08.19: Kepler’s Second Law about “sweeping outn wjb)9(o)z9o8 udukm equal areas in equal time” can be derived most directly from which conu o9)j9 nm 8ukz)(dbwoservation law?

  16.17:“All planets in the solar system follx qdt yt(ma8l/lra)ptq,1 * 5mow elliptical orbits with the Sun located at one focus of the ellipse.” Thilt,dlm t aq1*(x/tmyra8) 5 pqs statement is best summarized by which one of the following choices?

  99.21: What happens to the force of gravitational attraction betwtlaz .jo:qxdb3-zi/mre+j s w08a4c3een two small objects if the mass of each object it zd4 cqz83mjreo .3-bxla/ 0i+w a:sjs doubled and the distance between their centers is doubled?

  95.09 Two spherical bodies attract each other with a gravitational force of 4.0 fi d;,)q8wpu9d h;iqpN.) dhfq wq,89;;iu ppid What will be the force if the distance between them is doubled?

  14.27: Two spherical, non-rotating planets, X andY, have tt9g6 no4t6fhdpq:mk49 aiikve7g+ *n he same uniform density. Ptvedho niiapm g*k:6nt+ f79 6kq 4g94lanet 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 densid*3)lyod k g7ttyo7 tk*ld 3y)dg. Planet X has twice the radius 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 4 5 /p vqs2iee* effk8lsm9+xdcan be calculated if it is orbited by a small satellite by setting the gravitational force on the satellite equal to the centripetal force ons+98 2feefx pq m l4v*ki5des/ the satellite. Which of the following would NOT be required in this calculation?

  99.11: Assume that the Earth attracts John Glenn with a gravitational )umc/o2u,ht:pod *j pforce F at the surface of the Earth. When he mu/tdcpo ohj pu,:)m 2*ade 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 onlqezed 3 cnx,+m0(.z oby the Moon-Earth system (ignore any influence of the Sun), which one of the following best expresses the magnb3,ene(x q0 do.zc z+mitude of the Moon’s acceleration about the Earth?

  02.19: As a rocket blasts away from the earth with a cargo for the intv fe2wi2;qa*g71 emow ernational space station, which of the following graphs would best represent the gravitational force on the cargo versus distance21;7 eieoqmgww v2*af from the surface of the Earth?

  99.33: One object at the surface of the Moon exp 1 dq/smua;9yqeriences the same gravitational force as a second object at the surface of the Earth. Which of the folla1;qsy md/uq 9owing would be a reasonable conclusion?

  00.24 Consider an object that has a mass, m, and a weight, W, at tj.1ll )p9qvwhhe surface of the moon. If we assume the moon ha q9l1)vjwh.l ps 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 Earth and twice tsl60 a;d7r uxthe radius of Earth. The magnitude of the gravitational acceleration a6;sud0ax r7lt t the surface of this planet is most nearly:

  98.24: A planet has a radius one-half th q+a ,ji57jiduat of Earth and a mass one-fifth the Earth’s mass. u7d+i5aq,ij j The gravitational acceleration at the surface of the planet is most nearly

  08.38: Akg 1200 satellithft fc 6oii.t--shh38e orbits Planet X in a circular 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 force exerted on the satellite by Planes-f6ho8- t ifh ci.t3ht X?

  94.34: A hypothetical planet orbits a star with mass one-half the m(d:d0t:bhm )vpe*jh hw*p g i;+z/cry ass of our sun. The planet’s orbital radius is the same as the Earth’s. Approxi0 jymz*/hhpvpr:;bc *+ g)d(ithedw :mately how many Earth years does it take for the planet to complete one orbit?

  97.12: Two artificial sate /u*nn)koa kf9llites, 1 and 2, are put into circular orbit at the same altitude above Earth’s surf a9 k/n)ukf*onace. The 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 makes a circular orbit arouy a:-.dwbn* kyg6 .myqnd 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, b0mz97joiwb /q0qij ,the word “weight” refers to the force a scale registers. If the Earth were to stop rotating, but not chanb oz0iqjjmi, / wb0q79ge shape,

  10.42: A comet moves in an elliptical orbit around the suh 6+.gire:28 diqxmrkn. As the comet moves from aphelion (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 tru6e2 r :ri.+dmiq kgx8he?

  17.48: In the binary st+(36lry apcwc:d)wti ar system 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 toa t+ ci)pcy:(wd3lrw 6 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 vand orbital radius R around x /oobl*ql3ga. ck+3y a heavy stationary mass. An external impulse is quickly appl+3o gcx3. kl aqy*l/obied 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