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 a xcdgv92tkw3 9uda, ,nbout “sweeping out equal areas in equal time” can be derived most directly from which consg 2t, 9kdwvu3a9,ndcxervation law?

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16.17:“All planets in the solar system follow elliptical orbits stqs cowls 3cn4 i5r72o7qj0 *with the Sun located at one focus of the ellipse.” This statement is best summarized 7qn302rw4otoq c*7jscissl5 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 lt1/hptgk32 r-.ba 3sawec:/ odsrd1ion between two small objects if the mass of each object is doubled and the distance between tw-ltkg.a b1et/ 2a od:13shrrs3pd/cheir centers is doubled?

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95.09 Two spherical bodies attract / h0gy qv*i x ie(q57(sn;ef7htv*-j)fpoggaeach other with a gravitational force of 4.0 N. What will be the force if the distance between them is douojntqi(5-gfx ;gv( y*ag0 qh7) p7sei/ehfv* bled?

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14.27: Two spherical, non-rotating planets, X andY, have the same unifkneo vcraw5 g/ g m)(,iu/x*l,orm density. Planet X has twice the radius of Planet Y5, r cgolgu k*xw/m(n)/ a,evi. 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, nonq4 4y8y :mgaxn-rotating planets, X and Y, have the same uniform density. Planet X has twice the radius of Planet Y. Letaq4 n4xyg:8ym $v_x$ 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 ay yif4 q/-1pfl small satellite by setting the gravitational force on the satellite equal to the centripetal force on the satellite. qlfi-y/yfp 14 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 Earthwrwds2abdk w9 0o9f/0 attracts John 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 was closest to which of the followi9b0odw09wa f2k/w rsd ng?

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14.30: Considering onlybwa-,w*v--k-u l5 notaz+ y nu the Moon-Earth system (ignore any influence of the Sun), --lynuu+z-* ,abnv-kowta 5wwhich 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 awi3p jgr /6my43uh d:xkay from the earth with a cargo for the international space station, which of the following graphs would best represent the gravitational force h6jgmr3yxi 3pkud/ 4: 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:ikx7. x 3.bb +yyucwp the Moon experiences the same gravitational force as a y7cbbiw3+xp y: ..xkusecond 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 that has a mass, m, and a weight, W, at the surface oc/y 1f82z vlwok-qhn*f the moon. If we assume the moon has a nearly uniform density, which of the following would be closest to the object’s mass*/cy1f-ovkwhz 2 nq8l 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 twicer5deod,veo+s + b0ja/+pou-y the radius of Earth. The magnitude of the gravitational accelev-p+ d oooe+r0d5yb +u e/j,asration 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 o(,8 a1dgs :ibqi1j tuvf Earth and a mass one-fifth the Earth’s mass. The gravitational acceleration at the suav:s 1(1u tb8jgd i,qirface 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 circular orbitgnrw1 ht su62+ with a constant speed of 5,000m/s. The radius of orbit is 7,500,000 m. Whg hw 6u21s+nrtat 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 planetbzs+kjw64g p*,kp3 ir 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 p3 kzk+bg4 i6s w,pj*rthe planet to complete one orbit?

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17#

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97.12: Two artificial sx;w(5 s5a lb x -*,-lc6jrwmmontx4v jatellites, 1 and 2, are put into circular orbit at the same altitude above Earth’s surface. The mass of satellite 2 is twice the masswvwx;oanxl- j4mr b6x,*(5cl-j s5 tm 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 mac:/a ig iq1an951 fq: 3ttc)tton/ vwukes a circular 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, a pyj:7(hy*c*k bk9sathe word “weight” refers to the force a scale registec*a kkp by:y(9 h*j7asrs. If the Earth were to stop 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 x29 emxe )if3xin an elliptical orbit around the sun. As the comet moves from aphelion (the point on the orbit farthest from the sun) to perihelion (the pomx i x)39exf2eint 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 stao6u4 qish9 cw2r system shown, 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 attra2 q6cw 4is9uhoction. 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 orb ()hf;osxs ks;: hs3uah9 5i dy83vzpsital 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 a:hs vfpiyxod89)s h ;kssh (35zs3 ;uinto an elliptical orbit. In terms of R, the size of the semi-major axis a of this new elliptical orbit is