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 equal areas in equal time” ca4hic7qpl k 8/pn be derivp8l7p kih4cq /ed most directly from which conservation law?

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16.17:“All planets in the solar system follow elliptical orbits with the Sun loc;x2rtwe oc .g. .vms8s3saon 27aoe0 cated at one focus of the ellipse.” This statement is best summarized by which one of the .eg. .omeso3oa rwt;ssx ac7c 80v22n 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 gravitf j- uh3)z-vgwy*o6dj ational attraction between two small objects if the mass of each object is doubled and the distance between tw-gdv6-jfho 3yu)z *j heir centers is doubled?

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95.09 Two spherical bodies attract each other with a gravi6rt gau y2k82ftational force of 4.0 N. What will beyktaf 2gu26r8 the force if the distance between them is doubled?

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14.27: Two spherical, non-rotating planets, X and+ykuv ps.3i d/Y, have the same uniform density. Planet X haku.psi 3vy+d/s 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 sa m*ibztpzi rvr,, 7k2(me uniform density. Planet X has twice the radius of Plan,krp,viz* (t72 mzbiret 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 calculatedvd9/vz*xb5bj-ls r 5uzdr96 t if it is orbited by a small satellit5x9s/5zt d6b9zvrrlu -b*jd ve by setting the gravitational force on the satellite equal to the centripetal 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 Glenn with a gravitati .6bow d:o+omconal force F at the surface of the Earth. When he made his famous d ow 6mo.c:+bosecond 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 oni4(*zp4l ws mvi 7lm8uly the Moon-Earth system (ignore any influence of the Sun), which one of the following best expresses the mazi8u44wl* v 7lims( mpgnitude 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 fousfy3zw ls409,7 xm ahr the international space station, which of the following graphs would best represent the gravitational force o 3whxl sfya 0u,9m4z7sn the cargo versus distance from the surface of the Earth?

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11#

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99.33: One object at th; lex*z h+ u vx6ey.:nkixpg64e surface of the Moon experiences the same gravitational force as a second object at the surface of the Earthvx.zh46 g pyl:i uk*;xenx 6+e. 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 sur3j, xwj i6gyzaam6r*0d 9k9 nmface of the moon. If we assume the moon has a nearly uniform density, which of the following wjaaxd wr3*gnk9m 960 jmi6 ,yzould 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 sxl*z se* q5e;zdcq8 +leven times the mass of Earth and twice the radius of Earth. The magnitude of the gravitational acceleration at the surfa*sz *lezxec+ql8 5qd ;ce 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-fif w1uie5ese:ec bg+; ami-*tg4th the Earth’s mass. The gravitational acceleration at the surface of the planet is most 54*be ei;e1-ua icwget s+: mgnearly

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15#

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08.38: Akg 1200 satellite orbits Planet X in a circul 9h5njn3+q6is 6ny(ykxl 8la sar 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 satellite b(8nq yk 6ay3hnj9lsx+lsn5i6y Planet X?

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16#

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94.34: A hypothetical planet orbits a star with mass one-half the mass xi8 l6 i)w;kqmof our sun. The planet’s orbital radius is the same as the Earth’s. Approximately how many Earth years does it take for ti)8wi6l qxm;khe planet to complete one orbit?

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17#

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97.12: Two artificial satellites, 1 and 2, are psy 70;n 79fgbpda 9unzdu3b-6h3rvwcut 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 is3 sd- cb973 nz7p f0v9yrnw;b6 uahdug 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 around the Earth with a radius e4ww7y ky(dpu 2l-1f(d- zivw $r_1= R$. 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 followo 6mav;hk (hqn+ ii 03do.-jlging problem, the word “weight” refers to the force a scale registers. If the Earth wer-a 0lhvmik+6i;hj .n3 dog(qoe 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 in an elliptical orbit around the s b*m(hejw4 ds,ust 4t l9gc14fun. As the comet moves from aphelion (the point on the orbit farthest from the sun) to perihelion (the po fg(m4wd9ubh jl44et 1*sst,c int 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 stt *paoqu:j+y.y l0y8io rg) n4ars follow circular orbits about the system’s center of mass. The stars are separated by a distance D that is large comparedp:).oa8+jgoy r4ln q iyuy*0t 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 org-,;u ztcs*f5a.vbuq c; b wk,bit with speed vand orbital radius R around a heavy stationary mass. An external impulse is quickly applied to the rocket ,c;,bs tzk-cu;a * fbwuv5q.gdirectly 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

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