Gravity and Planetary Motion - 无忧得胜-网上国际课程 (5edu.win)

?作业考试练习?美国物理杯赛(Physics Bowl)?Gravity and Planetary Motion

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习题练习：Gravity and Planetary Motion

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作者: admin 发布日期: 2025-09-14 23:04 总分: 22分得分: _____________

答题人: 游客未登录开始时间: 24年08月17日 16:00 切换到: 整卷模式

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08.19: Kepler’s Second Law about “sweeping out equal areas in equal e0jkp* oue;m* time” can be derived most directly fr;ou p0mj*kee*om which conservation law?

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16.17:“All planets inc +j: hiw)b3xkmvr2. l the solar system follow elliptical orbits with the Sun located at one focus of the ellipse.” This statement 3r. jvbml):hci wk x+2is best summarized by which one of the following choices?

A. Kepler’s First Law

B. Kepler’s Second Law

C. Newton’s Universal Law of Gravitation

D. Einstein’s Law of Gravity

E. Schwarzchild’s Law of Orbits

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99.21: What happens to the force of gravitational attraction betwee c 8e* es6u v6w*hdib;oawch(;n two small objects if the mass of each object is doubled and the distance between their centers is dos w6u6*8ech a*vid( ohbwce;;ubled?

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95.09 Two spherical bodies attract each other wito.t*tkf 1syfu x*ias yg /)3-lp4 c3hsh a gravitational force of 4.0 N. What will be the force if the distance between*hkus ay o3/tl )y-4six1csf*.3tfpg them is doubled?

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14.27: Two spherical, non-rotating planets w;acrdhj tj2 pq.q f ,p5;un2yxh68c/, X andY, have the same uniform density. Planet X has pqj t8hhcx; / qyacpu;f wn,2 rd62.j5twice the radius 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 $g_x:g_y$?

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16.46 Two spherical, non-.svqb /bz: a-6gdlc m0rotating planets, X and Y, have the same uniform density. Planet X has twice the radius oq:-v dbms.b6glza c0/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 $v_x:v_y$?

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01.16: The mass of a planet can be calculated if it is orbited by a sma eq0mw i48l:ao0 k, :yvh8pwbfll satellite by setting the gravitational force on the satellite equal to twk8fweao8h4i :0 yb0vl m, p:qhe centripetal force on the satellite. Which of the following would NOT be required in this calculation?

A. the mass of the satellite

B. the radius of the satellite's orbit

C. the period of the satellite's orbit

D. Newton's universal gravitational constant

E. all of the above are required for this calculation

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99.11: Assume that the Earth attracts John Glenn with a gravitational force F j o8eo+08onhx2bfm2o r*luf) at the surface of the Earth. When he made his famous second flight in orbit, the gravitational force on John Glenn while he xfbo 02jm n 8u)lfe oo+2hor*8was in orbit was closest to which of the following?

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14.30: Considering onlyy d7nt;ebz1q 8 the Moon-Earth system (ignore any influence of the Sun), which one of the following best expresses the magnitude of the Moon’s acceleration aboenzybd t;8q 17ut the Earth?

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10#

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02.19: As a rocket blasts away from the earth with a /4pgngi 6c:kj cargo for the international space station, whi46/n:c kpgj gich of the following graphs would best represent the gravitational force on the cargo versus distance from the surface of the Earth?

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11#

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99.33: One object at the surface of the Moon experjqo7w;ihz k- 6iences the same gravitational force as a second object at the surface of thjok-w 6qihz7;e Earth. Which of the following would be a reasonable conclusion?

A. both objects would fall at the same acceleration

B. the object on the Moon has the greater mass

C. the object on the Earth has the greater mass

D. both objects have identical masses

E. the object on Earth has a greater mass but the Earth has a greater rate of rotation.

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12#

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00.24 Consider an object that has a mass, m, and a weight, W, at the surfacot*l6pzm;*06o i pygimo / v9je of the moon. If we assume the moon has a nearly un0ij;pp*yt*im96oov g o/6m lziform 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 surface?

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13#

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96.23: A hypothetical planet has se*cy)eie +t 5cjl-pubm8 y, :hra)ek(iven times the mass of Earth and twice the radihiueep+y8bce y: mrk)cjt () i,a5-*lus of Earth. The magnitude of the gravitational acceleration at the surface of this planet is most nearly:

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14#

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98.24: A planet has a radius one-half that of Earth and /kvtvb k91hy9o61aa o a mass one-fifth the Earth’s mass. The gravitational acceleration at the surfy9 ht6vo/9v1kkaab 1oace of the planet is most nearly

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15#

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08.38: Akg 1200 satellite orbits Planet X in a circular orbit withb jkeh- i9y pel+s2c6uu4:vh1 a constant speed of 5,000m/s. The radius of orbit is 7,500,000 m. What is the magnitude of t24: ci+yve1jlhs ph6ke ub 9-uhe gravitational force exerted on the satellite by Planet X?

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16#

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94.34: A hypothetical planet orbits a star with mascbuh8+cqe u,0s one-half the mass of our sun. Th cc80qu +bh,eue planet’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?

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17#

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97.12: Two artificial satellites, 1 and 2, are put into circu+m/ mn xc tkch1*4mlyvx w8ufk7t890 qlar orbit at the same altitude above Earth’s surface. The mass of satellite 2 is twice the mass of satfxtu8l8*m 410c9 y/nkqwvm7 +hx cmtkellite 1. If the period of satellite 1 is T, what is the period of satellite 2?

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18#

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15.22 Satellite 1 makes a circular orbit around the Earth with) kkbg c 01z,m;kfayn mugs.;+:f:e2sduhke 1 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?

A. $v_2=\frac{1}{\sqrt{2}}v_1,a_2=\frac{1}{4}a_1$

B. $v_2=\frac{1}{2}v_1,a_2=\frac{1}{4}a_1$

C. $v_2=\frac{1}{\sqrt{2}}v_1,a_2=\frac{1}{2}a_1$

D. $v_2=\frac{1}{2}v_1,a_2=\frac{1}{2}a_1$

E. $v_2=v_1,a_2=\frac{1}{2}a_1$

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19#

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98.33: In the following problemi h(i2uq2.mh w, the word “weight” refers to the force a scale registers. If the Earth were to stop rotating, but not chang2hq. i(m wui2he shape,

A. the weight of an object at the equator would increase.

B. the weight of an object at the equator would decrease.

C. the weight of an object at the north pole would increase.

D. the weight of an object at the north pole would decrease.

E. all objects on Earth would become weightless.

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20#

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10.42: A comet moves in an elliptical orbit around the sun. As the cocx:qrv 1gpq 4,.j1bdi met moves from aphelion (the point on the b:q1 vqx. icj d41rp,gorbit farthest from the sun) to perihelion (the point on the orbit closest to the sun), which of the following results is true?

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21#

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17.48: In the binary star system shown, the two stars follow circular orbits aboy(+dl8yqxlyn l02v *zsa8 .cdut the system’s center of mass. The st.da*(8d s2n lcq+yxvl80lz yyars 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?

A. $\frac{π^{2}D^{3}}{5GT^{2}}$

B. $\frac{4π^{2}D^{3}}{5GT^{2}}$

C. $\frac{4π^{2}D^{3}}{GT^{2}}$

D. $\frac{16π^{2}D^{3}}{5GT^{2}}$

E. $\frac{25π^{2}D^{3}}{4GT^{2}}$

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22#

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06.50: A rocket is in a circular orr/,15,pys zsdj,c ht7ba/knz bit 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 the rocket’s speed is slowed to v/2, putting the r ,tadkrb,j yhz1s/7cp5,z s/nocket into an elliptical orbit. In terms of R, the size of the semi-major axis a of this new elliptical orbit is

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