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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 dr(ncvd 9ogpz( -8mo) in equal time” can be derived mvc (g or9)nzmd-p(8doost directly from which conservation law?

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16.17:“All planets in the solar system folld3seex.z 80bw: d bef)xm(a+( go w;ekow elliptical orbits with the Sun located w oge fdwbx+ek3(:0abd xs8zm; e.e()at one focus of the ellipse.” This statement is 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 between two small oknd8:sy0oy7pohg kr0 qxs;8 2 bjects ig: y7sqhoo0p xnds2 0k8kr;8y f the 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 with a gravitationlj ucn,d.ozwh.h.m, 0dut9 a2/ xvz it: k,+zoal force of 4.0 N. What will be the force if the distancl ,mjzh09xh/ic k.w.u,v.,t+do: zdntoaz2 u e between them is doubled?

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14.27: Two spherical, non-rotjs2-c2i)(s f(hq wrq4pedhy. ating planets, X andY, have the same uniform density. Planet X has twice the radi wih s -(qcpj)e4d y2(r2fhq.sus 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 plafelm8+n uid( 4nets, X and Y, have the same uniform density. Pu+e(id mf8 4lnlanet 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 planet2(lsd1y r0awh/t gjb w;xe/2 f :4dxuubuj5e: can be calculated 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 of the following would NOT be required in this lhdba:2 euwxgtr5d:xu(e/by04 1 uj /2jwf; s 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 t(lrj soj6/:hogkorjvq )g qle+t 7-sw.z0e+ 7he Earth attracts John Glenn with a gravitational force F at the surface of the Earth. When he made his famous second flight in orbit, the gravitati/ o hel+0wtes7g)(:q-+kj7jloz g sq.rjr o6vonal 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 (ign5 sc0ncfte1 7aore any influence of the Sun), which one o n7a 15stccfe0f 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 blasts away from the earth with a cargo for the inte 3g1jn b4zx:dk2yi (+cxygca7rnational space station, which of the following graphs would best ryb g1agz2: cindxyx73jck +4(epresent 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 t a+.na xonf*,ihe Moon experiences the same gravitational force as a second object at the surface of the Earth. Which of the folna+., of *ianxlowing 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 hc 5;tffy2 zduo(7diezhh n60qa e4u,*as a mass, m, and a weight, W, at the surface of the moon. If we assume the moon has a nearly uniz7d h2;e (hd qe0f a5fuzto6 cy*,ni4uform 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 hypothetica3y-):pd ;+/u(qbu vm wio dpmt6fe0g ql planet has seven times the mass of Earth and twice the radius of Earth. The magnitude of the gravitational acceleration at y+op6m uqdwm ;f3ti)-vu g:/e(bpd0qthe 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 one-fifth the e+gx.rl e 3+8wxu6hgaEarth’s mass. The gravitational acceleration at the surface of the planet is mostrgleh.xg x8++we6a 3u nearly

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15#

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08.38: Akg 1200 satellite orbits Planet X in a circular orbit with a consk-(6- wtcq fjdtant speed of 5,000m/s. fq-ckwj d(t6-The radius of orbit is 7,500,000 m. What is the magnitude of the 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 stasb 6vsm.v- /tpr with mass one-half the mass of our sun. The planet’s orbital radius is th6sv/ ms p-.btve 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 sa+ yk2;ge s8* hr-bozwwtellites, 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 bw8w*s ygr ;+zoek-h2 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 a radius de+d48g l. a 4j)wprorj59lpgg2-b io$r_1= R$. 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 to the forcg(yokg +96vln 8 mzs)be a scale registers. If the Earth were to stop rotating, but not change sha l )k6 yng8o(m9gvbzs+pe,

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 tzy(qe3qjmi-y, e p zih*)0wx+ he sun. As the comet moves from aphelion (the point on the orbit faiqjz qwi+h0ey)x-e3*m , (zpyrthest 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#

单选题 ( 1.0 分) 切至整卷模式搜藏此题

17.48: In the binary star system shown, the m)vsq*s d4x6 mk4ml 8btwo 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 periodk*4qsmm lbx 8m vs4)d6 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#

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 with speed vand orbita+i.i/-ofb f;ta pg)osl 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 this new ellipti- gt; bs.opff)/a+i iocal orbit is

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