08.19: Kepler’s Second Law about “sweeping out equal areas in equalywsbb:m - ainv8-q6nf.(, aiy time” can be derived most directly frn--m,sbq: iw.ayv8b(6i f y naom which conservation law?

  16.17:“All planets in5 c0dz)rt(7u hjz2 fbm the solar system follow elliptical orbits with the Sun located at one focus of the ellipse.” This stat(5c)d jz2 0mbhurft 7zement is best summarized by which one of the following choices?

  99.21: What happens to the f40vzy zs /rxdlsm,t 1:orce of gravitational attraction between two small objects if the mass of each object is doubled and the distance between their cemv4d0y,ls/ :r1sz z xtnters is doubled?

  95.09 Two spherical bodies attract each other with a gravitational fetj+2 ,d0.a ulszkm,4prs +mcekpp*,q/m2sm orce of 4.0 N. What will be the force if the distance bete pkmm+sz22csr s +l ,,u mk a/p*deq4tj.,pm0ween them is doubled?

  14.27: Two spherical, non-rotating planets, X andY, have;sk kxjxjtt e:5 -.4kv the same uniform density. Planet X has twice the radius of Planet Yx4e.jx5kjv;kt :k-ts. 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*mp fe(a6/shph abv -:t udw5* and Y, have the same uniform density. Planet X has twice the radius of Pwa:pm(eh/s u* fa5*h p-t dv6blanet 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 iqx7ciw k+ydy2z57o u ;f it is orbited by a small satellite by setting the gravitational force on the satellite equal to the centripetal force on thq ckdyy7zou+52 7wx ;ie satellite. Which of the following would NOT be required in this calculation?

  99.11: Assume that the Earth attracts John Gleng mrtpep8/i;w47 *cefk sw67v n with a gravitational force F at the surface of the Earth. When he made his famous second flitie erp84spvc mw;*fw77 / kg6ght in orbit, the gravitational force on John Glenn while he was in orbit was closest to which of the following?

  14.30: Considering only the Moon-( b5bze rklddq i;((1hEarth system (ignore any influence of the Sun), which one of the following best expresses the magnitude of the Moon’s acceleration about bh(e(i 1 q5zk l(;drbdthe Earth?

  02.19: As a rocket blasts away from the earth with a cargo f1 eb5u dcydr82*;jmryor the international space station, which of the following graphs would best represent the gravitational force on the cargo versus distance from the surface of the rcy28dj1*d e 5;bmury Earth?

  99.33: One object at the surface of the Moovyo946 mtfm e i,nm:tacu1 */dn experiences the same gravitational force as a second object at the surface of the Earth. Which of the fo:yt mc/i1v*d9ot6memn u f,a4llowing would be a reasonable conclusion?

  00.24 Consider an object that has a 8grd41mp 5iaa9/pwf(e in9ej mass, 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 cl594dei9j8n(pa i ap/fg1 mrewosest 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 a p)jff 0z: -pg6zxi(a8 lgb9oknd twice the radiuspf igb6a p jzox8l:)-fzkg09 ( of Earth. The magnitude of the gravitational acceleration at the surface of this planet is most nearly:

  98.24: A planet has a radius one-half that of Earth and a mass oku5(ubw8 r3t*d/gybl d b9t-w0pr5 b ioaj/v 2ne-fifth the Earth’s mass. The gravitational acceleration at the surface of0jugpi( 5 bb /l95v2tb oukt* wywbdr 83rda-/ the planet is most nearly

  08.38: Akg 1200 satellite orbits Planet X i9dp0zv,al devs9+v 3 in a circular orbit with a constant speed of 5,000m/s. The rae,9 dpl3d ai+ vz09vsvdius of orbit is 7,500,000 m. What is the magnitude of the gravitational force exerted on the satellite by Planet X?

  94.34: A hypothetical planet orbits a star with mass one-half the mass of ofyh+egpr l970 puc 07rur sun. The planet’s orbital radius is the same as the Earth’s. Approximately how many Earth years doe07errlup 0h9 pg7+cyfs it take for the planet to complete one orbit?

  97.12: Two artificial satellites, 1 2nsaqh 4i)xl*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 a nq )*hl42isxsatellite 1. If the period of satellite 1 is T, what is the period of satellite 2?

  15.22 Satellite 1 makes a circular orbit a/jt-pna u0j2y round 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,on4 (0vkai7rj 5bq5 ej bh.zr9xdd-n word “weight” refers to the force a scale registers. If the E h kv -705d5,(jj4e bido.nxrranbq9 zarth were to stop rotating, but not change shape,

  10.42: A comet moves in an elliptical ortnk d x.d: *95hi/ :dhwpm*vn) 0et,gs4 wijmebit 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 the following resultsisgp/:wvneh0i h*,* t md:mjwkd)5d .ex9 nt4 is true?

  17.48: In the binary star system shown, the two stars follok dsyr8j9 4,4 5yjp-ck0wttxtw 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 mastkd8y-sk50jt tc49ry xpw4 ,js M is T. Which one of the following choices represents the total mass of the binary star system?

  06.50: A rocket is in ,b.s 1 pnw37otldliqv , k1b/wa circular orbit with speed vand orbital radius R around a heavy stationary mass. An extk/ , db 1b1wo.p 7nqlwilt3v,sernal 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 size of the semi-major axis a of this new elliptical orbit is