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 jz54 fjm .ba/7rwim8onaqxg hk,1q 1/ -sgb4x equal time” can be derived most dire - ig/4k8a ja.,f5qx1q1oxmm jr w7shn /bgb4zctly from which conservation law?

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16.17:“All planets in the solar system follow elliptical orbit0v cj fpmjrm5 +5p4fn2s with the Sun located at one focus of the ellipse.” This statement is best summarized by which one of the following 0pnrpj v 24fmf+5j5cmchoices?

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 betwee4 zn5ub qs9q:wn two small objects if the mass of each object is doubled and the distqw5zbus:n 9q4ance between their centers is doubled?

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95.09 Two spherical bodies attract each other with a gravitational force ct*8r3aug0u +qwgac7of 4.0 N. What will be the force3qcu g0ag8+r wut c*7a if the distance between them is doubled?

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14.27: Two spherical, non-rotating planets, X andY, have the same uniform dulkwsm: ri5x9qn: 2) tensity. Planet X has twice the radius 59 l2tk srw:u:xmq)in 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 x;gt2e q 88iiw: ex(6:vebd qisame uniform densityd8xqwxtii 6e2gv8 :b:i( ;eeq. Planet 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 calculated if it is orbited by a smal52zw y k hs;k/o*qcf1jl satellite by setting the gravitational force onhz1 y*jfc5w ;k2ko/qs the satellite 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 wiy)5ss,op n; yw8 jmz.oth a gravitational force F at the surface of the Earth. When he made his famous second flight in orbit, th )w5sojn ;zsymp, o8y.e 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 (ignor z sh-nyv*me/( :ov8vge any influence of the Sun), which one of the following bev/s yh -nve:gv*mo( z8st 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 inpq,(1 hf 8b;y3ndgy sfternational space station, which of the following graphs would best representy,( h;pfyq gfd1b3s n8 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 surfac6ynzvgg 8. a*m:bhh1m a)p /e4rwbk.te of the Moon experiences the same gravitational force as a second object at the surface of the Earth. Which of the follow4/y*mz ..na :hbhvt)wrgme6p1b8 gk aing 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 t0inx6dv2po d1hat has a mass, m, and a weight, W, at the surface of the moon. If we assume the moon has a nearly uniform dpn6dox1 0i2v 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 seven times the mass of Earth and twic.p x wnpepz.xn3/f/gu0.*r kje the radius of Earth. The magnitude of the gravitational acceleration at the surface of this planet is most n..rgpf/xw / x3n ujnp *0.ezpkearly:

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14#

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98.24: A planet has a radius one-half that of Earth and a mass ona- w 8-d0gv;mxlis o.me-fifth the Earth’s mass. The gravitational acceleration at the surface ofl8sogm w- -xa.mdi;0v the planet is most nearly

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15#

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08.38: Akg 1200 satellite orbits Planet X in : xt6a3+1 zjymg)jcug a circular orbit with a constant speed of 5,000m/s. The radius of orbit is 7,500,000 m. y:x) azum +3gj6tg 1jcWhat 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 star with mas +ve rb1yu8vd6jt;v1g :lxjo :ei zh6*s 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 orbxz t oebv:+ i*168jv hrgyv6:ueld;1jit?

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17#

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97.12: Two artificial satellites, 1 and 27:d so/al vyvpmhk714 , 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 im/: adphl4kv77s1 ovys T, what is the period of satellite 2?

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18#

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15.22 Satellite 1 makesjm5xm1 l;3h7b2u chsl a circular orbit 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” refers to t*b5y/pzfd x *e8y9c-sm dz:klhe force a scale registers. If the Earth were to stop rotating, but not chancdyyx58 -*bpm*szkdze/l 9 :fge 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 comet moves f(. km crnvo8.2t5*um, rk ukjgrom aphelion (the poijmg 2rk t(c*5.v,8n. krukmou nt 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 stars followa. h+d)si,eelprj67q) psn 7l 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 choijdi.)+7h,ee)lrq s 6sp l7np aces 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 tdv/va8b1 j;a /:kkm; .,h1 ucpwz dtuspeed 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 this ahtku kpja. t/,cdzb8 ;1md :1w/;vuvnew elliptical orbit is

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