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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 abu/h/q9*k 9it . spxp*tf( horvout “sweeping out equal areas in equal time” can be de/oxv9p9*k ( fq i *s.htu/rthprived most directly from which conservation law?

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16.17:“All planets in the solar system follow elliptical orbits pd46aiyl) 3);plz epswith the Sun located at one focus of the ellipse.” This statement is best summarized by which one of the folapz; i3 )splpld)y46elowing 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 graviv -kevji65 ,k9biybq.tational attraction between two small oe9jkv.6vyi- q ki, b5bbjects 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 gravitationa-gp6w* tgz.o il force of 4.0 N. What will be 6z *itp.gw go-the force if the distance between them is doubled?

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14.27: Two spherical, non-rotating planets, X andmw2xts23q2i q Y, have the same uniform density. Planet X has twiwx2mqt322si qce 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, nci:i *r gfw2bd u;mxoe (r6./non-rotating planets, X and Y, have the same uniform density. Planet X has twice the radius of Planet nc *;df:/io.rwmeu ( 2girbx 6Y. 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 hjojn +:+ e,xsif it is orbited by a small satellite by setting the gravitational force on the satellite equal to the centripetal force on the satellite. Whjneos: +j,x +hich 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 attracuo+ 0c wdf9oc4ts John Glenn with a gravitational force F at the surface of the Earth. When he made his famous second flight in orbit, the gravitati0 4oc+f9wcd ouonal 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 influence of 2 *e(d6rlek i0ycu11qn pbj*zthe Sun), which one of the f(bl* cd2*yri e16eqpnzj1 u0kollowing 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 ad.0+f93(ooftaw p pywj r)u6zway from the earth with a cargo for the international space station, which of the following graphs would best represent the gravitational force o( jrz+af)tu.3w pfd069 ywoop n 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 the Moon experiences the same gravimip*54n z7,atdg3vvd1i t +qctational force as a second object at the surface of the Earth. Which of the following would be a reasonable gz va7nvdmq+tipi 415,*c3t dconclusion?

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 ob 7 b -fe5x st:b tp;pk16yk:+qsenow,iject that has a mass, m, and a weight, W, at the surface of the moon. If we assume the moon has a nearly uniform densityk,7t; so:-5xtbs: e6pi fe1nq kb pyw+, 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 tn.qav4oq:f t27rg6pa;x xn2w he mass of Earth and twice the radius of Earth. The magnitude of the gravitational acceleration at the surface of this planet inxt.4 f ovq62gr w;nap:2qxa7 s 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 kyqf w95 a*l6cEarth’s mass. The gravitational acceleratioafqly wk96c *5n at the surface of the planet is most nearly

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15#

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08.38: Akg 1200 satellite orbits Planet X in a circular orbax0t1d2ol4 oxhd a x,*it 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 exe1x4lo*aoxtdx 0 ad2,hrted 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 ouln3 73wk: r4jjgc.jb)f5wpf yr 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 orb3jy4 3jrc. 5jpw)lfg:7nbf wkit?

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17#

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97.12: Two artificial satellites, 1 and 2, are put into circular (vuyews,jf3* el w/)yorbit at the same altitude above Earth’s surface. The mass of f*wyuwe/s)ej v,l(3ysatellite 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 Eartljy7u28kb gasf-.l 3l h 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, tav;xc2 ,jkv7d9alo 0fhe word “weight” refers to the force a scale registers. If the Earth were to stop rotating, but not change shape,kvdlox,f 2 v7aj;c a09

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. Asra ux*q;y/wmb 3s2)o n the comet moves from aphelion (the point on the orbit farthestqsxrum3b / ;n)a* y2ow 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 shoe-x/: vra wgf6gnr1 .t7ns9 mhwn, 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 a 1ren6fganhr97xs .w/gv-m : tttraction. 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#

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 orbit3vlfk 0+vt wv adr6j:5al 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, puttinglv+rawvvjkf6td3: 5 0 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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