2021USAAAO预赛选择题

题目

1. On December 21, 2020, Jupiter was at $$(\alpha,\delta)=(20^{h}10^{m},-20°34′)$$. Which constellation was Saturn in?

(a) Capricornus

(b) Aquarius

(c) Pisces

(d) Aquila

2. What is the spectral type of a star with a luminosity of 5.86 * 10²⁶ W and radius of 8.51 * 10⁸ m?

(a) A

(b) F

(c) G

(d) K

(e) M

3. The exoplanet HD 209458b has a mass of 0.71 Jupiter masses and orbits HD 209458 with an orbital period of 3.53 days. HD 209458 has a mass of 1.15 Solar masses. Assuming that the orbit of HD 209458b is circular (which is a good approximation here) and that its orbit lies perfectly in our line of sight, what is the radial velocity semi-amplitude of HD 209458 due to the orbital motion of HD 209458b, in m/s?

(a) 69.6 m/s

(b) 85.9 m/s

(c) 94.2 m/s

(d) 120.8 m/s

4. The photon number density of a blackbody depends on temperature as $$n_{d} = a(\frac{k_{B}T}{\hbar_{c}})^{n}$$ where $$k_{B}$$ is the Boltzman constant, $$\hbar$$ is the reduced Planck’s constant, $$c$$ is the speed of light and $$T$$ is the blackbody temperature. Here, $$a$$ is a dimensionless numerical constant. What is the value of $$n$$?

(a) 1

(b) 2

(c) 3

(d) 4

5. HD 209458b has a radius of 1.35 Jupiter radii, while the radius of HD 209458 is 1.20 Solar radii. What is the transit depth of HD 209458b, in percent?

(a) 0.013%

(b) 0.13%

(c) 1.3%

(d) 13%

6. Which of the following is a problem of the conventional Big Bang theory that is resolved by the theory of inflation?

(a) Under the conventional Big Bang theory, it is extremely unlikely for our universe to be flat or nearly flat today, contrary to observation.

(b) Under the conventional Big Bang theory, it is impossible for the Cosmic Microwave Background to have come into thermal equilibrium by the time of recombination, despite its observed uniform temperature.

(c) The conventional Big Bang theory predicts a huge abundance of magnetic monopoles, while no magnetic monopoles have ever been discovered.

(d) All of the above

7. Comet C/2020 F3 (NEOWISE) last reached perihelion on July 3, 2020. Comet NEOWISE has an orbital period of ≈ 4400 years and its eccentricity is 0.99921. What is the perihelion distance of Comet NEOWISE, in AU?

(a) 0.0123 AU

(b) 0.212 AU

(c) 2.69 AU

(d) 26.8 AU

8. An astronomer detected a galaxy and decided to analyze its different parts and physical aspects. The frequency generated by a “spin-flip” transition of atomic hydrogen is $$v_{0} = 1420.406MHz$$, however it was detected on the galaxy as $$v = 1422.73$$. He finds that:

1. Population I stars are (1) and are metal-(2).

2. The galaxy is (3) from us with a speed of (4) $$km * s^{-1}$$.

Choose the alternative that correctly completes sentences above.

(a) (1) young; (2) poor; (3) distancing; (4) 245

(b) (1) old; (2) rich; (3) approaching; (4) 490

(c) (1)old; (2) poor; (3) distancing; (4) 490

(d) (1) young; (2) rich; (3) approaching; (4) 490

(e) (1) young; (2) rich; (3) approaching; (4) 245

9. A stable open cluster of about $$N = 1000$$ sun-like stars has an angulardiameter of $$\theta$$ = 30 arc minutes and distance of $$d$$ = 500 pc. Assuming the cluster can be approximated by a sphere of uniform density, estimate the average velocities of stars in the cluster. The gravitational potential energy of a sphere of uniform density and radius $$r$$ is

$$U_{sphere} = -\frac{3}{5}\frac{GM^{2}_{sphere}}{r}$$

(a) 507 m/s

(b) 643 m/s

(c) 894 m/s

(d) 1021 m/s

(e) 771 m/s

10. What would happen to the analemma of the Sun if the obliquity of the Earth’s orbit suddenly went to zero degrees and its eccentricity remained unchanged?

(a) The anallema would be perfectly symmetric in both axes and would have the shape of an“8”.

(b) The analemma would look like a dot.

(c) The analemma would be the arc of a great circle.

(d) The analemma would look like a circle.

(e) The analemma would be a spherical triangle.

11. Let $$T_{{\odot},C}$$ and $$T_{{\odot},S}$$ be the temperatures at the core and the surface of the sun, respectively. Similarly, let $$T_{A,C}$$ and $$T_{A,S}$$ be the temperatures at the core and surface of the red giant Arcturus, and let $$T_{S,C}$$ and $$T_{S,S}$$ be the temperatures at the core and surface of the white dwarf Sirius B. Which of the following inequalities is true?

(a) $$\frac{T_{{\odot},C}}{T_{{\odot},S}} < \frac{T_{A,C}}{T_{A,S}} < \frac{T_{S,C}}{T_{S,S}}$$

(b) $$\frac{T_{{\odot},C}}{T_{{\odot},S}} < \frac{T_{S,C}}{T_{S,S}} < \frac{T_{A,C}}{T_{A,S}}$$

(c) $$\frac{T_{A,C}}{T_{A,S}} < \frac{T_{{\odot},C}}{T_{{\odot},S}} < \frac{T_{S,C}}{T_{S,S}}$$

(d) $$\frac{T_{S,C}}{T_{S,S}} < \frac{T_{{\odot},C}}{T_{{\odot},S}} < \frac{T_{A,C}}{T_{A,S}}$$

(e) $$\frac{T_{S,C}}{T_{S,S}} < \frac{T_{A,C}}{T_{A,S}} < \frac{T_{{\odot},C}}{T_{{\odot},S}}$$

12. The spectral line $$H_{\alpha}$$ in the spectrum of a star is recorded as having displacement of $${\Delta}{\lambda} = 0.043 {\times} 10^{-10}$$ m. At rest, the spectral line has a wavelength of $${\lambda}_{0} = 6.536 {\times} 10^{-7}$$ m. Calculate the period of rotation for this star, if it is observed from its equatorial plane. We also know: $$R_{star} = 8 {\times} 10^{5}$$ km.

(a) 29.59 days

(b) 14.63 days

(c) 21.15 days

(d) 34.39 days

13. The reflector telescope built by Sir Issac Newton was a f/5 telescope and had a primary mirror of diameter 30mm. He used an eyepiece with a focal length of 5mm. What is the focal length and magnification obtained by this telescope?

(a) 150mm, 30×

(b) 300mm, 15×

(c) 300mm, 30×

(d) 150mm, 15×

14.Take a look at the following image:

Three Messier objects are circled in the image. Select the alternative that correctly matches each object with its type.

(a) 1 - Open cluster; 2 - Open cluster; 3 - Nebula.

(b) 1 - Open Cluster; 2 - Nebula; 3 - Galaxy.

(c) 1 - Galaxy; 2 - Nebula; 3 - Globular cluster.

(d) 1 - Open cluster; 2 - Galaxy; 3 - Globular cluster.

(e) 1 - Open cluster; 2 - Nebula; 3 - Open cluster.

15. An interesting phenomena that happens in the Solar System is the capture of comets in the interstellar medium. Assume that a comet with a mass of 7.15 * 10¹⁶ kg is captured by the solar system. The perihelion of this comet’s orbit after it is captured is equal to 4.64 AU, and its velocity with respect to the Sun before being captured by the Solar System was very small. Calculate the velocity of the comet at the perihelion.

(a) 87.1 km/s

(b) 45.9 km/s

(c) 5.67 km/s

(d) 105.4 km/s

(e) 19.6 km/s

16. In a certain day, when it is 0h UT, the sidereal time of Prime Meridian is 5h 56min 9.4s. For this day, with start and end based on UT, find the civil time of Chicago, whose longitude and time zone are respectively, 87.65004722° W and UT-6, when the sidereal time there is 20h. The difference between solar time and sidereal time SHOULD be accounted for.

(a) 14h 1min 32s

(b) 13h 26min 17s

(c) 14h 36min 47s

(d) 14h 0min 43s

(e) 13h 51min 11s

17. Consider the following horrifying scenario. The Sun has become a Red Giant, and its radius is doubling every 100 years. Rank the following of humanity’s concerns in order of immediate importance.

I: Orbital decay due to direct contact between the Earth and Sun

II: As the distance between the Earth and Sun shrinks, the Earth will enter the Sun’s Roche limit and start to be ripped apart

III: Orbital decay due to tidal effects on the Sun’s outer atmosphere, the same way the Moon loses energy when forming the Earth’s tides

IV: Runaway greenhouse effect due to extreme temperatures, leading to the Earth becoming a hot, Venus-like planet with no habitability

(a) III, IV, II, I

(b) IV, III, II, I

(c) IV, II, III, I

(d) IV, III, I, II

18. TESS Object of Interest (TOI) 402.01 has an orbital period of 4.756 ± 0.000023 (days) and was last observed to transit on 2139.1 ± 0.0027008 (in TESS Julian days, i.e. BJD - 2457000). For follow-up observation, we would like to predict the next transit – this would be the 23rd transit since the last observation. In TESS Julian days, when will the next transit occur?

(a) 2243.732 ± 0.0027238 TESS JD

(b) 2248.488 ± 0.000529 TESS JD

(c) 2248.488 ± 0.0027238 TESS JD

(d) 2248.488 ± 0.0032298 TESS JD

19. Jupiter has a mass of 1.90 * 10²⁷ kg and a radius of 7.15 * 10⁷ m. To the closest order of magnitude, estimate the pressure at the center of Jupiter, in Megabars.

(a) 0.1

(b) 1

(c) 10

(d) 100

20. Which of the following statements is wrong?

(a) It is believed that elements with atomic number greater than that of iron are formed mostly by the explosion of supernovas.

(b) What holds a star together is the hydrostatic equilibrium between pressure and gravity.

(c) The granulations of the Sun happen on its corona.

(d) Protostars are actually not stars because their main source of heat is not fusion.

(e) The earlier type the main-sequence star, the more massive it is.

21. Consider a horizontal sundial where the triangular gnomon rises at an angle equal to the sundial site's latitude, $${\phi}$$ = 38°. If the area of the triangular gnomon is 2 m², what would be the area of the shadow in $$m^{2}$$ three hours after the noon in the first day of spring (vernal equinox)?

(a) 3.0

(b) 3.5

(c) 2.5

(d) 1.5

(e) 4.0

22. Consider an eclipsing binary star system observed (in some fixed band) to have a combined apparent magnitude of 5.67. During the secondary transit, the second star is totally eclipsed by the first star, and the apparent magnitude dims to 6.28. What percent of the combined flux is produced by the second star?

(a) 10.8%

(b) 43.0%

(c) 57.0%

(d) 89.2%

23. An astronomer observes that a Solar type star has an apparent V magnitude of 6.73 when seen from the Earth. Assuming that the average interstellar extinction in V is 1.00 mag/kpc, determine the distance between this star and the Solar system.

(a) 11.5 pc

(b) 49.5 pc

(c) 34.2 pc

(d) 23.7 pc

(e) 18.9 pc

24. 1. The temperature of the Sun is 5000K while that of Sirius is 10000K. Which star has a higher integrated radiance i.e. net energy emitted per unit time per unit area?

(a) Sun

(b) Sirius

(c) Depends on value of the respective radii

(d) The integrated radiance is equal.

25. Suppose a spaceship is attempting a slingshot maneuver on a gas giant with mass 100 times that of the spaceship. Because the spaceship somewhat entered the planet’s atmosphere, kinetic energy was not conserved—only momentum. What is the ratio of the spaceship’s change in velocity to the planet’s change in velocity, $$\frac{{\Delta}v_{s}}{{\Delta}v_{p}}$$?

(a) 10

(b) 100

(c) -10

(d) -100

26. Let’s imagine that our Universe would be filled with basketballs, each having a mass of $$m_{b}$$ = 0.62 kg. What would be the necessary numerical density ($$n_{b}$$) of basketballs in the Universe such that the mass density of the basketballs would equal the current critical density of our Universe?

(a) 1.5 * 10^-26 balls/$$m_{3}$$

(b) 1.7 * 10²⁶ balls/$$m_{3}$$

(c) 1.5 * 10^-27 balls/$$m_{3}$$

(d) 1.7 * 10²⁷ balls/$$m_{3}$$

27. When binary systems are really close together, they can execute an accretion process, in which one star (called the primary star) ”eats” the mass of the other (called the secondary star), whose mass spirals down into the primary star, creating an accretion disk!

For an accretion disk with the outer edge 3R from the center of the primary star (radius R and mass M), calculate the energy lost by a test mass (mass m) where it touches the primary star from where it first enters the accretion disk.

Consider the orbits to be Keplerian.

(a)$$\frac{GMm}{R}$$

(b)$$\frac{1}{2}\frac{GMm}{R}$$

(c)$$\frac{2}{5}\frac{GMm}{R}$$

(d)$$\frac{2}{3}\frac{GMm}{R}$$

(e)$$\frac{3}{4}\frac{GMm}{R}$$

28. An often-repeated fun fact is that humans produce more power per unit volume than stars. If the sun were the same size, but it produced the same amount of power per unit volume as a human, what would its surface temperature be? Assume the “average human” produces 100 watts of power and has a volume of 66400 cubic centimeters.

(a) 3500 K

(b) 10000 K

(c) 25000 K

(d) 40000 K

(e) 50000 K

29. Given that the redshift of cosmic microwave background (CMB) is 1100, what was the temperature of the Universe when photon decoupled from matter and neutral hydrogen started to get formed? The present temperature of the CMB is 2.73 K.

(a) 10000 K

(b) 30000 K

(c) 3000 K

(d) 1000 K

(e) 300 K

30. Where and when should we place a radio telescope such that, when combined with a radio telescope on Earth, the system could ”see” the supermassive black hole in Sculptor’s Galaxy (NGC253)?

Sculptor’s Galaxy’s supermassive black hole’s mass is estimated to be around 5• 10⁶$$M_{\odot}$$, and its distance is estimated to be around 3.5 Mpc.

Out of the options below, pick the one closest to the estimate you obtain, rounding up. Consider the energy of a radio wave to be around 10^-5 eV.

Use the following formula to estimate the angular resolution:$${\theta}=\frac{\lambda}{D}$$

(a) On the Moon when it is at its apogee.

(b) On Mars when it is in conjunction.

(c) On Venus when it is in its greatest elongation.

(d) On one of Jupiter’s moons when it is in opposition.

(e) Somewhere in the farthest points of the Oort cloud when Earth is at its perihelion.

翻译

1.2020年12月21日， 木星在$$(\alpha,\delta)=(20^{h}10^{m},-20°34′)$$。土星在哪个星座？

(a) 摩羯座

(b) 宝瓶座

(c) 双鱼座

(d) 天鹰座

2.光度5.86 * 10²⁶ W，半径8.51 * 10⁸m的恒星光谱型是什么？

(a) A

(b) F

(c) G

(d) K

(e) M

3.系外行星HD209458b质量是0.71倍木星质量，绕HD209458的公转周期是3.53天。HD209458质量是1.15倍太阳质量。假设它的公转轨道是圆轨道且恰好能被我们观测到，HD209458由HD209458b公转产生的径向速度的半振幅是多少？

(a) 69.6m/s

(b) 85.9m/s

(c) 94.2m/s

(d) 120.8m/s

4.黑体的光子数密度和温度的关系：$$n_{d} = a(\frac{k_{B}T}{\hbar_{c}})^{n}$$，其中$$k_{B}$$是玻尔兹曼常数，$$\hbar$$是约化普朗克常数，$$c$$是光速，$$T$$是黑体的温度。$$a$$是一个无量纲的常数。$$n$$的值是多少？

(a) 1

(b) 2

(c) 3

(d) 4

5.HD209458b的半径是木星的1.35倍，HD209458的半径是太阳的1.20倍，HD209458b的掩食深度是多少？

(a) 0.013%

(b) 0.13%

(c) 1.3%

(d) 13%

6.关于大爆炸理论，以下哪项是正确的？

(a)在大爆炸理论下，我们的宇宙不可能是平坦的或接近平坦的，这与观测结果相符。

(b)在大爆炸理论下，复合前宇宙微波背景辐射达到热平衡是不可能的，尽管我们今天观测已经达到热平衡。

(c)大爆炸理论预言有大量磁单极粒子，但我们还没有观测到它。

(d)以上都对

7.彗星C/2020 F3（NEOWISE）于2020年6月3日到达近日点。NEOWISE的周期是4400年，轨道偏心率是0.99921｡它的近日距是多少？

(a) 0.0123AU

(b) 0.212AU

(c) 2.69AU

(d) 26.8AU

8.一位天文学家发现了一个星系并决定分析它不同的部分。氢原子的自旋翻转跃迁的频率$$v_{0} = 1420.406MHz$$，在这个星系中被观测到$$v=1422.73MHz$$。

1. 星族I恒星（1），它们含有（2）金属。

2. 这个星系正在（3）我们，它的速度是（4）$$km*s^{-1}$$。

(a) （1）年轻；（2）很少；（3）远离；（4）245

(b) （1）年老；（2）很多；（3）靠近；（4）490

(c) （1）年老；（2）很少；（3）远离；（4）490

(d) （1）年轻；（2）很多；（3）靠近；（4）490

(e) （1）年轻；（2）很多；（3）靠近；（4）245

9. 一个稳定的疏散星国有大约$$N = 1000$$个太阳这样的恒星，它的视直径$$\theta = 30’$$，距离$$d$$=500pc。假设这个星国可以近似成一个分布均匀的球，估计这个星团中恒星的平均速度。密度均匀的球的半径$$r$$与引力势能存在以下关系：

$$U_{sphere} = -\frac{3}{5}\frac{GM^{2}_{sphere}}{r}$$

(a) 507 m/s

(b) 643 m/s

(c) 894 m/s

(d) 1021 m/s

(e) 771 m/s

10. 如果地球的轨道倾角变为0度，太阳的日行迹会发生什么？

(a) 日行迹会呈现为一个关于两个轴的完美对称图形且仍然是“8”的形状。

(b) 日行迹会变成一个点

(c) 日行迹会变成一个圆

(d) 日行迹会变成一个球面三角形

11. 用$$T_{{\odot},C}$$和$$T_{{\odot},S}表示太阳的核心温度和表面温度。用$$T_{A,C}$$和$$T_{A,S}$表示大角星（Arcturus）的核心温度和表面温度，用$$T_{S,C}$$和$$T_{S,S}$$表示白矮星天狼星B（Sirius B）的核心温度和表面温度。以下哪个选项是正确的？

(a) $$\frac{T_{{\odot},C}}{T_{{\odot},S}} < \frac{T_{A,C}}{T_{A,S}} < \frac{T_{S,C}}{T_{S,S}}$$

(b) $$\frac{T_{{\odot},C}}{T_{{\odot},S}} < \frac{T_{S,C}}{T_{S,S}} < \frac{T_{A,C}}{T_{A,S}}$$

(c) $$\frac{T_{A,C}}{T_{A,S}} < \frac{T_{{\odot},C}}{T_{{\odot},S}} < \frac{T_{S,C}}{T_{S,S}}$$

(d) $$\frac{T_{S,C}}{T_{S,S}} < \frac{T_{{\odot},C}}{T_{{\odot},S}} < \frac{T_{A,C}}{T_{A,S}}$$

(e) $$\frac{T_{S,C}}{T_{S,S}} < \frac{T_{A,C}}{T_{A,S}} < \frac{T_{{\odot},C}}{T_{{\odot},S}}$$

12. 某颗恒星的$$H_{\alpha}$$谱线波长和有$${\Delta}{\lambda} = 0.043 {\times} 10^{-10}$$m的位移。静止状态下这条谱线的波长是$${\lambda}_{0} = 6.536 {\times} 10^{-7}$$m。如果这是在赤道上观测到的，请计算它的自转周期。已知这颗恒星的半径$$R_{star} = 8 {\times} 10^{5}$$km。

(a) 29.59天

(b) 14.63天

(c) 21.15天

(d) 34.39天

13. 艾萨克牛顿制造的反射式望远镜是一台焦比f/5的望远镜，它有一个口径30mm的副镜。牛顿使用的目镜焦距是5mm。这台望远镜的焦距和放大倍数是多少？

(a) 150mm, 30×

(b) 300mm, 15×

(c) 300mm, 30×

(d) 150mm, 15×

14. 请看下面这张图片：

这张图片中有三个被标记的梅西耶天体。选择出和标记相对应的类型。

(a) 1 - 疏散星团；2 - 疏散星团；3 - 星云。

(b) 1 - 疏散星团；2 - 星云；3 - 星系。

(c) 1 - 星系；2 - 星云；3 - 球状星团。

(d) 1 - 疏散星团；2 - 星系；3 - 球状星团。

(e) 1 - 疏散星团；2 - 星云；3 - 疏散星团。

15. 太阳系中的一个有趣现象是在星际物质中捕获彗星。假设一颗质量7.15 * 10¹⁶kg的彗星被太阳系捕获。它被捕获后的近日点是4.64AU，它在被捕获前相对于太阳的运动速度非常小。请计算它在近日点的速度。

(a) 87.1 km/s

(b) 45.9 km/s

(c) 5.67 km/s

(d) 105.4 km/s

(e) 19.6 km/s

16. 某一天，世界时（UT）是0h时，本初子午线上的恒星时是5h 56min 9.4s。请计算这一天芝加哥恒星时为20h时的以世界时（UT）为标准的地方时间，芝加哥的地理纬度是87.65004722° W，时区是UT-6。你应当考虑太阳时和恒星时的差异。

(a) 14h 1min 32s

(b) 13h 26min 17s

(c) 14h 36min 47s

(d) 14h 0min 43s

(e) 13h 51min 11s

17. 想象一个可怕的场景：太阳已经变成一颗红巨星，其半径每100年就会增加一倍。请把一下要考虑的问题按照对人类的重要性排序。

I：地球和太阳接触造成的轨道衰减。

II：随着地球和太阳的距离越来越小，地球将会落入太阳的洛希极限并开始被太阳撕裂。

III：地球对太阳外层大气的潮汐影响引起地球的轨道衰减，就像月球形成地球的潮汐时会失去能量。

IV：极度高温引发失控的温室效应使地球变成像金星一样不适宜生存。

(a) III, IV, II, I

(b) IV, III, II, I

(c) IV, II, III, I

(d) IV, III, I, II

18. TESS Object of Interest (TOI) 402.01的公转周期是4.756 ± 0.000023 (days)，它最后一次观测到的凌日在2139.1 ± 0.0027008（TESS儒略日，及BJD-2457000）。在接下来的观测中，我们想要预测下一次凌日——它将被观测到的第23次凌日。用TESS儒略日表示，下一次凌日在什么时间？

(a) 2243.732 ± 0.0027238 TESS JD

(b) 2248.488 ± 0.000529 TESS JD

(c) 2248.488 ± 0.0027238 TESS JD

(d) 2248.488 ± 0.0032298 TESS JD

19. 木星的质量是1.90 * 10²⁷kg，半径是7.15 * 10⁷m。估算木星中心的压力最接近哪个数量级，以兆巴为单位（Megabar，译者注：1bar=10⁵Pa）

(a) 0.1

(b) 1

(c) 10

(d) 100

20. 以下哪个选项是错的？

(a) 目前普遍认为恒星中重于铁的元素是超新星爆炸产生的。

(b) 维持恒星的是压力和重力之间的流体静力平衡。

(c) 米粒组织存在于太阳的日冕层。

(d) 原恒星不是恒星，因为它们的主要热量来源不是核聚变。

(e) 主序星的类型越早，质量越大。

21. 这是一个水平放置的日冕，它的三角形冕针与当地的地理纬度$${\phi}$$ = 38°一致。如果三角形冕针的面积是2m²，春天第一天（春分）中午过后3小时阴影部分（Shadow）的面积是多少m²？

(a) 3.0

(b) 3.5

(c) 2.5

(d) 1.5

(e) 4.0

22. 一个食双星系统（在特定的波段）观测时它们两个的总视星等是5.67。第二次凌日时，第二颗恒星完全被第一颗恒星遮住了，这是视星等变暗为6.28。第二颗恒星产生的总光通量战整个双星系统的多少？

(a) 10.8%

(b) 43.0%

(c) 57.0%

(d) 89.2%

23. 一位天文学家在地球上观测到一颗太阳型恒星的V星等是6.73。假设V波长的平均星际消光是1.00mag/kps，计算这颗恒星和太阳系的距离。

(a) 11.5 pc

(b) 49.5 pc

(c) 34.2 pc

(d) 23.7 pc

(e) 18.9 pc

24. 1. 太阳的温度是5000K，天狼星（Sirius）的温度是10000K。哪颗恒星的累计辐射及单位时间单位面积辐射的净能量更大？

(a) 太阳

(b) 天狼星

(c) 取决于它们各自的半径

(d) 它们的累计辐射相等

25. 假设一艘宇宙飞船正在借助一颗质量是其100倍的巨大的气体星球实现引力弹弓。由于飞船进入和它的大气，飞船的动能不再守恒，只有动量仍然守恒。宇宙飞船的速度变化与行星的速度变化之比$$\frac{{\Delta}v_{s}}{{\Delta}v_{p}}$$是多少？

(a) 10

(b) 100

(c) -10

(d) -100