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?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 timeezuy yl (t ((85aolye1” can be derived most directly from which conyy5(zu e( e(lal 1oty8servation law?

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16.17:“All planets in the solar system follow elliptical orbits with the Sun lk+2w 7 jj(ew f- e3zl0mm654bhwzoav xocated at one focus of the ellipse.” This statement is best summarized by which one of them -6 wf5b37e+mez xww0z(2lkvj4 oha j 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 (w8qzlgjqu5a)qy1, f between two small objects ,)f qay qq jzg58(l1wuif the mass of each object is doubled and the distance between their centers is doubled?

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95.09 Two spherical bodies attractjoo o8. zx(kk. each other with a gravitational force of 4.0 N. What will be the force if the distance between them is d j.k(k.8oxozooubled?

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14.27: Two spherical, non-rotating planets, X andY, have the s qlt62pc7x a:p 40m: mzza 9qtu3au)dkame uniform density. Planet X has tw )uxdqpt7qmat cp4l2za6: :0az9m u 3kice 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-rotating planets, X and Y, have the same uniform den y2wo,spze/8vsity. Planet X has twice the ,sz wye2/vp8oradius 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 $v_x:v_y$?

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01.16: The mass of a pf4bxt40.u4 ti6uh 1zht(uu dblanet can be calculated if it is orbited by a small satellite by setting the gravitational force on the satelu64tb(4uu bh1.fh di 0t ztxu4lite equal to the 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 wi;x;, juau m53p1(t;d-o4vx rhnxb bcgth a gravitational force F at the surfacej 53; (xp,;-;uxrvh4ntdbbm xg1au oc of the Earth. When he made his famous second flight in orbit, the gravitational force on John Glenn while he was in orbit was closest to which of the following?

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14.30: Considering only the Moon-Earth system (ig+a/y fvnabkn09vp8 z6nore any influence of the Sun), which one of the following best expv vaa/ z9by+p kfn6n08resses the magnitude of the Moon’s acceleration about the Earth?

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10#

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02.19: As a rocket blasts away from the earth with a cargo for the internatiod0pl8 z:on2y 7:03 rokzbrmnpm*w9 oqnal space station, which of the following graphs would best represent the gravitational force on the cargo versus distance from the surface of the Earto*l72rqd0ppbn8omw0: z9o yr n :k3z mh?

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11#

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99.33: One object at the surface of the Moon experiences the same gravitationaipmofs0jhyq/a:06 2q l force as a second object at the surface of the Earth. Which of/qi: 2ys hpao0jm0qf6 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,w hgok+d+qckv/( 0u ln.wm7a( at the surface of the moon. If we assume the moon has a nearly uniform density, which of the fu (.d/whm7no+w kcq+ g k(vl0aollowing 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 seven times the mass of Earth and twice4yj8 l i/* js3txv/di, 6vyklj3av9zk the radius of Earth. The magnitude of the gravitalt vakx/3,3i 9ijj yy8 vk/4zvj6lsd *tional 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 th+qrxh /oozmo7.p 6tl- at of Earth and a mass one-fifth the Earth’s mass. The gravitational acceleration at the surface of the planet is most 7/o omht ozlxp+.qr6-nearly

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15#

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08.38: Akg 1200 satellite orbits Planet X in a cp9txty0x tv3 a7x,i +uk wfi)7vf(ki0ircular 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 byx3 itx +0f7 9,vkxif(uv0yat7t pw i)k Planet X?

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16#

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94.34: A hypothetical planet orbits a star with mass one-hal/sjo kr842+*-wf tnfcl4rhh hf the mass of our sun. The planet’s orbital radius is the same as the Earth’s. Approximately how many Earth yh/r s2k+fjowh* 4fc84rn l-htears 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 circ:r(e-iogv-;ev 6gd ; sg,bbidular 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, what is the periodeb(d,;ie;6vvgb-d: -sg iogr of satellite 2?

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18#

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15.22 Satellite 1 makes a circular orbit around the Earth with a radius 1cmp k+:) isqaxqtt7: $r_1= R$. 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 problem, the word2yzfn+61 bwga 80zeol “weight” refers to the force a scale registers. If the Earth were zb2egf0zy a +nw ol816to stop rotating, but not change 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#

单选题 ( 1.0 分) 切至整卷模式搜藏此题

10.42: A comet moves in an elliptical orbit around the sun. As the com9oh0v,y p wk(qet moves from aphelion (the point on the orbit farthest from the sun) to perihelion (th9 ,phq 0wyk(ove 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 systemz/ q hw(6 x+0b0ym. ivcynyo63p f)gam shown, the two stars follow circular orbits about the system’s center of mass. The stars are separated by a distance D thxi0p/mn qwy .cb03ghm f+)a 66y(yzvoat 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 orbit with speed vand orbital radius R around af 4y9 hbxc9y fd,v9qc; 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 size of the semi-major axis a o 9cvd,qhxy ;yfc499fb f this new elliptical orbit is

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