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 :6jpx*.q3t9h l z/ wriciq*es equal areas in equal time” can be derived mo/j*hr6 zwt:*qci 9 q.3li spexst directly from which conservation law?

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16.17:“All planets in the solar system follow elliptical orbits with tg xej37sb(y )lhe Sun located at one focus of the ellipse.” This ys)jbeg (3l7 xstatement 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 attral o4djn )3rx uzukguyzd4(p 9 nn:5wj5h/ n,r4ction between two small objects if the mass of each object is doubled and the distance bu/z yxwpnzlu5 94k5r3j,r njgn :4( hodn)ud4etween their centers is doubled?

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95.09 Two spherical bodies attract each other witt ;axnvv.o90ih a gravitational force of 4.0 N. What will be the force if the distance b9ant oiv x0.v;etween them is doubled?

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14.27: Two spherical, non-rotating planets, X andY, have the same ymqg;w/a/lc x78h lgf-tkp s9a//(j2oen h 7iuniform densitg fe-(i7;n9/cmpy2/ 7kqhwlxol tsjg8ha/ a/y. Planet 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, have the same /)d rr b;1jxt-yisjczn jm +;er yf-++uniform density. Planet X has twice the radius of Pl/rzj+)xfr+;1- jdtcyj;re yi b s-m+n anet 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 if v9+sx6mslhwy/ tqr9u:.fb; t is orbited by a small satellite by setting the gravitational force on the satellite equal to the centripetal force on the satellite. Which of the folqv:.fs+u t69bflhs 9x;/y r mwlowing 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 aa43xrrtbhwro8 ,*/r tttracts John Glenn with a gravitational force F at the surface of the Earth. When he made his famousr3rrax b, hr/t84tw*o 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 Moon-Earth system (ignore acz)ye d83ykzjo l;h+3ny influence of the Sun), which one of the following best expresses the magnitude of the Moo hj eykozd83c;+)z ly3n’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 cargo for the inte)oh,po7:n p7akgrozhc 2z++ 2j xzj2lrnational space stzlzgh j no7)ao: ,kp+2p+xjhro 72z2cation, which of 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 surfc10ybbmu o/v1ace of the Moon experiences the same gravitational force abc0o /vumb1y1s a second object 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 that41y x leuu.(j1j1xul r has a mass, m, and a weight, 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 distanjy.xj 1rxle4u1u1( luce 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 the mass of Eart1 h2oy0shiar4y pe(.kqc kh4-h and twice the radius of Earth. The magnitude oks44qh -pk(12y0oeiy. chahr f 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 ontxnk3.cabx /25a/ su +ixg t;ie-fifth the Earth’s mass. The gravitational acceleration at the surface of the3x 2. xixgint5ba /+cu st/ka; planet is most nearly

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15#

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08.38: Akg 1200 satellite orbits Planet X in a(tt t5 ly )tbehqn;)6rq49ycyrj: fy 0 circular orbit with a constant speed of 5,000m/s. The radius yl fj: 4tq9(etnbcyyq ;tt5)) 6y rhr0of 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 plan2o .n:c .wdc(o)xah nqet orbits a star with mass one-half the mass of our sun. The planet’s orbital radius is tnaw 2no.x cd :.c)h(qohe 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 and 2, are put into 2zv2(y)q/2ec4 ykq3lis q a oscircular orbit at the same altitude above Earth’s surface. The masiqqv yscyqs2k4 oe)2/(la2z3s 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 a; r*xhtnsc7wti*lsh,k +q (h )round 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, the word “we 6vc(tqif lp o759ob5dor(r6eight” refers to the force a scale registers. If the Earth were to 7o56( qrtor(fd iv 95 cb6loepstop 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 coxu9hu, noen 7h(h49 qjmet moves from aphelion (the on4q99j( , unu xhh7ehpoint 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 s:5g2pfr+l qahtar system shown, the two stars follow circular orbits about the syst:5g + 2pfqahrlem’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 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 ora;9+ xjz41 ipv-rggu /clr)q jbit with speed vand orbital 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 orbiz4ar jq/9 j+-xr)1v;lpgguc it. In terms of R, the size of the semi-major axis a of this new elliptical orbit is

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