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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 tt8gxr70lz y .ixtj9/n(u o( clime” can be derived mos. xt8/z( rox7i lyu(jctg0l9 nt directly from which conservation law?

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16.17:“All planets in the solar system follow elliptical orbits with the Skq,p v mnmano9fo51v pq44p(m4 hf 8z. fhb(7qun located at one focus of the ellipse.” This statement is best summarized by whichv5(4 mfna(,nm pp hbq 4fqm.7ph9 zqo1fo48 vk 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 gravityv a2o/d*xa q9;,nzxyational attraction between two small objects if t,xa 9/ *oxydy2az;nvqhe mass of each object is doubled and the distance between their centers is doubled?

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95.09 Two spherical bodies attract each other w2k .ndz;08g hs uhhgu(mq(h1r goz.7h ith a gravitational force of 4.0 N. What will be the force if the distk 8rqo.h1u(hhz 7 s.mzun(dg2 0g;hghance between them is doubled?

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14.27: Two spherical, non-rotating planeh3ue-leu .9 mmwv 2q*tts, X andY, have the same uniform density. Planet mlte9e*quuv3w. - mh2X has twice 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 plany 7uet9 7zi/:s jvl/ikets, X and Y, have the same uniform density. Planet X has twice9/j7ei7uki v:styz/ l 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 $v_x:v_y$?

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01.16: The mass of a planet can be calculated if it is orbited by a small sateb-(ld:fer y cr8s)/sun 7r4ad ;4ln jtllite by setting the gravitational force on the satellite equal to the centripetal force on the satellite srd 4n -j;/t(: cfud7laesrr8b4)ynl. 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 Joh96c3optc,z:kqi 67 se cx 4e33 pjaston 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 he was in orbit was closest to which of the follk66s oxtc 39 p3ecszp ta7q,c4iej :3oowing?

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14.30: Considering only the Moon-Earth system (ignore any inr6 kwo **r)n3rhin2dm fluence of the Sun), which one of the following b hdn w mio)2*r6rnk*3rest expresses 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 ta-y2d czj( mz2he international space station, which of the following graphs would best represent the gravitational force on the cargo versus distance from thec22jym-zd(za surface of the Earth?

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11#

单选题 ( 1.0 分) 切至整卷模式搜藏此题

99.33: One object at4*4 qft6qk. 5cd yzgae the surface of the Moon experiences the same gravitational force as a second object at the surface of the Earth. Which of the following would be a reasona4gqf*q56zk4.d tcey able 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 a qf0,r2nxo /dvu 5zc9p 2o3vzthe 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 between M3p,udf2rcav zqx 20 /zvno95ooon’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 twice the rad*vm/k527- gjyrkmiza ius of Earth. The magnitude of the g ma k-g2/kyi5j* zv7rmravitational 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 a mass on2b/cup ygc1caa 3k(s 5e-fifth the Earth’s mass. The gravitational acceleration at the surface of the plabc(/25ag c cp1y3suk anet is most nearly

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15#

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08.38: Akg 1200 satellite orbits Planet X in a circug mc5mu;/vw+ nlar 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 satelli+mc5; /nvumgwte by Planet X?

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16#

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94.34: A hypothetical planet orbits a star with a p.9tpzu,tks6 dn9)tmass 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 planet to complete one orbi9tk.udznsp 6 t)ap9t, t?

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17#

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97.12: Two artificial satellites, 1 and 2, are put into circular orbith6d9o:oq c(n t 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 period of satellqo6n(ch o9:td ite 2?

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18#

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15.22 Satellite 1 makes a circular orbit around tqmvs6bcghg*p z2q- 4;qc(l* zhe 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?

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 word “weight” refers h (*,zyo nkj3x tye;u*to the force a scale registers. If the Earth were to stop j(*tz un ,xo3;* yykherotating, 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#

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10.42: A comet moves in an elliptical orbit around the sun. kh,qp6lc1wx2w/ffwrlto4 r l /14 0cpAs the comet moves from aphe4,fwwlch ft0xrolr p /q164cp2l/wk1 lion (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 is true?

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21#

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17.48: In the binary star system shown, the two u5w3 5d;3d:iutjiad estars 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 period of the star of mass M is T. Which one of the following choices represents the totat:3;d5jde5 diiawu 3u l 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 or wfw vmk02omvorjv*+ vi53y), bit with speed vand orbital radius R around a heavy stat+oo3rj*m v vf0y2kmw,v iv5)wionary 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 of this new elliptical orbit is

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