科幻問題 :如果地球逆轉、從火星看地球

mca

(問題源自 Jack Lai，藍色字是回應)

----- Original Message -----
From: Jack Lai
To: [email protected]
Sent: Monday, September 28, 2009 9:04 PM
Subject: Astronomy Questions

Dear Sir/ Madam,
  I am a beginner who is very interested in subjects related to astronomy. Recently, I find out two questions from the internet which I do not know the answers…. I wonder if you can help me to solve the questions and explain in details.

1. If the direction of rotation of the Earth was reversed and the direction of revolution remained the same, would the sidereal day be longer than the solar day?

2. Let's assume for simplicity that the orbital plane of Mars is the same as the orbital plane of Earth, and the angle between its rotational axis and revolution axis is 25°. For observers on Mars, is their north celestial pole same as ours? Is their ecliptic same as ours? Are their zodiac same as ours? Can they observe retrograde motion of the Earth?

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Answers：

A1.   At present, the Earth takes 23h 56m (one sidereal day) to rotate 360 deg clockwise. Assuming this rate not changed when the Earth rotated anticlockwise, the average solar day would become 23h 52 m. See Figure 1. In this case, the Sun would rise from the west instead of the east, and one year would have ~367 “new solar days”.





A2.   At present, the orbit of Mars is not strictly parallel to the ecliptic but inclines at 1.9 deg, see Figure 2. If the inclination angle (i) was reduced to zero, k would become j = 25.2 deg. Axis Earth and Axis Mars would be more parallel. In this case both rotation axes would point “almost” to same celestial north pole. The zodiac is expected nearly same for both planets. This of course assumes both the Mars and Earth tilt to same side of the celestial sphere.

“Watching Earth from Mars” is analogue to “Watching Venus from Earth”. Seen from Mars, the Sun-Earth separation in the sky never exceeds 41 degrees. (You can verify this by simple math.) The Earth shall appear temporarily like a “morning” or “evening” star at low altitudes. The Earth does have retrograde motion with respect to Mars, but this happens mostly in Martian daytime and hence it is invisible. See the orbital simulation in Figure 3. Even the Earth is seen retrograding slowly above the horizon during a Martian evening or dawn, I am afraid that the dust haze in the Martian atmosphere is no good for sky observation.

AC  (a personal view, may not be best fitted.)

題外話：  這條「如果」的科幻題相當有趣。如果地球逆轉早在 45 億年前出現，那是天意，不過如果地球現在突然逆轉，人類就會立即死亡，因為住在溫帶的人，本身也以時速過千公里繞地軸旋轉，因此人體也儲藏龐大的動能，當地球由順轉速度過渡至零速時，基於動量恆守原理 (Conservation of angular momemtum)，人體的動能會立即化為熱能，地球再由零速過渡至逆轉之前，人類已被熱死了。另一天文現象是月地距離的劇變，當地球由順轉減至零速時，月球會由現時的 38 萬公里距離飛去 56 萬公里，當地球逆轉完成後，月球又回歸 38 萬公里之處 ......， 一連串的科幻現象，你可想到多少 ?