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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 Second Law about “sweeping out j6) dpa iyq,t5equal areas in equal time” can be derived most directly from which conservyt ,a qj65d)ipation law?

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16.17:“All planets in the solar system follow8nczm)i0 b)gtyk9+gi: p yaafp2rj:2c i9 oi) elliptical orbits with the Sun located at one focus of the ellipse.” This statement is best )i z yjaikgpp 9n cc9fa8:got2b+)r)0im2yi: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 attractionj v6gy;vl n4m5 between two small objects if the mass of each object is doubled and the distance between their centerjvnm 4 gyl65;vs is doubled?

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95.09 Two spherical bodies attracth ko g4+p+9l3m .8jkruvrra5z each other with a gravitational force of 4.0 N. What will be the force if the distan9+8 rj o 3.rzrhu+pkagm k5vl4ce between them is doubled?

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14.27: Two spherical, non-rotating planets, X andY, hap)t wbgc7:nr;4p1 sixve the same uniform density. Planet X has twice the radius of Planet Y.b ;ri74s1gp xw )npc:t 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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单选题 ( 1.0 分) 切至整卷模式搜藏此题

16.46 Two spherical, non-rotating planets, X and Y, have theeluw5i(u+ qfvfc(n20 same uniform density. Planet X has twice the radius of Planc 2 u(u+l5wie0f(qfvn et 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 calculatedh/n + zliwj h/xg:dz16 if it is orbited by a small satellite by setting the gravitational force on the satellite equal to the centrip1i/gh+zx/w 6hdzn jl:etal 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 Ehz 3 e8lrvxs;-arth 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 whi ;e8s3 hrlz-vxle he was in orbit was closest to which of the following?

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14.30: Considering only the Moon-Earth system (it.z(ec(0ct1jwjl gcrlh )o6sul0 ,7 kgnore any influence of the Sun), which one of the following best expresses the magnitude of the Moon’s acceleratio0c7cr t. )wze6o,k jl l 0h((gjts1lcun about the Earth?

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10#

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02.19: As a rocket blasts away from the kgdnk;z sya4*z+yp *f,s .0zrearth with a cargo for the international space station, which of the following graphs would best represent the zk,s.r pysydkz;* +4an0gzf* 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 surqi* e02 wy 3it4p0bwb 2bjirgugeo- 8.face of the Moon experiences the same gravitational force as a second object at the surface of the Earth. Which of the followi i 80g023u-bbi2 ew qywrbj.g*oie4t png 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, and a weight, W, at the surface of c ib2 g-ryrf/3p55 v)b/ howzaa8 sk*vthe moon. If we assume the moon has a nearly uniform density, which of the following would be closest to the object’s mass/5bpariwf)yz2 5 vvhb3sgk*8c/- rao 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 hypotheticalug zdb. (1j7jc-fcox) planet has seven times the mass of Earth and twice the radius of Earth. The magnit71gz-djo(xc )u c b.jfude of the gravitational acceleration at the surface of this planet is most nearly:

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14#

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98.24: A planet has a radius3gs. 3+p4 rmku7knqqp 5 wjg3s1htkd 7 one-half that of Earth and a mass one-fifth the Earth’s mass. The gravitational acceleration at the surface of the planet is most nearl n5g tku7qks1k4qh7+r d gj3pm.3wsp3y

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15#

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08.38: Akg 1200 satellite orbits Planet X in a circular orbit wi5v6g3l c n*ndgth 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 sat ldngn3*c65gvellite by Planet X?

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16#

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94.34: A hypothetical planet orb6/qqxfm 7.nwh8i /u,t.ys6 qv pk:nkaits a star with mass one-half the mass of our sun. The planet’s orbital radi ktfq 6.hwnk/nx,q6y q.vu78/s ampi:us is the same as the Earth’s. Approximately how many Earth years does it take for the planet to complete one orbit?

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17#

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97.12: Two artificial satellites, 1 and 2, arzz c /(q:r8nf sabk9yyiz tz u4x*5a92e 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 the perioia*q9x9 nyzrza uc/8z:t5f4byzsk2 (d 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 orbit around thsxv.u0q d2qr g0- 5rnme 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 cgi .jh8q3- rvjvm;u :.pr3ca“weight” refers to the force a scale registers. If the Earth were to 38vc;. r qjjhvp 3ium -a.cr:gstop 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 sun. As g*ruz;ix1 ix67v 0tje the comet moves from aphelion g u6 irx*ie;1x7zvt j0(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 true?

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21#

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17.48: In the binary star system shown, the two stars follow circul n.wc);za14bwth(zf 7o(x2v ygonhj4w.m q2ear 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 attraction. The orbital period of the star of mass M is T. Which one of the following choices rea;42)(qo ywgmjhwnf1.ce4 o 2 .7bt(n x hvzzwpresents 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#

单选题 ( 1.0 分) 切至整卷模式搜藏此题

06.50: A rocket is in a circular orbit with speed vand orbital rz)0gb.vj /jww adius 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 into an elliptical orbit. In terms of R, the size of the semi-major axis a of this new ellipticwjg j) z0/w.bval orbit is

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