08.19: Kepler’s Second Law mrj l uw qo5*nf,0c;h+v;z4d tabout “sweeping out equal areas in equal time” can be derived most directly from which conservation;wrc ft,ml 5jqd+h0n*v;ouz4 law?

  16.17:“All planets in the solar system follow y)6b5-jt(doh pj68 yjqq9b.gk qno 3lelliptical orbits with the Sun located at one focus of the ellipse.” This- byg8 n )h6(kjo3pd.5b9jyqj lqqt6 o statement is best summarized by which one of the following choices?

  99.21: What happens to the force of gravitatio a0ifkl6uy, 2onal attraction between two small objects if the mass of each object is doubled and the distance betwee6youl2i f a0k,n their centers is doubled?

  95.09 Two spherical bodies attract each other with a gravitational force oe iucayu. egf492; 0etf 4.0 N. What will ba 2 ft9yeueiue0.g;4c e the force if the distance between them is doubled?

  14.27: Two spherical, ei0 7qd bh8qj5ee0 4onnon-rotating planets, X andY, have the same uniform density. Planet X has twice the radius nqhbq oe58i0047jedeof 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,fmvsn 3bp.9y.tg68z c have the same uniform density. Planet X has twice the radius of Planet Yg6ms8t 3 .y9cnf bzvp.. 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 p f9//5 mrhtxwolanet can be calculated if it is orbited by a small satellite by setting the gravitational force on the satellite equal to the centripetal force on the satellite. Which of the followi o9 /xt/5mwrfhng would NOT be required in this calculation?

  99.11: Assume that the Earth k w8 crbjje);t;swn9 3attracts 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 oj r9tj ;ekw83sbc)nw;rbit was closest to which of the following?

  14.30: Considering only the Moon-Er ycrqmdx s/*-a))z1v 0 mjt)larth system (ignore any influence of the Sun), which one of the following best expresses the magnitude of the Moon’s acrr)c l a-y *)s jdvx/q0t1)mmzceleration about the Earth?

  02.19: As a rocket blasts away from the earth with a cargo for the i6(n q4 87k ( d+p9tosz7dhl+lchu dlarnternational space station, which of the foll h6tk(dd7 nzoqlhas4 l+lr(d +pcu97 8owing 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 Moq: obo 7jsm7:( )s rpjofry8e,on experiences the same gravitational force as a second object at 8of :r )qjsbje7m(o,so7ry: pthe surface of the Earth. Which of the following would be a reasonable conclusion?

  00.24 Consider an object that has a mass, m,lan.-qxdqojj j.c)v y -73z3l and 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 sundlq .aj 7l3. jy-jv)3qczo-xrface?

  96.23: A hypothetical phsz .:hx2 hynb2/ e/x+dqtd(planet has seven times the mass of Earth and twice the radius of Earth. The magnitude of the gravitational acceleratip t/2xhdqd +:eb/s.( y x2hznhon at the surface of this planet is most nearly:

  98.24: A planet has efo2fj5n+ /p),;n gvcx cq)era radius one-half that of Earth and a mass one-fifth the Earth’s mass. The gravitatio;egp5qn jer c) /fc,n)vx+2 ofnal acceleration at the surface of the planet is most nearly

  08.38: Akg 1200 satellite njk1;;6e y,lhd w;qnby d:dnl2 (lmku:ek ;1 rorbits 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 byhmkdwy;nr; dun 6 ke;blq (::ly2knd11jle; , Planet X?

  94.34: A hypothetical planet orbits a st wrvd+w:b)pa4h nxc uerv(x-6vj.w7 .ar with mass one-half the mass of our sun. The planet’s orbital radius is the same as thub nx w vp(d-x)v.4we hrj:wr7.cv6a+e Earth’s. Approximately how many Earth years does it take for the planet to complete one orbit?

  97.12: Two artificial satellites, 1 and 2, are put into circular orbit at then /rn j)e.vx.s same altitude above Earth’s surface. The mass of satellite 2 v)/.e nrs.nxj 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 around the Earth with a 7 qru2n/+ad)( jpc - rux1 )l(hyretghradius $r_1= R$. 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 followi8z-iky 0 nhj3m ffy)8mng problem, the word “weight” refers to the force a scale registers. If the Earth wejm8-y i h)yf0fnzk38mre to stop rotating, but not change shape,

  10.42: A comet moves in an elliptical b3-i(ktdz)f1x kp u-w07xu itorbit around the sun. As the comet moves from aphelion (the point on the orbit farthest from the sun) t-iuf 7kkxw0zp )ib(t t1d-x u3o 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 two stax-d +jd-(fxic rs follow circular orbits about the system’s center of mass. The stars are separated by a dista+c(jix -f-xd dnce 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 system?

  06.50: A rocket is in a circu 6lf9qq8pt/hhlar 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 t hq6hl8qp9f/t he 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