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?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 Secob ycwyg0/ (txe; c +x;)ptywm1nd Law about “sweeping out equal areas in equal time” can be derived ct;p+ey0xb wygt/1)xy;c w(m most directly from which conservation law?

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16.17:“All planets in the solar system follow ellipticaz2nd;a)8 r: 0gsxsu 8wusncs/ l orbits with the Sun located at one focus of the ellipse.” This statement is; xs8sasu)dgcz8/rsn 2:u0wn 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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单选题 ( 1.0 分) 切至整卷模式搜藏此题

99.21: What happens to the force of gravitational attraction between two s-u*wd +rwrx3 n; dtgu8mall objects if the mass of each object is doubled and the distance between thei*-rgu r;wxddt3n w+ 8ur centers is doubled?

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95.09 Two spherical bodies2c9 0g+* gerx(zl)qfg2djk6nna.fg k attract each other with a gravitational force of 4.0 N. W+c)rnf*2q.2f k6g agn0jl 9ge(gdxk zhat will be the force if the distance between them is doubled?

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14.27: Two spherical, non-rotating planets, X andY, have the same msds 9r(a ogen4i 0hw 67x4m-cuniform density. Planet X has twice the nrwm4me9so (d- 0h6sixc4g a7radius 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 unixpw3 bs,2iq:)xe7s r.x t)yglform density. Planet X has twice the radius of Planet Y.) )pxetb xisr.,xl2 :g7 qw3ys 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 satf yh s c+wibp61;xgcs *hle:16ellite by setting the gravitational force on the satellite equal to the centripetal force on the satellite. Which of s+:;xhbh*f1gcspiyl6w e c16the 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 gravitationz2g+x0ff/,37vov p oy ao i0mral force F at the surface of the Earth. When he made his famous second flight in orbit, the gravitational force on John Glenn while hig+0 o3,r o/0xyo afv fmpz7v2e was in orbit was closest to which of the following?

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单选题 ( 1.0 分) 切至整卷模式搜藏此题

14.30: Considering only the Moon-Earth system (ignore any influence of the-ld50 c eh0y26wezd ne Sun), which one of the following beszee6c5 dd-we 0y0n h2lt 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 la lbs-,2: oaxa cargo for the international space station, which of the following graphslx-,bas :l ao2 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 gravitatioyz2ycn tj(0tl 6 *kq:onal force as a second object at the surface of thn:0*k (y6c jto 2qzylte 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#

单选题 ( 1.0 分) 切至整卷模式搜藏此题

00.24 Consider an object that has a mass, m, in)b9hs*.,rkicurz +ovp* akx8f5 4rand a weight, W, at the surface of the moon. If we assume the moon has a nearly uniform density, which of thvarri *95o ,u*8 4ifkbhpc .+rzxk) nse 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 tn*z .bsa:ewse- 5wg/rhe radius of Earth. The magnitude of the gravitational acceleration at the surface of this planet is-r/5neaweg:. wz*ssb most nearly:

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14#

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98.24: A planet has a radius one-:4 ctb3k2ktnb half that of Earth and a mass one-fifth the Earth’s mass. The gravitatio43tbkn c:kt2 bnal acceleration at the 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 circular orbit with a9*je ew s5 nwg4/le8gi constant speed of 5,000m/s. je9 gli45/wgwesen8*The radius of 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 planet orbits a star with mass )q 22xz.p4 wkc*oda gohart30.ebbf:g 3ga) xone-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 pgf3eto4akb:x)g rcdp b awoa 2.hx2 g3.)z0q* lanet to complete one orbit?

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17#

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97.12: Two artificial satellites, 1 and 2, are put into circular orbit a70l/fp sk)y gjt 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 is T, what is the period gfpyl)j /07 ksof satellite 2?

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18#

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15.22 Satellite 1 makes a circular orbit around the n v b0ec7)zk3gEarth 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 “weight” rej2 o, zfh;61.ffcr ietfers to the force a scale registers. If the Ehr6z;tj f e2oc.i1 f,farth 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 in an ellipgi3-i1c/ t5siheh2vd tical orbit around the sun. As the comet moves from aphelion (the point on the orbit farthest from the sun) to perihelion (the point on the orbit closest to the sun), which of the following results is trues i1i25iveg 3d/ thch-?

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21#

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17.48: In the binary star system shown, the two stars follow circular orbirrpru /5 /edgjj ++lb(ar.ypfe w +):sts 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 attraction. The orbital period of the star of mass M is T. Which one of the following choices reprea u+s5gr )jp (rybrrfed/w /e+. +plj:sents 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 orbital radius R arouu g 0giuxnf6 j9h/1o:nnd a heavy stai/g6g:9ux onufn 1j0 htionary 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 orbit. In terms of R, the size of the semi-major axis a of this new elliptical orbit is

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