How the motion of the Earth affects that of the and Moon
The Sunday Nation
Nairobi,
25 August 2013
Joseph Wainaina asks
this direct question: “In last week’s article, you said that the moon
takes 29 days to go around the Earth, yet I know from school that it is
slightly over 27 days: is it you who is wrong or my teacher?”
Well Joseph, if you
read the article again, you will notice that nowhere did I write about
the movement of the moon around the Earth! The only thing I mentioned
was “The duration from one Full Moon to the next” and this is known very
accurately to be 29 days, 12 hours, 44 minutes and 2.877 seconds.
The period of
revolution of the moon has also been measured to a great precision: it
is 27 days, 7 hours, 43 minutes and 10 seconds. Now there appears to be
a discrepancy; the phases of the moon are caused by its revolution
around the Earth. So which duration is correct?
The reason for the
two values is that one is a relative quantity measured in relation to
the Earth while the other is an absolute one. The phases of the moon are
what we see from Earth thus the duration for one complete cycle is
relative to our location. That is, it does not take into account the
fact that the Earth itself is moving around the Sun.
In the time the moon
completes one revolution around the Earth (27.3 days), our planet also
moves round the Sun by about 7.5 per cent of its orbit (27.3 divided by
365.25). Therefore, at the completion of the one moon revolution, the
three bodies (Moon, Earth and Sun) are not in the same relative
positions that they were at the beginning.
For that reason, the
moon as viewed from Earth does not appear the same way it was at the
beginning. It takes some more time for the moon to complete its phase
cycle. The extra duration is approximately 7.5 percent of the
revolutionary cycle. That is another 2 days.
Thus the phase cycle of the moon comes to
approximately 27.3 + 2 = 29.3 days. The exact measured duration is about
29.53 days. The
difference between our theoretical estimate and the observed value is
because we have still ignored the fact that, as the moon is catching up
over the 2 days, the Earth is still moving around the Sun!
Nevertheless, the
principle is now demonstrated. For similar reasons, the rotation of the
Earth on its axis take 23 hours, 56 minutes and 4 seconds; yet we know
that a day is 24 hours long, exactly.
The 24 hours are the
duration from midday on one day to midday the following day while 23h,
56m and 4s is from midnight to midnight. Notice again that I am careful
not to call these two reference points 12 o’clock!
Midday is the moment
when the sun is at its highest point is the sky. Midnight a little more
complicated; it requires one to identify a star in the sky. Any star
will do as long as you stick to the same one the following day.
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