 s6avkx-mp8i,w k(gl to the force a scale registers. If the Earth were to stop rotating, but not change sha8kl-mps va8,w k6xig(pe,

  10.42: A comet moves in an elliptical orbit around the sun. As the comet moves fzagycr.fm 2/2c84xeg k5ura- rom aphelion (the point on the orbit farthest 58f/a4a cc k.e zry- grx2um2gfrom 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 systekxl a/60mtt( im shown, the 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 of the binary star mlxi/ t0a (kt6system?

  06.50: A rocket is in a circular orbit with speed vand or 42 jsa:ge /bv.8yufivbital radius R around a heavy stationary mass. An external impulse is quickly applied to the rocket dis4 iy8ue vgfavj2./b:rectly 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