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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 ip4di(ks6/wee xagr 4.r6 7ga13bmal i n equal time” can be des6rl1imxaaeik wgb43 4dga6 7 p/.(errived most directly from which conservation law?

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16.17:“All planets in the solar system follow elliqu i5:spt ,7f7 *noee0ih wh4qptical orbits with the Sun located at one focus of the ellipse.” This statement is best s etiq07sqiw*47e, nu h:o5hp fummarized 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 gravitaep-y ha eu9,j7tional attraction between two small objects if the mass of each object hu,ee y 9-ap7jis doubled and the distance between their centers is doubled?

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95.09 Two spherical bodi to,-s n)kd7dbt -xz(c8e6ztees attract each other with a gravitational force of 4.0 N. What will be the force if the distance -cbtd78z- ,6o ztee)(tdxnksbetween them is doubled?

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14.27: Two spherical, non-rotating planets, X andY, have the same unifn uvg7(ffqye +) e7t(j4b eqw-orm density. P7b)f g q4ef+vy uw 7tejqe(n(-lanet X has 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, non-rotating planets, X and Y, hav6lq/:i tmkj7 ie the same uniform density. Planet X has twice the radiumi6tj/ 7i: klqs 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 blr-fdi6c /(ch6 a4s/plqez;y n0n5 :kwd2 u kce calculated if it is orbited by a small satellite by setting thuc fn6zp/6ca s/d-elyh 0kdqki5 2cn;w( 4lr: e gravitational 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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99.11: Assume that the Earth attracts John Glenn with a gravit27noc5 a5 lofjational force F at the 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 t55f7a olo c2njo which of the following?

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14.30: Considering only the Moon-Earth system (ignore any influence of+umb. ;gcoriur6 ;oug4:d 4qi the Sun), which one of the following best expresses the magnitude rrqbugguo4i o; u;cm.:6+ d4iof the Moon’s acceleration about the Earth?

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10#

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02.19: As a rocket blasts away06(z naddi z,kiype0u4o02sh from the earth with a cargo for the international space station, which of the following graphs would best represent the gravitational force on the cargo versus distanc06nkdao0i zzs0hy2id(u e,p4e 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 o ccijuo s23qi9;8vr2 lf the Moon experiences the same gravitational force as a second object at the surface of the Earth. Which of the follocsu o9i2j3c v2 l;r8iqwing 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 has a mass, m, and a weight, W, at the (yy f 0))dzlf8g we*hisurface 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 halfleh( 8gw dzfy)0i )*yfway between Moon’s center and its surface?

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13#

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96.23: A hypothetical p7+ 01lytfw4jbzkc, js0)xqqylanet has seven times the mass of Earth and twice the rad0cj7 tzw s+jf)yqx4 b0lyk1,qius of Earth. The magnitude of the 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 a mass one-fifth qj zm0mcmmg 7/m/ 8s+uthe Earth’s mass. The gravitational acceleration at the surface of the planjmqum/mg 07smz /m8c +et is most nearly

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15#

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08.38: Akg 1200 satellite orbits Planet X in a circular orbit with a constant s g01 2f,obunyepegob2 e1f ,y0nued of 5,000m/s. 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 star with mass one-half the mass of our 8qhyn un1*rbu8y+ de- sun. The planet’s orbital radius n rye+y1u qudh-8b*8n is the 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 satellites, 1 ando:a4 yu/iem*to ossf hjiq- +,:p7:le 2, are put into circular orbit at the same altitude above Earth’s surface. The mass of satellite 2 is twice the ma -:q:lt oefhju+eo i/smos y74*:pa,i ss 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 ax b o*-bf)i35jb;hd tsqj6l;y 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 followa3ak )/a 11siqd,ux tking problem, the word “weight” refers to the force a scale registersa1sud 3tq),ax/kai1k. If 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 elliptical orbit around the sun. As the comet mo7e9l0pki 7unn 3)yn olves from aphelion (the point )7 9n0pely ko nln3u7ion 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+98(ocb -t f4ejnsuzslb)ampd(m) y; system shown, 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 attraction. The orbital period of the star of mass M is T. Wh +) ujna cltsb-do)e;fmy s (pb9m4z8(ich 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 sp+ bk65dunj3to zdsj:s,c3 xd8 eed vand orbital radius R around a heavy stationary mass. An external impulse is quickly applied to the rocket directly opposite to sdcjt ozn,s3bd3+d: ux658j k 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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