08.19: Kepler’s Second Law about “sweeping out equal areas in equal time” canek) 4gs-yha bvp8:)*aorj mpg4y 5 )ag be derived most directly from wye4 k:bsam ggg)pv*) 8y)p-aha5 o4rjhich conservation law?

  16.17:“All planets in the solar system follow elliptical orbits with tcoj :8n(qh m2u/;nemtj,tsu 0he Sun located at out,2:enm 8umo nq;jjcs(t 0 h/ne 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 small tnd *b* .uw*7mlmw*mw objenwm l*bw7t*. mumw**d cts if the mass of each object is doubled and the distance between their centers is doubled?

  95.09 Two spherical bodies attract each other with a gravitaj+ *uq oajq( wiv:3fo3tional force of 4.0 N. What will be the force if the dq wa:f uj( q3iv+3o*ojistance between them is doubled?

  14.27: Two spherical, non-rotating planets, X andYoup2m)k ztj;-, have the same uniform density. Planet X kt- pzj; m)2ouhas 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, l ;1h:cj2artmiw5/q:d ynmq wv r3d,8X and Y, have the same uniform density. Planet X has twice the radius of Pla q w3qj8dn1va5c h m,irly2dm :t:;r/wnet 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 orbited by a small satwzx21h*v ak, b-ba3y yellite by setting the gravitational force on the satellite equal to the centripetal force on the satellite. Which of 2vb1z ,ba k-yahwyx *3the following would NOT be required in this calculation?

  99.11: Assume that the Earth attracts John Glenn with a gravitational force F atu1pi j729j wzx 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 followi 1xpw792j ujzing?

  14.30: Considering only +4f;pwc0 , pj quxu0frpld w5,the Moon-Earth system (ignore any influence of the Sun), which one of the following best expresses the magnitude of the pfru, jqufww ;l,p05d p0xc4+Moon’s acceleration about the Earth?

  02.19: As a rocket blasts away from the earth with a cars6 m71f ogz 51 ph85emw(wrxgzgo for the international soh5gsw 5 gmp w17zx8mf(1er6zpace station, which of the following graphs would best represent the gravitational force on the cargo versus distance from the surface of the Earth?

  99.33: One object at the surface of the Moon experiences the ipfg2j +d /qte*te.6bsame gravitational force as a s.fp 2etitj*e+6 bgq/ decond object at the surface of the Earth. Which of the following would be a reasonable conclusion?

  00.24 Consider an object ts(y6 pqde5ls,hat has a mass, m, and a weight, W, at the surface of the moon. If we assume the moon has a nearly uniform density, whiys, ds(e6p ql5ch 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 xhehlwt4crvt1 + 6/:u the radius of Eartheuw lxcr14v: +t t/h6h. The magnitude of the gravitational acceleration at the surface of this planet is most nearly:

  98.24: A planet has a radius ,8tg q2ty.z-b5 sc,yw+ azqcfone-half that of Earth and a mass one-fifth the Earth’s mass. The gravitational acceleration at the surface of the planet is +fg,zq y5cc.say-8,w zt2qtb most nearly

  08.38: Akg 1200 satelli3m-z jaxm :bcs)36va hte orbits Planet X in a circular orbit with a constant speed of 5,000m/s. The radius of orbit is 7,500,000 m. Whac)- z m:a6jvmbsh ax33t is the magnitude of the gravitational force exerted on the satellite by Planet X?

  94.34: A hypothetical planetir8nte; k 8x2x orbits a star with mass one-half the mass of our sun. Threx k; 2ni8x8te 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?

  97.12: Two artificial satellites, fl* +c/kebp. e1 and 2, are put into circular orbit at the same altitude above Earth’s surface. 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 2fp +/*ke lc.be?

  15.22 Satellite 1 makes a circular orbit around the Earth wtp,:nmv) a9.uj)ppug ith 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 7w;y ()yso.vqntfh( q” refers to the force a scale registers. If the Earth were to stop rotating, but not change sh( (o7yhn tw)v;q. sqyfape,

  10.42: A comet moves in an elliptisj ;k m9(vudjlv:z:y5 cal orbit around the sun. 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 :kl vy5;duzjv : (9mjsthe following results is true?

  17.48: In the binary star system shown, itfy:ec. r6d(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 tt6fe rc:.yd( iheir 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 around094wpqs/g ad9 0d glzq a heavy stationary mass. An external impulse is quickly applied to the rocket directly opposite tq 9gws/g qdp0ld0 a9z4o 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