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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 a8hu9rc: -x0rlrhdl+ ubout “sweeping out equal areas in equal time” can be derived most directly from which conserv-uh h rcl0rl+rd :xu89ation law?

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16.17:“All planets in dkk ei*olky45rr896o the solar system follow elliptical orbits with the Sun located at one focor6koe8 lk95rk y* id4us of the ellipse.” This statement is best summarized 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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单选题 ( 1.0 分) 切至整卷模式搜藏此题

99.21: What happens to the force of gravitational attraction between two sma+qtfxw28hk7 oll objects if the mass of each object is doubled and the dista fk7h+xwq8t2 once between their centers is doubled?

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单选题 ( 1.0 分) 切至整卷模式搜藏此题

95.09 Two spherical bodies 5fso1l l2yz;,mksy. mattract each other with a gravitational force of 4.0 N. What will be the force if the distance betwe z 1o5m;sylf lmk,.sy2en them is doubled?

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14.27: Two spherical, non-rotating planett ry5 h 4(ulyhwp5rj-3s, X andY, have the same uniform density. Planet X has twice the jh-y4ltrh y5p ur3(w 5radius 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-rotcni, .vq-*nxxa apc*x..8fqu ating planets, X and Y, have the same uniform density. Planecx.n -ui,* .a xqa .p8qvxnf*ct 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 qa0f8e:h -kzfu )t 3v6x ecb3cby a small satellite by setting the gravitational force on the satellite equal to fq ba 6tcke-c zxvh38)0eu f:3the 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 gravitational forcm:6.3wdlrf 6okn 5x a4xdx mk/w96ed se F at the surface of the Earth. When he made his famous second flight in orbit, the gravitational force on John Glenn while he wasxwmo596xefd6 s/lx6r4k3. a:dn w dmk in orbit was closest to which of the following?

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单选题 ( 1.0 分) 切至整卷模式搜藏此题

14.30: Considering only the Moonr7wxu i6y 5qt(-Earth system (ignore any influence of the Sun), which one of the following best7w5 6rtuiqy( x 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 sl +g,q1y ho+0kmue;aqkw-+ icargo for the international space station, which of the following graphs would best represent the gravitational force on the cargo versusams+e;kg -+yl wiq+01,hq ok u 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 surface100z 7o1bhd ckrqggm9 of the Moon experiences the same gravitational force as a second object at the s9bog7d z 0cmgkh10 1rqurface of the Earth. Which of the following 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 objec-kgv 3y;n ig(nt that has a mass, m, and a weight, W, at the surface of the moon. If we assume the moon has a nearly unif(gy;v -ki3nng orm 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 aa .xett+u1 0nib;0k2mp7x z zric*j ,seven times the mass of Earth and twice the radius of Earth. The magnitude of the gravitational k0 anc ,t0p mti2e1auixzxr* zj;7b.+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 on4ykrbl3(f4p3 ub z we 9*9gx5gfcb4a ne-fifth the Earth’s mass. The gravitatiy9 gagrz3b4npl4 4b 3f * exwb9(ufk5conal acceleration at the surface of the planet is most nearly

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15#

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08.38: Akg 1200 satell6* 7h0tze4-n nygx o*mqc6skbite orbits Planet X in a circular orbit 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 exer0s7h6tn6 exb- *kmgc nyq4z o*ted on the satellite by Planet X?

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16#

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94.34: A hypothetical planet orbits a star with1n0j qay-ttj4 /uk 1ba mass 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 planetn/1aatqj1y0-b j4 t ku to complete one orbit?

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17#

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97.12: Two artificial satellites, 1 and 2, are put into circux (; (u*vnwub nynn(hxu 13m2plar 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 is T, what is the period1nhn 2up(m (xun*;3 vnuxy(bw 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 radius cn2z*a4dq wt n8;/zmm$r_1= R$. 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 word72fkn q)llsv z2 +cb4s “weight” refers to the force a scale registers. If the Earth were to stop rotating, but lqfn)z4sk2l72v+ csbnot 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 sunuxm1a ,6gkf:n. As the comet moves from aphelion (the point on the orbit farthest from the sun) to perihelion (the point on the orbit clf6 n,k :xug1amosest to the sun), which of the following results is true?

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21#

单选题 ( 1.0 分) 切至整卷模式搜藏此题

17.48: In the binary star system shown, the two stars follow circular orbits ag 9- mtrqaixtv7qk-3d9;3px / pf i7vgbout 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 t vkrqxd3g-x/pgttm;p9737 aq- vi9ifheir 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#

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 p7wty:v. 0 no jf rg:*,emko:1xhzc1lvand orbital radius R around a heavy stationary mass. An external impulse n*zf:l hoxw mo0ck,gte:.1rjp:1yv 7is 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 new elliptical orbit is

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