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 equal time” can +vw8lf//hg ek; li -aybe derived most direc wl;i8v /l g-/yfeah+ktly from which conservation law?

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16.17:“All planets in the solar system(; ;lbgnx )bys.(ny 2dtj7 bkq follow elliptical orbits with the Sun located at one focus of the ellipse.” This statement is best summarizeb2; 7 qtb((yjybsl;. nnxd)gkd 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 betor ;pmp 8rd 99h*jqnc1ween two small obj*nh1jpp qcor89 ;r m9dects if 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 gravita on0jfz: a:g. h 8ln/bcw1s j.brmmn9)tional force of 4.0 N. What will be the force if the distance between them w.)ns.mj/b ghnm:r08a9c :b zfo1 nljis doubled?

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14.27: Two spherical, -7/ibpml1.qp) ytqj o non-rotating planets, X andY, have the same uniform density. Planet X has twice the radius of Planet Y. Let q)7.ilp t1 -myq pboj/$g_x$ 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 planexgf.v/;yefz*:q xu4dts, X and Y, have the same uniform density. Planet X has twice thv4uzge:xd;q/y f*. xf e 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 calcutk12v *cngvk o669i hpu au71m8,ltmou9oo9hlated if it is orbited by a small satellite by setting the vnm6hcl p9ka v oghu o2 ,t8o9m 9i6t*1u7ou1kgravitational force on 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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单选题 ( 1.0 分) 切至整卷模式搜藏此题

99.11: Assume that the Earth attra0v ac7asbx 96lcts John Glenn with a gravitational force F at the su 0l9s7bv 6axcarface 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 Mo4r1 eof o2e*unon-Earth system (ignore any influence of the Sun), which one of the following best expresses the magnitude of the Moon’s acceleration about the Ear2o e*fone1 4urth?

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10#

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02.19: As a rocket blasts away from the earth with a,pvx+48 0 pri2vr trhh cargo for the international space station, which of the following graphs would best represent the gravitational force on the cargo verh 2tvirx8p+r4v,h p0rsus 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 lr hyb7;yh ce e,n)agq..9n,s9b+jp g the same gravitational force as a second object at the surface of the Earth. Which of the following would be a reasonable conclusion?;hjlc + ,7hpaqr. g9yensy)n9 b. g,eb

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 a weightry1wq(*v ,p qzk)s,e t, W, at the 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 Moon’s center and its surface?)rsw,( t*,kvq qz eyp1

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13#

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96.23: A hypothetical planet has seven times the mass of Earth and twice the radud++h z3c h1qmius of Earth. The magnitude of the gravimzh3qdh +1u+ ctational 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 ad.0n:idgxpn) me-. wrnd a mass one-fifth the Earth’s mass. The gravitational acceleration at the surface of the planet is m)dm .xp0in-wndr.e g:ost nearly

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15#

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08.38: Akg 1200 satellite orbits Planet X in a circular orbit with a constzad-xr bc6 h i-;/el-want speed of 5,000m/s. The radius of orbit is 7,500,000 m.ze-6 xwl- b-h/c ;ardi 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 star with mass one-half the mass of o u .nplf:a;x6xur sun. The planet’s orbital radius is the same as the Earth’s. Approximat6fx; .:alup nxely 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 satellites, 1 and 2, are put vv 5:rp1z jn1*fxro)s into circular orbit at the same altitude above Earth’s surface. The mvp1)rjsr*z :5 xf vn1oass of satellite 2 is twice the mass 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 around the Earth with a rcoxd )xs 4f- lj-ulamal3q(;0adius $r_1= R$. 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 “weig;s fscl8dmf8(3cc /f eht” refers to the force a scale registers. If the Earth were to stop rotating, bcme (flscs388df;/fc ut 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. As the qo: c8igh s t(-z,xq;qcomet moves from aphelion (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 trz -qt8is: ,cg oxq;hq(ue?

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21#

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17.48: In the binary star system shown, the two stars follow circular 9k1 y:lx g)acg70ouskorbits 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 total mass of yg0g xc: oks79 ulka)1the 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 speed vand orbital radf0o(ow1nm3d qk(r i)2 tuef* nk+p(yc ius R around a heavy stationary mass. An external impulse is quickly applied to the rocket directly opposite to t c*uo (+on (qntpdf)kir( 123kef w0myhe 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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