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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 “sweepiri-6 d5ov a4stjp:.as ng out equal areas in equal time” can be derived mr5josdits-4 : p6va.a ost directly from which conservation law?

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16.17:“All planets in the solar system follow elliptical zwio9 k0xrqs)f0 n ,e:orbits with the Sun located at one focus of the ellipse.” This statement is best summarized by which one of the following chqk xoizn wf 00esr,:)9oices?

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 attracti v 1x+vbw 3983hpc/pecwg ymxx(r8n:ron between two small objects if the mass of each object is doubled and the distance between th:rrmph+8nxcx pe 3v1w3v ( b/yc8gxw9eir centers is doubled?

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95.09 Two spherical bodies attract each other with a gravitational fh/brokptr-s*qt* f66oqc*1 v orce of 4.0 N. What will be the force if the distance bet6hr*c6*- rqf ovktobpqs/1* tween them is doubled?

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14.27: Two spherical, non-rotating planets, X andY, have the same uni wo uk+5r5pdtgvd7* /lform density. Planet X ha7*p+lw r gku/5t5oddv s 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, z2ox1crw: sg nj( i l*)g)6vxtnon-rotating planets, X and Y, have the same uniform density. Planet X has twice the 6 2vz i1gxl wgcs)noj(:)x*r tradius 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 orbii.el;cchm c;.ted by a small satellite by setting the gravitational force on the satellite equal to the centripetal force on the satellite. Which of the following wouldc ec;m ;c.hil. 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 attract our ,jwow/,sk6on* ;y(+du2efnh9gut ) rrt -s John Glenn with a gravitational force F at thed ,y9t(ouowje2 -n6tu /fgr)u, hr*wsk on;+r 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 following?

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14.30: Considering only the Moon-Earth system st kpu -*,t-zi16wnmjne8. hg(ignore any influence of the Sun), which one of the following best expresses thetun-e ,-1.mwg t* i k8zps6nhj 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 i*1nvi2yr3 d0 hoge4)icbt z9 hnternational space station, which of the following graphs would best reprv yhbo 3t0eg21n 94rd)zc* hiiesent 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 experiences the same gravitationvdnvn n(6i )+1p/wtig /i zax(al force as a second object at the surface of the Earth. Which of the following would be a t(nvi/ xdanii)g/61 v( p +nwzreasonable 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 has a mass, m, and 3 y3nwpi k6nmvf52lg9 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 closes mly3 gfki62w n5v9pn3t 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 hanv7 n wv ft11r)(6eu; mzozda0s seven times the mass of Earth and twice the radius of Earth. The magnitude of th16wf(1am u t)r eo;n7v0zvdnze gravitational 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 ags (2wo 9dzhh:aru5z i:w .;il mass one-fifth the Earth’s mass. The gravitational acceleration at the surface of the planet is most nearl; .(w5r :auhlz2godsizw :i 9hy

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15#

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08.38: Akg 1200 satellite orbits Planet X in a cirrwr 1ntjp n1yn h)k)3:cular orbit with a constant speed of 5,000m/s. The radius of orbit is 7,500,000 m. What is the magnitj1: y1) rtnhp wn)nr3kude 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 wi1v cyff4;,ck cth mass one-half the mass of our sun. The planet’s orbital radius is the same as the Earth’s. Approximately y,;cf4 kcv f1chow 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 satellites,c; .0::pyy:mub sz dlhu2kph5f)gd 7:9sp vsj 1 and 2, are put into circular orbit at the same altitude above Earth’s surface. The mass of satellite 2 is twice the masy:ug5 sh: b2fz hp;vs .yd plsk07jdu ::p)mc9s of satellite 1. If the period of satellite 1 is 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 aroun 2 hni0(g)zc+1 bt2w5u3gwqjfeke qx* d 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 “be 9 s,8enzmry fxt8+7weight” refers to the force a scale registers. It8b,78 eym zxsfne +r9f the Earth were 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 ellevjhyos k+x8: j2u.1niptical orbit around 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 sh:jx8s2 uo.e+ n1jy kvun), 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 fol ok,r9k xv6:relow 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 subjexe 6,rokv r:9kct 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 sr e 73b ehbch5 zzg2::w;fwww7peed vand orbital radius R around a heavy stationary mass. An external impulse is quickly applied to the rocket directlhzwh:g;c27e: bbw fzwewr 37 5y 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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