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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 “r y-w*:hr/yw asweeping out equal areas in equal time” can be derived most directyr h: wa-/*wyrly from which conservation law?

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16.17:“All planets in the solar system follow elliptical orbits with the Su /fekjc6c3bw j. h)j3cn located at one focus ofk6wjjcebh33f/jc ) c . 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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99.21: What happens to the force of gravitational attraction beqfdl 73 b8 y:p.xw+mtq; fqc1dtween two small objects if the mass of each object is doubled and the distance between their c7x 3mf+:t ;q8lf qybpwq1d.d centers is doubled?

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95.09 Two spherical bodies attract each other with a gravitational force of /i-h w1wrikvl79o)-j *tkqsh 4.0 N. What wi-*iwo kht rs/kw) 9jq-v1 h7lill be the force if the distance between them is doubled?

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14.27: Two spherical, non-rotating planets, X andY, have. meughvr:o*,ec25jv 8g wu( x the same uniform density. Planet X has twice thrx2j*vu.ou5e me hw(gv 8cg:, e 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, have qnp;esv 8hmn1zf-)*uthe same uniform density. Planet X has twice the radius of Planet Y. Let unef1mz)*sv8-;q p n h$v_x$ 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 calcul) rdx2; up-gufated if it is orbited by a small satellite by setting the gravitational force on the satellite equal to the centrp ud2x -fu;g)ripetal 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 G(8 xsptrz g -sql(4oz3lenn with a gravitational 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 wpx4 3 r (tzlgs(os-z8qas in orbit was closest to which of the following?

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14.30: Considering onjmo*o hqf-ga(,lz u/n8 4 vd)wly the Moon-Earth system (ignore any influence of the Sun), which one of the following best expresses the magnitude of the Moon’s acceleration about d,gh( -fvm /zwouanlq)4 *8jothe 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 internationjmmc f)/*6:aqf90xrbsu cxd2 al space station, which sd)2cm0qxu :/ f9 j xcm*6abfrof the following graphs would best represent the gravitational force on 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 uur. 8m y7eho:gravitational force as a second objerhum7y8 :.uoect at the surface 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 object that has a mass, m, and a weight.s6j*w4nxdz30r5 lfku( ej kt , 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 massz(ukewdfkjr 6t*n4x . s03j5l 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 sevzv2* / ssul2wkv vb4/qen times the mass of Earth and twice the radius of Earth.2q/vvsb4k lz2/vuw *s 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 the jdbff) 2m lg(7Earth’s mass. The gravitational acceleration at the surface of the plf( jdfg 2l7bm)anet is most nearly

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15#

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08.38: Akg 1200 satellite orbits Planet X hs+yqdra 0ka6 .tji7 fjup6h s/7+d1 bin 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 exerted ouk rji ssa0df/a +1h6 .h jtbq67d+py7n the satellite by Planet X?

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16#

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94.34: A hypothetical planet orbits a star w90xq qlry88dkq1rofpy 82 h5uith mass one-half the mass of our sun. The planet’s orbital radius is the same as the Earfr2d8uyqxhq88qrp150 l ky9oth’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, 1g i wy- /3uxkv2tsa(g3 and 2, are put into circular 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 t/uag y23sv(w3x tg -kihe period of satellite 2?

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18#

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15.22 Satellite 1 makes a circulzv 8y2 5swyas,ar 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 following problem, t+.3loz z r8yj*ybaad(he word “weight” refers to the force a scale registers. If the Earth were to stop rotatinlzr 8(y bozay+3.j* dag, 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 n7rzhcny3: t;7 git9m in an elliptical orbit around the sun. As the comet moves from aphelion (tcr 3nym: iz7n9tg 7;thhe 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 true?

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21#

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17.48: In the binary star system shown,mm 8e13ek9uq / nvh;xj 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. uv/k1ej 89xqmh mne3; 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 speed vand orb1ck d -2tfuu w7ihky9c0f9/bz ital 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, putting the rocket into an elliptical orbit. In terms of R, the si-tz hckcfduwu9y0k7/ 19 i2bfze of the semi-major axis a of this new elliptical orbit is

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