phys0001_assignment

# phys0001_assignment - Assignment 1 Due date October 5 2009...

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Assignment 1 Due date: October 5, 2009 1) a) One common length unit in astronomy is astronomical unit (A.U.). How long is 1 A.U. in terms of meters? b) Look up the mean diameter of the Moon and the mean Earth-Moon distance. c) By using the above data, calculate the mean angular size of the Moon. d) During total solar eclipses, the angular size of the Moon is just large enough to cover the Sun. Estimate the diameter of the Sun. 2) 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? 3) Is Venus a morning star or evening star in these two weeks (end of September)? How about Mercury? (This is Question 4 of Assignment 1 in 2007-2008.) 4) In the Chinese Agricultural Calendar, a month is defined by the synodic month and a year consists of integral number of month. Hence, in some years, there are thirteen, instead of usual twelve, months. That extra month is called leap month. Given that a year has 365.24 solar days and a synodic month has 29.53 solar days. How many leap months are there in 19 years? 5) 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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Solutions of Assignment 1 Due date: October 5, 2009 1) a) 1 A.U. = 1.5x10 11 m. b) The diameter of the Moon is about 3.5x10 6 m, and the mean Earth-Moon distance is about 3.9x10 8 m. c) The mean angular size of the Moon is tan -1 (3.5x10 6 / 3.9x10 8 ) = 0.51° d) The Sun has about the same angular size with the Moon. Hence, the diameter of the Sun is about (3.5x10 6 / 3.9x10 8 ) x 1.5x10 11 = 1.3x10 9 m 2) The sidereal day would be longer than a solar day. This is because if the directions of rotation and revolution were not the same, the advancing of the Earth in its orbit would take it to a position that it did not need to rotate a full turn to face the Sun again. This led to a shorter solar day. (Recall that in the actual Sun-Earth system, the Earth has to rotate a bit more than a full turn to face the Sun again.) 3) Looking up some websites or astronomical almanac, one will find that both Venus
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phys0001_assignment - Assignment 1 Due date October 5 2009...

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