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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 o3, ) :o )dn2 a.d0qg6komdjvklla o/xout equal areas in equal time” can be derived most direc0 oqm26da, lkl3oa dgo)kn:djv. )o/x tly from which conservation law?

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16.17:“All planets in the solar system follow elliptical orbits with the Sun locbjxxcn yl/f74fy +- -rated at one focus of the ellipse.” This statement is best summarized by which one of the following cxcf+j7 l /y-f- nbrxy4hoices?

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 gravity+n6wtwe. 3 ,uzmuyh) ational attraction between two small objects if the mass of ehy,yut)6+neuzw .wm3ach object is doubled and the distance between their centers is doubled?

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95.09 Two spherical bodies attract each ot ztv dhquf,+9 t+5m 5295 tfsn6sdwjbqher with a gravitational force of 4.0 N. Whatm z+52fd 5s6w,9d5ut9vjt +nthb sqfq will be the force if the distance between them is doubled?

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14.27: Two spherical, non-rotat3p6(zkw8 bhf8l3q lba ing planets, X andY, have the same uniform density. Planet X has twice the radius of Planet Y. Lepk 3qzw38l8 b(fl abh6t $g_x$ 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, h* opspc3 a 1mr6zi2im;ave the same uniform density. Pi6p* m1;iapo2r3c s mzlanet 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 $v_x:v_y$?

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01.16: The mass of a planet can be u+6ll *gleb k8calculated if it is orbited by a small satellite by setting the gravitational force on the satellite equal to the centripetal force on the satellite. Which ofelb6 l*gku8l+ 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 l9gy j. 1ipo;uEarth attracts John Glenn with a gravitational force F at the surface of t9 l1. poi;gjuyhe 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 (ignore any influen2;hx7belr ke6c hf ;b-ce of the Sun), lr 67feebxh-;hk bc 2;which one of the following best 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 bla4/g+q ;zfqn rusts away from the earth with a cargo for the international space station, which of the folln;4 ru+zgfqq/ owing graphs would best represent the gravitational force on the cargo versus distance from the 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 at the surface of the Moon ex b6q s6:latvxes e(.ot/j78ikperiences the same gravitational force as a second object at the surface of the Eartx v/qjso(t7skl 8:e bit6 6ea.h. 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#

单选题 ( 1.0 分) 切至整卷模式搜藏此题

00.24 Consider an object that hrh ti9z sjp+3rk/rf6+ as 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 closestrp 6h 3jfkr+ zr+9i/st 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 ou//huo uwuck7w;)w0kx: b sz /ni gl,4f Earth and twice the radius of Earth. The magnitude of the gravitational acceleration at the sui,zox;0cuk/ /u :7hw sulwwb4k)/nug rface 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 eu8n0 bil7.im a mass one-fifth the Earth’s mass. The gravitational acceleration at the surface of the planet is most neimb en80i7 .luarly

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15#

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08.38: Akg 1200 satellite orbits Planet X/i52toq1 og9/ z oru--ifh3amt/ bymc in a circular 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 satellit/ohmz35gfot- qi/ 1c or2my/b - tui9ae by Planet X?

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16#

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94.34: A hypothetical planet orbits a3h8p qzxa31 :uwv*oovcl nzz97,:h i u star with mass one-half the mass of our sun. The planet’s orbital radius is the same as thz9pzox:3nc 8u:3 hqv7oaz *u,hlwi v1e 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 satellitf(k2* 7 0wd.k2 pu dgoga2xcvhes, 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, what is the period of s2 d0wkox2puk7dhg. *ag2fv( catellite 2?

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18#

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15.22 Satellite 1 makes a circular orbitem lw/ ma 6+b9j j,m2p5ury,9rjf0wvt 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?

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” +aab/)mwif vm+ua x,5refers to the force a scale registers. If the Earth were+a)+am, xb/ mifvw a5u to 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#

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10.42: A comet moves in an elliptical orbit ape 0rkk)qm en;ts)*94a4cl jiround the sun. 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 o s9r4ic4emt0)kenl) * ajk;pqf the following results is true?

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21#

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17.48: In the binary staru+p (rc9nb0c m system shown, 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 period of the star of mass M is T. Which one of the following choices represr(+0 up9 cnmcbents 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#

单选题 ( 1.0 分) 切至整卷模式搜藏此题

06.50: A rocket is in a circular orbit withrw*2w* jdrid d:o1ii4 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 rocket into an elliptical orbit. In terms of R, the size of the semi-major axis a of thir2r4 *: dwdidi*joiw1s new elliptical orbit is

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