08.19: Kepler’s Second Law about “sweeping oukdhq2x2 p +fzks mxkdvy )7/2+t equal areas in equal time” can be derived most directly from which conservatim 2d+7kxkfd+k)xvyh/ 2sz 2qpon law?

  16.17:“All planets in the solar system follow elliptical -7/j zx+dzhcaq+8cg s.)grfcorbits with the Sun locat)d rxz gza.c/-7shcgc q +jf+8ed at one focus of the ellipse.” This statement is best summarized by which one of the following choices?

  99.21: What happens to the f l:5v 4jp:wxd s+empm4bm(b2zorce of gravitational attraction between two small objects if the mass of each object is doubled and the disbp+e 2jvd(mwb4 p msl x4z::m5tance between their centers is doubled?

  95.09 Two spherical bodies attract each oth.ckhw:1+xo 7 rcu,l39j pnkzh er with a gravitational force of 4.0 N. What will be the force:+cp13 ukh,zljcr n 97whx.k o if the distance between them is doubled?

  14.27: Two spherical, non-rotating planetq d5 9nbt0./sv ipwaj4s, X andY, have the same uniform density. Planet X has twice the radius of Planet Y. Lets.w/va5 dnp jti 409qb $g_x$ 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 den;v2yf kkt7z n8sity.7nzf kyk tv;28 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 kn c;e.- i(n+uux -c5d0vgwqwplanet can be calculated if it is orbited by a small satellite by setting the gravitational force on thew0q-ce; .xuck -dwi(vnu5 ng+ 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 f/z+ 5:lxw(9mnlz y qcattracts 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 9nclym5 zf:zxl/ +(wq he was in orbit was closest to which of the following?

  14.30: Considering only the Moon-E)t b7 zis:qa4varth system (ignore any influence of the Sun), which one of the following best expresses the ma:tab4)7sivz qgnitude of the Moon’s acceleration about the Earth?

  02.19: As a rocket blasts away from the earth with a cargo for the inter.b64* mn tzfnvb7vg 9;)svqwhnational space station, which of the following graphs wo b46w9svnhng 7fq.m v* tb)z;vuld 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 ex7k6sdbs ;z- boq*scf3periences the same gravitational force as a second object at the surface of the Earth. Which of the following would be a reasonable ccbzq 6bs7 dkss;fo- 3*onclusion?

  00.24 Consider an object t: ;57;alzcybw4 q4t.hcor t pmhat has a 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 closest to the object’s mass and weight at a distance halfway 4rhbo wzml4a:py7q;cc5 ;tt. between Moon’s center and its surface?

  96.23: A hypothetical planet has seven times the mass of Earth and twice the radw1-a 5v 6sfnenius of Earth. The magnitude of the gravitationaa1 fs6nenw5v-l 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 one-fifbozj4 ( 9t:amith the Earth’s mass. The gravitational acceleration at the surface of the planet is mozjb4:(mta o i9st nearly

  08.38: Akg 1200 satellite orbits Planet X in a circular orbit witr4 *-1j zi4jodvv.ug th a constant speed of 5,000m/s. The radius of orbit is 7,500,000 m. What is the magnitude of the gravitatigo.u rt44 1zdjji*v-v onal force exerted on the satellite by Planet X?

  94.34: A hypothetical planet orbits a star with8 v*;n z,cqy .q apn+0f a2xr37ufnwex mass one-half the mass 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 planetxqnw pya32qvua80n f+7nxr,e*cz;.f to complete one orbit?

  97.12: Two artificial sat)ir cx-dr:e ;h6, i9avj 9acxsellites, 1 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, whatdvasa9ehr ;:- ii)c6c,r9jxx is the period of satellite 2?

  15.22 Satellite 1 makes a circular0bza5a*u g6r s9 hims0 orbit 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, 52b7y)uvyvx36v fmv yml8 6a gthe word “weight” refers to the force a scale registers. If the Earth were to stop rotating, but not gvmmyfbv)a53v82vl y6 u7y x6 change shape,

  10.42: A comet moves in an elliptical orbit around the swh ru 7x7r9 v1 1aq,jpv0r0cb/e whab,un. 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 twwae,jrqv1 b uphx/h70v7ab9, r0 rc 1he following results is true?

  17.48: In the binary star system z8 nrds,,qg*x nf x54qshown, 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 their mutual gravitational attraction. The orbital periodf5sq8x4qrxn ,n gz*, d 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 spxo8khlop.ci )ewa 1n0 *i;3yieed vand orbital radius R around a heavy stationary mass. An external impulse is quickly applied to the rocket directly opposite to the velocity and the rock.loyxwoi 3a;hek )8 cini1p0 *et’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