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 Seco- oq3gq: k6ux((,ar ipr9qn gnnd Law about “sweeping out equal areas in equal time” can be deri6 q q39a-ir ok,g :(nup(ngrqxved most directly from which conservation law?

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16.17:“All planets in the solar system follow elliptical ea qxl +- elhy. 4/jvmzh/8)uhorbits with the Sun located aev/ .q)zyja-mh4lh l /8e hx+ut one focus 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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99.21: What happens to the force of gravitational attract f ;zafw*cg6f .4( pln7fdpk9eion between two small objects if the mass of each object is doubled and the distance between their centerf*p ;w cn.lza4fed7 ffp9k(g6 s is doubled?

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95.09 Two spherical bodies attract eacd. z1h*cg0/ kxq.qhajh other with a gravitational force of 4.0 N. What will be the force if the distance betw*hg.q 1adxjk h/.zqc0een them is doubled?

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14.27: Two spherical, non-rotatixx;ep fkf/7z2 5 zhq 6 7jg-fv;ib65iz7ld gafng planets, X andY, have the same uniform densitk;g2afezf677f-dh/g7; 5f5qvi ixb zjl xp z 6y. 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, hay:z(egpp+, y*rsu6n mve the same uniform density. Planet X has twice thymue+ 6r gn:z,pp s(y*e 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 planem )b2d;j+fug9osv : 7nh9 c4ck3j lzhbt can be calculated if it is orbited by a small satellite by setting the gravitational force on the satellite equal to the centripetal force on the satellitucb9o )d2cbzgs :437lvmh f+9;kjjnhe. 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 gravitationallc. p9cf+sc. *i w)gqf 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 to whiclsqcw* fg.9 p)cc+f.i h of the following?

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14.30: Considering only the Moon-Earthj3j(:uzh5m i b system (ignore any influence of the Sun), whib h3 :jm(5jizuch one of the following 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 away from the earth with a cargo for the internatios-7qr vv-swk5. 4 ylurxyrk90nal space station, which of the following grap4kr-x9ku5 wv r0q yslrsyv-. 7hs 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 gravit m(a5cvv 5m7 (c 9i-tbyh5alrwational force as a second object at the surface of the Earth. Which of the flm mc5r(7 5hy9v5(wtba-icv aollowing 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, fm yz(tvo6x s;g./81uimp li8 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 av1 8 x(ysiitmf6;.8pozu/ gmlt 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 the mah4b giju 7af0*n7) qnbmf ne73ss of Earth and twice the radius of Earth. The magnitude of the gravitational accelerae7guq*ibj nf73 0 n) f4bmahn7tion 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 z6za u0tzk1xq-nc 6b p skb:;0Earth’s mass. The gravitational acceleration at the surface of the planet is most nearpun6bcazbk; z -0q01sx6 z t:kly

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15#

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08.38: Akg 1200 satellite orbits Planet X in a circular orbit wit.p,,g7+g *ovwbvf ldepv; 7 seh 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 on the satellite by Planete l7v7 ovpg;e+d.,w ,*fb pgsv X?

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16#

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94.34: A hypothetical planek0ol*bsk+ (ohx(rft02j*zpz n:i s y 7t orbits a star with 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 planet to complete one orolp(zsrz nk7+h2 y(* b0stji 0:x*kofbit?

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17#

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97.12: Two artificial sa p)kumv1dixm3vr/x0/v+9 o24slpb d ztellites, 1 and 2, are put into circular orbit at the same altitude above Earth’s surface. The mass of satel9p x3v0pui 2vzrk dm /sx1)/bm lod+v4lite 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 o g4y;3)fmsh8gr8m le ij:kuh3za6.rn rbit 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, the word “weijf))hh26 )+vntttl clght” refers to the force a scale registers. If the Earth were to stop ro 2 )vfl)jht6 hnt+clt)tating, 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 cometg;g hg6cz)( )rtt0szu ak lr32 moves from aphelion (the point on the orbit farthest from the sun) to perihelion (the point on the orbit cg2zt)hctk) asr zl g3rg u;(06losest 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, the two stars follow circulc.: la -v2q1n hw7gntlar 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 attracti:1h wl7.t- agcqnlv2n on. 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 orbituwv va2mef.5os)gz ( ,al radius R around a heavy stationary mass. An external impulse is quickly applied to the rocket directly opposit(m 5 efowsvaz 2)uvg.,e 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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