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 equyhc( 4q -pqehi 6s88daal areas in equal time” can be derived most dirq -h46s8c y dh8e(piaqectly from which conservation law?

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16.17:“All planets in the solar system follow elliptical orbits with the Sun w(q exa4h ft8lc.lb/.iaj4w7located at one focus of the ellipse.” This statement is b8wa4.tb/ h q .xc(4i7 awjlfelest 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 attractio rm8/n(;mw xzfn between two small objects if the mass of each object is doubled and the distance between theirfr (; nwxmm8z/ centers is doubled?

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95.09 Two spherical bodies attract each othe778;e3a; es; g*ittmybstrwm 4kc fo/r with a gravitational force of 4.0 N. What will be the force if the distance between them is d3io*yf ; tem asgksct;r4 t/emw8;7b 7oubled?

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14.27: Two spherical, non-rotating pla4n z8au wt fqlyn86827b,fij tnets, X andY, have the same uniform density. Planeiff ,z2yntl7uanjt 68w8b48qt 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 ty4 eiiaeh/g 5:g jsw./ewci6v;x)s 3 uniform density. Planet X has twice the ;i/w: y vg3e.)eas4gejwxh/6tsi c5iradius 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 by a small sat u.;4ls+lm;l8c rdsdhxg :q6zellite by setting the gravitational force on the satellite equal to the centripetal force on the satellite. . 6ruslsz;m qhl8x d:4;+c gdlWhich 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 Johna/a.bmze77j p Glenn 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 was in orbit wa7 .mjbza/ ap7es closest to which of the following?

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14.30: Considering only the Moon-Earth4 z6w1cxxg,7u zehuk6 system (ignore any influence of the Sun), which one of the following best expresses the magnitude of the Moon’s accelerati6,kugzxcxeuzhw 4716 on 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 internatioym d k17bp-g*y1s; vxonal space station, which ox*g11pky-y do7; vbsm f 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 Moc/ kfnd1 cu5ey n2x;z7on experiences the same gravitational force as a second object at the syzex un;c12f 57 c/kdnurface 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, W, at the surf -pkk1x rz(1zcol-q+ cace of the moon. If we assume the moon ha1z -k 1clz (-pokcxqr+s a nearly uniform 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 seven times the mass of Earth and twice the h3hug+c:;6jkpy fo7 mradius of Earth. The magnitude of the gravitational acceleration at the surface of this planet is most nearlky3ucp h6; +ohj7fmg:y:

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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 * uigw+axsm ghc7 -yg7b;oy6; Earth’s mass. The gravitational acceleration at thea7hg6; cy-xgbymswuo*+7 ;gi surface of the planet is most nearly

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15#

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08.38: Akg 1200 satellite orbits Planet X in a circula8u6 7bz/n .ym+usr oqqr 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 on the satell/q qunm o y7rb86zu+.site by Planet X?

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16#

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94.34: A hypothetical planet orbits a star with mass o z2s:s,h;xw /htkp9uone-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 tou2zhhs/w:,kxpot9 ;s complete one orbit?

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17#

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97.12: Two artificial satellites, 1 at( 3bi rb 0a4oirlssw84p 1/v.vn yp/xnd 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.8 0wps /r/4br4a y1ixbo ( vnptis3vl 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 orbitidbd c6kpa y u/8867gl 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 (r*d k ;kff-zkbbk y7: g*ei,k -jxte0word “weight” refers to the force a scale registers. If the Earth were to stop rb-kf:;ti(gkrze-* yb7k dj x0 ,kek* fotating, 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 +; ev.wzazc6r xf1*t; 6afkwb the comet moves from aphelion (the point on the orbit farthest from the sun) to perihelior .fe6; kwtb fv+xc* awz1;za6n (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, the two stars follc:,15 k9gqgy: wvqm(mt ra ei4ow 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 attracq 15rmt:gye(gac,q :wvimk49 tion. 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 iq y:ewfol0u59myub),00pl wf .5ureon a circular orbit with speed vand orbital radius R around a heavy stationary mass. An external impulse is quickly applied to the reypl0r:m)5 uw 0 5fuoulo w.q,e0 y9bfocket 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