08.19: Kepler’s Second Law about “sweepiwe/l+(g :kaq1z ov b-jng out equal areas in equal time” can be derived most directvl/-o :1a(j q+z gebwkly from which conservation law?

  16.17:“All planets in the sol5 9p9zu azb)f3rua8ow ar system follow elliptical orbits with the Sun located at one focus of the ellipsef wz 5azp38 burau9)o9.” This statement is best summarized by which one of the following choices?

  99.21: What happens to the force of gravitat/r- c 7l*asm6( mseksuional attraction between two small objects if the mass of each object is doubled and the distance between their centersce( -7slas/*skm6 u mr is doubled?

  95.09 Two spherical bodies attract each other with a gravitational foia1p/ 36bwd+hn +vgmyrce of 4.0 N. What will be the force if then3vwdp6+1 mb y ihga/+ distance between them is doubled?

  14.27: Two spherical, non-rotating planets, X andY, have thebi2u ;9 72dqq.rziz+8:vu 13 er,d wpqtife di same uniform density. Planet X has twice the radius of Planet Yq:1zde8quviep.r 2dit+dbirw,u i72f9 ;3zq. 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 densci,)yk. sr45( u dcnuxoj 2ss.ity. Planud.,nrsy.5su kcxc4i2( o js )et 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 can be calculated if it is orbited by a small-b cb wo +tsf3so2),zp satellite by setting the gravitational z)+twbfc,bp s3s-2oo force on the satellite equal to the centripetal force on the satellite. Which of the following would NOT be required in this calculation?

  99.11: Assume that the Earth at 8-olm3q;u9 +oyphr9 efso pj*tracts 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 wasq9-rj y u+m3*oohoep8 f;ps9 l closest to which of the following?

  14.30: Considering only the Moon-Earth system (ignore any inf r y8(5osr 5x59pay5eztp :cmmluence of the Sun), which one of the following best expmt5oz(erp y apy 595sx:5 rc8mresses the magnitude of the Moon’s acceleration about the Earth?

  02.19: As a rocket blasts away from the earth with a cargo for 4q d28gtvuedk9/ / 6bblaq/ bcthe international space station, which of the fo/d gk u2bcbbaq96 /dv q/4el8tllowing 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 tp( ft40 d rcdtb j5k25i0vnth;he same gravitational force as a second object at the surface of the Earth. Which of the following would be ;jr05np (5c0khdtft4 vti 2bda reasonable conclusion?

  00.24 Consider an object that has a zz-:j8u obu6rmass, m, 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 masz6uozbj ur-: 8s and weight at a distance halfway between Moon’s center and its surface?

  96.23: A hypothetical planet has seven times the mass oj+:5d mig(h1nn a y 7rob+7hepf Earth and twice the radiud :mgp57erah(n7on +hjb1 +yis of Earth. The magnitude of the gravitational acceleration at the surface of this planet is most nearly:

  98.24: A planet has a:b 0 qwwj0e w.;c pgiuf:bs+v8 radius one-half that of Earth and a mass one-fifth the Earth’ecb s 8wjpb.wuvg i;00w:+f:qs mass. The gravitational acceleration at the surface of the planet is most nearly

  08.38: Akg 1200 satellite orbits Planet X in a cibgl6qxy31v hb; a 4/e(cks/lrrcular 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 Plane/c4lser 6h 1l (g;3bya/kbv xqt X?

  94.34: A hypothetical planet orbits a star with mass one-half the mas )pna-h0kevkq*u1x )fe: s,gsk s-/hl s of our sun. The planet’s orbital radius is the same as the Earth’s. Approximately how many Earth years does it take for the planet to complete k*hkhl skqne,vs)fs-p ag/ u0):e-1 x one orbit?

  97.12: Two artificial satellites, 1 and 2,7yakqp qn3idhnxd ,2ajl ;2)2g/5wjt 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)kt 7/wjad2 h 25gp qa,x n;qliyjn32d of satellite 1 is T, what is the period of satellite 2?

  15.22 Satellite 1 makes a circular orbit 9tp lu 2jogg5:vx39l0rdgh/x 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 “wei.km; 0z1vhh g)m;qp ocght” refers to the force a scale registers. If the Earth were to stop rotating, b 1o ;p h;cmz)mkhq0.vgut not change shape,

  10.42: A comet moves in an elliptical orbit around the sto0v,f;l; m fv76 glipun. As the comet moves from aphelion (the point on the orbit farthest from the; ll;mvv0o,gftfp 7i6 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, the two stars follow circular orqjy udg8oab:qai4- ,6t t6ys: bits 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 fo:ti4ysyq866,-a tuo :gdbj aqllowing 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 arounddpeb;r6b7f.vu 3+w4uc c)l yml9 8dvs 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 into an elliptical orbit. In terms of R, the siu+ 7yc;l .r4 dp96m)ve8bfbd3ul wvcsze of the semi-major axis a of this new elliptical orbit is