astro-init - 用户贡献 [zh-cn]

2020年GeCAA理论第8题-木星大红斑

2024-04-14T08:16:46Z

Zqian-LT：

[[文件:Jupiter’s Great Red Spot.png|有框|居中]]
In the following problem the fluid mechanics of Jupiter’s Great Red Spot (GRS) is studied based on the velocity field data. The diagram on the next page shows a map of relative velocity for GRS and the surrounding region. The arrows are oriented and scaled as per the directions and magnitudes of winds at different points.

Due to the combined effects of gravity and rotation, Jupiter is slightly flattened at its poles. The equation of a spheroid approximating for the shape of Jupiter can be stated as:

<big>$$\frac{x^{2} +y^{2} }{R_{e}^{2} } +\frac{z^{2} }{R_{p}^{2}} =1$$</big>

where $$R_{e}=7.15\times 10^{7} m$$ is the equatorial radius of Jupiter, and $$R_{p}=6.69\times 10^{7}m$$ the polar radius. The radii of curvature of this spheroid in any direction can be calculated by the following equations $$(\epsilon =\frac{R_{e}}{R_{p}} )$$:

<big>$$r(\phi )=R_{e} (1+\epsilon^{-2}\tan ^{2}\phi)^{-\frac{1}{2} }$$</big>

<big>$$R(\phi )=R_{e}\epsilon^{-2}(\frac{r(\phi )}{R_{e}\cos\phi } )^{3} $$</big>

where $$r$$ and $$R$$ are the zonal (aka in the zone of a particular latitude) and meridional (aka longitudinal) radii of curvature, respectively, as a function of planetographic latitude $$\phi $$. The sidereal rotation period of Jupiter is $$P=3.57\times 10^{4}s $$.

(a) (4 points) Calculate the zonal and meridional radii values ($$\bar{r}$$ and $$\bar{R}$$ respectively) at the location of the centre of the GRS.

(b) (5 points) Estimate the eccentricity of the GRS.

(c) (6 points) ’Vorticity’ at any point is a measure of local spinning of the fluid as measured by an observer situated in the reference frame of the fluid. Mathematically, it is calculated as ’curl’ (vector derivative product) of the velocity field. In this case, the average relative vorticity may be estimated by the equation:

<big>$$\xi =\frac{V_{w} L_{GRS} }{A_{GRS} } $$</big>

where $$V_{w}$$ is the maximum value of winds as per the velocity field, $$L_{GRS}$$ is the length of the circumference of the GRS and $$A_{GRS}$$ is the area of the GRS.

Estimate average relative vorticity of the GRS.Hint: The circumference of an ellipse is well approximated by an average of circumferences of the corresponding auxiliary and minor circles.

(d) (2 points) Find the absolute vorticity $$\xi _{a} =(\xi +f)$$ by adding the Coriolis paramete

<big>$$f=2\Omega \sin \phi $$</big>

where $$\Omega$$ is the angular velocity of the Jupiter (due to axial rotation) and is the appropriate latitude.

(e) (1 point) If the absolute vorticity has the same sign as the latitude, we call the storm a ‘cyclonic storm’. If they have opposite signs, the system is ‘anticyclonic’. Is the GRS cyclonic or anticyclonic?

(f) (12 points) Imagine that the GRS moves to another latitude $$\phi _{1}$$ , where the absolute vorticity changes the sign (changes from anti-cyclonic to cyclonic or vice versa). Assuming minimum possible displacement of the GRS, at what value of $$\phi _{1}$$ do we expect this change？
In your analysis, assume that the GRS at the new location would occupy the same angular span in latitude, as well as have the same wind velocities and eccentricity as the original.

2022-10-04T14:18:54Z

Zqian-LT：/* 英文题目 */

==英文题目==
A spacecraft of mass $$m=5.0\times 10^{4} kg$$ approaches in a parabolic orbit 𝐴𝐵, with respect to Mars. When the spacecraft reaches point 𝐵 of least distance to the center of Mars,$$r_{B} =6.8\times 10^{6} m$$, it undergoes an instantaneous deceleration using its rockets and goes into a perfectly calculated orbit so that it will touch the Martian surface exactly at point 𝐶, diametrically opposite 𝐵, as shown in the figure.

3.1 Determine the speed ($$km\cdot s^{-1} $$) of the spacecraft at point 𝐵 just before the deceleration.

3.2 Calculate the total energy (𝐽) of the spacecraft as it is moving between points B and C.

3.3 Calculate the speed ($$km\cdot s^{-1} $$) of the spacecraft at point 𝐶.

==中文翻译==

==解答==

2019-11-08T15:30:00Z

Zqian-LT：/* 中文题目 */

==英文题目==
Time Limit: 75 Minutes

1. (1 point) Which of the following relates the intrinsic luminosity of a spiral galaxy with its asymptotic rotation velocity?

A. The Fundamental Plane

B. The Tully-Fisher Relation

C. The Press-Schechter Formalism

D. The Faber-Jackson Relation

2. (1 point) Which of the following correctly gives the location of Population I vs. Population II stars in the Milky Way?

A. Population I - Thin Disk, Spiral Arms; Population II - Halo, Bulge

B. Population I - Thin Disk, Bulge; Population II - Spiral Arms, Halo

C. Population I - Halo, Bulge; Population II - Thin Disk, Spiral Arms

D. Population I - Halo, Thin Disk; Population II - Bulge, Spiral Arms

3. (1 point) A quasar with a bolometric flux of approximately 10−12 erg s−1 cm−2 is observed at a redshift of 1.5, i.e. its comoving radial distance is about 4.4 Gpc. What is the bolometric luminosity of the quasar?

A.6.0×1011 L⨀ B.3.8×1012 L⨀ C.2.4×1013 L⨀ D.6.3×1014 L⨀

4. (1 point) Now, let’s assume that the quasar in the previous question is observed to have a companion galaxy which is 5 arcseconds apart. What is the projected linear separation of the companion galaxy from the quasar?

A. 107 kpc B. 29 kpc C. 74 kpc D. 43 kpc

5. (1 point) An observer is standing atop the Burj Khalifa, the tallest building on earth (height = 830m, latitude = 25.2N, longitude = 55.3E). Which of the following options is the closest to the shortest and longest shadow on the ground at the local noon time due to the building in a given year?

A. 10m, 1050m B. 25m, 950m C. 35m, 850m D. 45m, 750m

6. (1 point) Which of the following is closest to the ratio of the farthest distance to the horizon that can be seen by an observer standing top of the Mount Everest on Earth (height = 8.8 km) and Olympus Mons on Mars (height = 25 km)?

A. 0.1 B. 1 C. 5 D. 10

7. (1 point) An observer measures the black-body spectrum for a variety of bodies as a function of temperature and wavelength in the long wavelength limit ( hc λ ≪ kBT) and finds that his data approximately fits the relationship log(I) = a+b log(T)+c log(λ)). Here, I is the spectral intensity in terms of wavelength, T is the temperature of the body and λ is the wavelength. Which of the following are the expected values of b and c?

A. 1,-4 B. 1,4 C. 4,1 D. -4,1

8. (1 point) Suppose a spacecraft were orbiting in a low Earth orbit at an altitude of 400 km. The spacecraft makes a single orbital maneuver to place it into a Mars transfer orbit. Delta-v (∆v) refers to the change in velocity during an orbital maneuver. What is the ∆v required for this trans-Mars injection? The semimajor axes of the orbits of Earth and Mars are 1.496 × 108 km and 2.279 × 108 km, respectively.

A. 2.94 km/s B. 3.57 km/s C. 6.12 km/s D. 10.85 km/s E. 11.24 km/s

9. (1 point) After entering Mars orbit, the spacecraft finds that over the course of the martian year, the position of Star A varies by 613.7 milliarcseconds (mas) due to the movement of the spacecraft around the sun. Determine the distance to Star A.

A. 1.629 pc B. 2.482 pc C. 3.259 pc D. 4.965 pc E. 6.518 pc

10. (1 point) Star A, of mass 3.5 M⊙, shows radial velocity variations 24.2 m/s in amplitude and 23.22 years in period, suggesting the presence of an orbiting exoplanet. Which of the following is closest to the mass of the exoplanet in terms of Jupiter’s masses (MJ )? Assume the exoplanet’s orbit is circular and has inclination 90◦ . The mass of Jupiter is 1.898 × 1027 kg. Assume the mass of the planet is much smaller than that of Star A.

A. 0.7 MJ B. 2.1 MJ C. 5.6 MJ D. 9.9 MJ E. 13.2 MJ

11. (1 point) Whether or not a diffraction-limited optical system is able to resolve two points as distinct can be determined by the Rayleigh criterion. β Pictoris b is one of the first exoplanets discovered using direct imaging. The star system is located 19.44 pc away, and β Pictoris b is located 9.2 AU from the host star. When viewing in infrared (λ = 1650 nm), what is the minimum telescope diameter that is able to resolve β Pictoris and its exoplanet under the Rayleigh criterion?

A. 0.719 m B. 0.877 m C. 1.142 m D. 1.438 m E. 1.755 m

12. (1 point) The celestial coordinates of the Orion Nebula are RA 05h35m, dec − 05◦230 . Which of the following is closest to the time (local solar time) when the Orion Nebula would cross the meridian on the night of February 1st 2019? The date of the vernal equinox of 2019 is March 20th.

A. 08:40 PM B. 10:22 PM C. 12:00 AM D. 01:38 AM E. 03:20 AM

13. (1 point) A yellow hypergiant located 1.04 kpc away has an apparent visual magnitude of 1.49 and a B − V color excess of 0.29. Assuming RV , the ratio of V -band extinction to B − V color excess, is 3.1, determine the absolute visual magnitude of the star.

A. -9.5 B. -8.9 C. -8.6 D. -8.3 E. -7.7

14. (1 point) The pp chain is a primary energy generation mechanism in the Sun. Each run of the process 2H + e → D + ν releases 26.73 MeV of energy. Calculate the neutrino flux on the surface of Mars (in neutrinos per m2 ), assuming that the pp chain is responsible for 100% of the Sun’s energy generation. (Mars is at a distance of 1.52 AU)

A. 2.54 × 1013 B. 3.17 × 1016 C. 1.37 × 1014 D. 5.94 × 1012 E. 4.45 × 1015

15. (1 point) A relation between which of the following pairs of properties of Cepheids variables makes Cepheids variables, specifically, useful objects for determining stellar distances?

A. Mass and Temperature

B. Period and Luminosity

C. Temperature and Period

D. Mass and Luminosity

E. Period and Radius

16. (1 point) Assuming that the Chandrasekhar Limit is 1.4 Solar masses, estimate the maximum average density (in kg/m3 ) of a Chandrashekhar mass black hole.

A. 1.5 × 1022 B. 4.7 × 1014 C. 8.2 × 1010 D. 9.4 × 1018 E. 7.1 × 1026

17. (1 point) The Sun’s differential rotation can be estimated with the equation ω = X+Y sin2 (φ)+ Zsin4 (φ), where ω is the angular velocity in degrees per day, φ is solar latitude, and X, Y , and Z are constants (equal to 15, -2.5, and -2 degrees per day respectively). Two sunspots are spotted along the same solar meridian, one at 0◦ and the other at 40◦ . Assuming that the sunspots do not disappear or change latitude and move with the same velocity as the surface of the sun, after how many days will the sunspots be aligned once again? Round your answer to the nearest day.

A. 142 B. 202 C. 262 D. 312 E. 372

18. (1 point) An observer generates a light curve of a binary system, and notices two different minima that repeat periodically (in an alternating fashion). The time between when the light curve reaches the first minima and the second minima is 285.7 days. In solar masses, estimate the total mass of the binary system if the two stellar bodies are separated by a mean distance of 4.1 AU.

A. 0.0002 B. 0.0008 C. 28 D. 56 E. 112

19. (1 point) Eltanin, the brightest star in Draco, has the approximate coordinates RA: 17h 56m, Dec: +51.5◦ . Given that at the observer’s location, the latitude is +50◦ and the local sidereal time is 14:00, how far above the horizon will Eltanin appear? Round your answer to the nearest degree.

A. 26 B. 54 C. 59 D. 89 E. The star is below the horizon

20. (1 point) Stellar bodies located in the top left of a Hertzsprung-Russell diagram necessarily have which properties?

A. Low absolute magnitude, Low effective temperature

B. Low absolute magnitude, High effective temperature

C. High absolute magnitude, High effective temperature

D. High absolute magnitude, Low effective temperature

E. Intermediate absolute magnitude, Intermediate effective temperature

21. (1 point) Which of the following correctly orders the following distance indicators from the smallest to largest scale?

A. Stellar parallax, spectroscopic parallax, RR Lyrae variables, Hubble constant

B. Spectroscopic parallax, stellar parallax, RR Lyrae variables, Hubble constant

C. Stellar parallax, RR Lyrae variables, spectroscopic parallax, Hubble constant

D. Stellar parallax, spectroscopic parallax, Hubble constant, RR Lyrae variables

E. Spectroscopic parallax, stellar parallax, Hubble constant, RR Lyrae variables

22. (1 point) As seen from Mars, what phase will Earth appear to be in when Mars is at quadrature from Earth?

A. New B. Crescent C. Quarter D. Gibbous E. Full

23. (1 point) Which of the following stars is almost always never visible to observers in the Northern hemisphere?

A. Alpha Aurigae B. Gamma Cygni C. Alpha Lyrae D. Sigma Octantis E. Beta Orionis

24. (1 point) Two amateur astronomers A and B living in Ecuador are standing on the Equator at the Galapagos Islands (height 0 m, longitude 91◦ W) and Volcan Cayambe (height 5790 m, longitude 78◦ W) respectively. What are the differences (in degrees) of the altitudes from the horizon and zenith distances of the Sun measured by these two astronomers on March 20, 2019 when it is local noon for observer B? Neglect refraction and give your answer to the nearest degree.

A. Difference in altitudes: 15, Difference in zenith distances: 13.

B. Difference in altitudes: 13, Difference in zenith distances: 13.

C. Difference in altitudes: 13, Difference in zenith distances: 15.

D. Difference in altitudes: 11, Difference in zenith distances: 13.

25. (1 point) The spectra of two stars A and B peak at wavelengths 500 nm and 250 nm respectively. What is the ratio of their luminosities if they form black holes with Schwarzschild radii in the ratio 8:1? Assume that their densities were uniform and identical before they collapsed to form a black holes and that they did not lose any mass while forming the black holes.

A. 2:1 B. 4:1 C. 1:4 D. 1:2

26. (1 point) Two stationary observers at a distance 100 AU from the sun observe transits of Mercury across the diameter of the Sun’s disk when Mercury is at perihelion and aphelion respectively. Which of the following is closest to the ratio of the aphelion transit time to the perihelion transit time? You are given that the semi-major axis and eccentricity of Mercury’s orbit are 0.387 AU and 0.21 respectively.

A. 1:1 B. 2:1 C. 4:1 D. 8:1

27. (1 point) Find the total sum of the binary system of the star Capella, if semi-major axis between them is 0.85 AU, and period of 0.285 years.

A. 5.5 solar masses B. 6.5 solar masses C. 7.6 solar masses D. 8.5 solar masses E. 9.5 solar masses

28. (1 point) The New Horizons spacecraft completed a flyby of 2014 MU69 on New Year’s day of this year. 2014 MU69 is a Kuiper Belt Object with a semi-major axis of 44.58 AU. Estimate the maximum temperature at the surface of 2014 MU69, in Kelvin, assuming the object has zero albedo.

A. 41.7 Kelvin B. 58.9 Kelvin C. 83.3 Kelvin D. 117.9 Kelvin

29. (1 point) HD 209458b is an extrasolar gas giant planet with a radius of 1.38 Jupiter radii and a mass of 0.69 Jupiter masses (1 Jupiter radius = 6.99·107 m, 1 Jupiter mass = 1.90·1027 kg). Which of the following is closest to the pressure at the very center of HD 209458b, in bars?

A. 109 bars B. 106 bars C. 105 bars D. 103 bars

30. (1 point) Imagine that our Sun was suddenly replaced by an M-dwarf with a mass half that of the Sun. If our Earth kept the same semi-major axis during this change, what would Earth’s new orbital period be around the M-dwarf?

A. 0.707 years B. 1 year C. 1.414 years D. 2 years

==中文题目==

1.(1 point)以下哪一项将螺旋星系的固有亮度与其渐近旋转速度联系起来?

A.基本面

B.图利-费希尔关系

C.普雷斯-谢克特公式

D.法伯-杰克逊关系

2.(1 point)下面哪一项正确地给出了银河系中星族I和星族II恒星的位置?

A.星族I-薄盘，旋臂；星族II-晕，核球

B.星族I-薄盘，核球；星族II-旋臂，晕

C.星族I-晕，核球；星族II-薄盘，旋臂

d.星族I-光晕，薄盘；星族II-核球，旋臂

3.(1 point)在红移为1.5 时观察到具有大约为10-12 erg∙ s ^-1 ∙ cm -2 的辐射通量的类星体，即它的径向距离约为4.4Gpc。该类星体的辐射光度为多少?

A.6.0×1011 L⨀
B.3.8×1012 L⨀
C.2.4×1013 L⨀
D.6.3×1014 L⨀

4.(1 point)现在，我们假设观察到前一个问题中谈到的类星体具有一个相距5角秒的伴星系。则伴星系与类星体的线距离是多少?

A.107 kpc
B.29 kpc
C.74 kpc
D.43 kpc

5.(1 point)一位观测者站在地球上最高的建筑——哈利法塔顶（高度=830m，纬度=25.2N，经度=55.3E）。下列哪一个选项最接近某一年中当地中午建筑物在地面上最短和最长的阴影?

A.10m, 1050m
B.25m, 950m
C.35m, 850m
D.45m, 750m

6.(1 point)以下哪一项最接近地球上最高的珠穆朗玛峰(高度=8.8km)和火星奥林巴斯蒙斯(高度=25km)的观察者可以看到的最远距离与地平线之比?

A.0.1
B.1
C.5
D.10

7.(1 point)设一观察者测量了各种物体的黑体光谱，以此来作为长波长极限(hc/λ≪k_B T)中温度和波长的函数，发现其数据近似符合关系：log(i)=a+blog(t)+clogλ。这里，i是波长的光谱强度，t是物体的温度，λ是波长。下面哪个是b和c的值?

A.1,-4
B.1,4
C.4,1
D.-4,1

8.(1 point)假设一个航天器在400km的低地球轨道上运行。航天器进行单轨道机动，将其置于火星转移轨道。delta-v(∆v)是指轨道机动期间速度的变化。则所需增加的∆V是多少?地球和火星轨道的半长轴分别为1.496×108km 和2.279×108km 。

A.2.94 km/s
B.3.57 km/s
C.6.12 km/s
D.10.85 km/s
E.11.24 km/s

9.(1 point)进入火星轨道后，探测器发现，在火星一年的时间里，由于航天器绕太阳运行，恒星A的位置变化了613.7毫弧秒(mas)，试确定此时探测器与A星的距离。

A.1.629pc
B.2.482pc
C.3.259pc
D.4.965pc
E.6.518pc

10.(1 point)质量为3.5M⊙ 的A星，在23.22年里的径向速度变化为24.2m/s，表明其存在一颗绕轨道运行的外行星。根据木星的质量(MJ)，下列哪一个最接近外行星的质量?(假设外行星的轨道是圆形的，倾角为90度，木星的质量是1.898×1027kg 千克，且行星的质量比A星小得多。)

A.0.7MJ
B.2.1MJ
C.5.6MJ
D.9.9MJ
E.13.2MJ

11.(1 point)衍射限制光学系统是否能分辨两个不同的点，可用瑞利判据来确定。β- 绘架座 b是最早使用直接成像发现的系外行星之一，该系统位于19.44pc以外，β- 绘架座 b位于距主星9.2AU的位置。在红外波段(λ=1650 nm)观察时，根据瑞利准则，能够分辨β- 绘架座及其外行星的最小望远镜直径是多少?

A.0.719m
B.0.877m
C.1.142m
D.1.438m
E.1.755m

12.(1 point)猎户座星云的天体坐标是RA，05h 35m ，del-5°23' 。以下哪个时间(当地太阳时)最接近猎户座星云在2019年2月1日晚上穿过子午线的时间(当地太阳时)?2019年春分为3月20日。

A.08:40PM
B.10:22PM
C.12:00AM
D.01:38AM
E.03:20AM

13.(1 point)一个位于1.04 kpc以外的黄色超巨星，其视星等为1.49，B-V颜色超过0.29。假设RV，V波段消光与B-V颜色过剩之比为3.1，确定恒星的绝对星等。

A.-9.5
B.-8.9
C.-8.6
D.-8.3
E.-7.7

14.(1 point)pp链是太阳中的主要能量产生机制，每一次2H+e→D+v 过程将释放26.73MeV的能量。计算火星表面的中微子通量(以每平方米中微子为单位)，假设pp链承担了太阳产能的100%。(火星距离1.52 AU)

A.2.54×1013
B.3.17×1016
C.1.37×1014
D.5.94×1012
E.4.45×1015

15.(1 point)以下哪对造父变星的属性使造父变星可以用来确定恒星的距离关系?

A.质量和温度
B.周期和亮度
C.温度和周期
D.质量和亮度
E.周期和半径

16.(1 point)假设钱德拉塞卡尔极限为1.4太阳质量，请估计一个钱德拉塞卡质量大小的黑洞的最大平均密度应该为多少?(单位：kg/m3 )。

A.1.5×1022
B.4.7×1014
C.8.2×1010
D.9.4×1018
E.7.1×1026

17.(1 point)太阳的较差自转可以用公式ω=X+Ysin2(φ)+Zsin4(φ)来估算，其中ω是每天度数的角速度，φ是太阳纬度，X，Y和Z是常数(分别等于每天15°，-2.5°和-2°)。沿同一个太阳子午线发现两个太阳黑子，一个在0°，另一个在40°，假设太阳黑子不会消失或改变纬度并以与太阳表面相同的速度移动，那么太阳黑子会在多少天后再次对齐?(将答案舍入到最近的一天)。

A.142
B.202
C.262
D.312
E.372

18.(1 point)假设观察者记录一个双星系统的光变曲线，并注意到两个不同的最小值周期性重复(以交替的方式)，光变曲线达到第一个最小值和第二个最小值之间的时间为285.7天。以一个太阳质量为单位，如果这两颗恒星的平均距离为4.1 AU，根据以上信息，请估计该双星系统的总质量。

A.0.0002
B.0.0008
C.28
D.56
E.112

19.(1 point)天棓四是天龙座中最亮的恒星，其大致坐标为RA：17h 56m ，Rec：+51.5°。考虑到在观察者所在的位置，纬度是+50°，而当地的恒星时是14:00，那么天棓四会出现在地平线以上多远的地方?(把你的答案四舍五入到最接近的程度)

A.26
B.54
C.59
D.89
E.该恒星位于地平线以下

20.(1 point)位于赫罗图左上方的恒星体必然具有哪些特点?

A.绝对星等低，有效温度低

B.绝对星等低，有效温度高

C.绝对星等高，有效温度高

D.绝对星等高，有效温度低

E.中间绝对星等，中间有效温度

21.(1 point)下列距离“指示器”从最小到最大排列正确的一项是?

A.恒星视差、光谱视差、RR天琴座变星、哈勃常数

B.光谱视差、恒星视差、RR天琴座变星、哈勃常数

C.恒星视差、RR天琴座变星、光谱视差、哈勃常数

D.恒星视差、光谱视差、哈勃常数、RR天琴座变星

E.光谱视差、恒星视差、哈勃常数、RR天琴座变星

22.(1 point)从地球上看，当火星正处于方照时，地球应该是怎样的?

A.朔
B.新月状
C.四分之一可见
D.凸月状
E.满月形

23.(1 point)在北半球的观察者几乎永远看不到下列哪一颗恒星?

A.御夫座α
B.天鹅座γ
C.天琴座α
D.南极座σ
E.猎户座β

24.(1 point)居住在厄瓜多尔的两名业余天文学家A和B分别站在加拉帕戈斯群岛(高度0米，经度91°W)和火山卡扬贝(高度5790米，经度78°W)的赤道上。这两位天文学家在2019年3月20日观察到B的当地正午时测得的太阳高度和太阳天顶距离的差异(以度为单位)有多大差异?忽略折射并给出最接近的答案。

A.海拔差异：15，天顶距离的差异：13

B.海拔差异：13，天顶距离的差异：13

C.海拔差异：13，天顶距离的差异：15

D.海拔差异：11，天顶距离的差异：13

25.(1 point)两颗恒星A和B的光谱分别在500nm和250nm波长处达到峰值。如果他们形成黑洞时的史瓦西半径比为8:1，那么它们的光度比是多少?假设它们在坍塌收缩之前它们的密度是均匀和形成相同的黑洞，并且在形成黑洞时它们不会失去任何质量。

A.2:1
B.4:1
C.1:4
D.1:2

26.(1 point)当水星处于近日点和远日点时，距离太阳100 AU的两个静止观测者观察水星穿过太阳日面直径的凌日现象。以下哪一项最接近在远日点观察，测得完整凌日的时间与近日点观察，所测得的完整凌日时间的比率? 你得知水星轨道的半长轴和偏心率分别为0.387 AU和0.21。

A.1:1
B.2:1
C.4:1
D.8:1

27.(1 point)如果五车二与伴星之间的半长轴为0.85 AU，周期为0.285年，求五车二与该恒星组成的双星系统的总质量。

A.5.5M⊙
B.6.5M⊙
C.7.6M⊙
D.8.5M⊙
E.9.5M⊙

28.(1 point)新视野号在今年元旦完成了2014 MU69的飞越。2014 MU69是柯伊伯带状物体，半长轴为44.58 AU。假设物体的反照率为零，则以开尔文为单位估算2014 MU69表面的最高温度。

A.41.7K
B.58.9K
C.83.3 K
D.117.9K

29.(1 point)HD209458b是一颗太阳系外气体巨行星，其半径为1.38木星半径，质量为0.69木星质量(1木星半径=6.99×107 米，1木星质量=1.90×1027 千克)。以下哪一个最接近HD209458b中心的压强(单位：巴)?

A.109bar
B.106bar
C.105bar
D.103bar

30.(1 point)想象一下，我们的太阳突然被一个质量只有太阳一半的M矮星所取代。如果我们的地球在这个变化过程中保持相同的半长轴，那么地球绕M矮星公转的新轨道周期为多少?

A.0.707yr
B.1yr
C.1.414yr
D.2yr

==解答==
BABDB BABDC BAACB DCCBB ACDDC BCBBC