On Dec 1 at 10.00pm apparent solar time you observe that the star procyon is just rising above the eastern?


Question:
horoizon. Determine the approximate apparent soalr time at which procyon will rise two weeks later on dec 15.

Answer:
9:04 PM
Procyon will rise approximately 4 minutes earlier each night, or, if you want to be more precise, it will rise 3 minutes, 55.9 seconds earlier each night.

So, using 4 minutes, it will rise at 9:04pm apparent solar time on Dec. 15. Or you can add 57.4 seconds to that time if you want to be more precise.

This is due to the Earth's rotation around the Sun. For a fuller explanation, see Wikipedia's discussion of sidereal time:

http://en.wikipedia.org/wiki/sidereal_ti...
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