08.19: Kepler’s Second Law about “sweeping out equal areas in equal time” ec 6gq:d:d;io can be derived most dirido6:g d:qec ;ectly from which conservation law?

  16.17:“All planets in the solar sys *qmg vl22j 1uoj60 lbvn-y)xmtem follow elliptical orbits with the Sun located at one focus of the ellipse.” This statement is best summarized by whi - nvv)oqm6mg u21jyll2*0bjxch one of the following choices?

  99.21: What happens to the force of gravitational attraction between two smb ds.s;jfnin4 8egi67all objects if the mass of each object is doubled and the distance between their cien;67d. n8si bjf 4sgenters is doubled?

  95.09 Two spherical bodies attract each other with a gravitational force of mhp/ro*)5joa1rg/3nck b t (e4.0 N. What will be the forcj1 e3/t/ nbo)p(rmk cgho*ar5e if the distance between them is doubled?

  14.27: Two spherical, non-rotating planets, X andY, haver x5oosl3)sfvuy ;3+v the same uniform density. Planet X has twice the ru3o f + 3s;rsy5xvv)loadius 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-roej4ulomf g0k,. k ao:5tating planets, X and Y, have the same uniform density. Planet X has twice the radius o0 gj. mkuo45kl oa,ef:f 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 planetlqqyv p:1kv 1q n5eh1z g7fp(. can be calculated if it is orbited by a small satellite by setting the gra(1.z5 glf kp1q evv:7 q1ynpqhvitational 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 attrcl;3qxc 3) mtuj 6p1zpacts John Glenn with a gravitational force F at the surface of the Earth. When he made his famous second flight in orbit,6z3cmtp ;xulq) 1 3cpj the gravitational force on John Glenn while he was in orbit was closest to which of the following?

  14.30: Considering only t3 ;p)m+cejq u0jajnz3 he Moon-Earth system (ignore any influence of the Sun), which one of the following best ex+p0e3)u; z3mqjcnaj jpresses the magnitude of the Moon’s acceleration about the Earth?

  02.19: As a rocket blasts away from the earth with a-)yqel /jn3isni1*+ osaiy0dvtnc6 5 cargo for the international space station, which of the following graphs would best represent the gravitational force on the cargo versus distance from the casy*3its1 /d- )v+iiey0non5 6lnq j surface of the Earth?

  99.33: One object at the surface of the Moon experq e1 u.bkbp-b*ska;w/ iences the same gravitational force as a second object at the surface of the Earth. Which oesb* bkpqwk/;a1.u b-f the following would be a reasonable conclusion?

  00.24 Consider an object that has a mass, m, and m;q *gxtb+wos+u .rn/ 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 ma/sguw*;mqb+ t+x n .ross and weight at a distance halfway between Moon’s center and its surface?

  96.23: A hypothetical planet has seven times thek.or -kc)lu 6o mass of Earth and twice the radius of Earth. The magnitude of the gravc.-k)uo klor6itational acceleration at the surface of this planet is most nearly:

  98.24: A planet has a radius one-ha snh;cs8ab l3 .jil-ef)h6)jqm i 5(nulf that of Earth and a mass one-fifth the Earth’s mass. The gravitational ac);hs fclm 5l()3b.6njniuh8e qsja-iceleration at the surface of the planet is most nearly

  08.38: Akg 1200 satellite orbits Planet X in a circular orbit with 9*e-k * xozf sb*8:rzmdiuc3ya 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-ofk*u3 r:b*siz9xcemz * d8y satellite by Planet X?

  94.34: A hypothetical planet orbits a star w (7ilcu lsu /-pq5sdt4ith mass one-half the mass of our sun. The plan t u(i/7sus5p4l -lcdqet’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, 1 and 2, are put into circular oru h.yez ,5ce-kbit at the same altitude above Earth’u,ec-y z e.kh5s 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 2?

  15.22 Satellite 1 makes a circular orb/q+;- ffrpyh ddxu.5i it 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 “weight” refersx s4j6tw;c7e7o bd 4oo to the force a scale registers. If the Earth were to stop r;ex 7oo6jbod 74ctsw4 otating, but not change shape,

  10.42: A comet moves in an elliptical orbit around the sun. As zm8nkx9srik0 ny)s **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 results ik0z insky*rx8m*)ns 9s true?

  17.48: In the binary star system shown, the two stars fo wc f 3uolrl69(8uv4ycllow circular orbits about the system’s center of4 3l( ufclr6cwu89vo y 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 following choices represents the total mass of the binary star system?

  06.50: A rocket is in a circular orbit with speshf/4o8 t zm1cs.6phjf/ qi.g ed vand orbital radius R around a heavy stationary mass. An external impulse is quickly f op1 i4jmfg. zc6s8/st.qhh/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