Ask A Scientist Physics Archive

name         John E. G.
status       other
age          50s

Question -   Sometimes we discuss that what is obviously correct is
not correct. I
just did a brief search and your web site cam up with the rotational
speed of the Earth match. I found your answer unsatisfactory for me
or anyone in school. One simple question that has an obvious answer
is how long does it take the earth to make one revolution on its axis.
The obvious answer that is incorrect is 24 hours. The next factor
people realize is that the is the leap year issue, but this issue has
less of an effect that the fact that one of our years days is due to
the orbit of out earth around the Sun. I think that subtracts a day
rather than adds a day.
So we would have 365 24 hour days / 366 revolutions x 24 hours =
hours per revolution = 23.934 hours, or 23 hours 56 minutes.
Then the next order effect may come from the Leap year issue with our
time base of 24 hour days, which as is not obvious is not how long
it take the earth to rotate once. From the point of view of
centripetal forces, which are necessary to understand for satellite
orbits, ocean tides, etc., what is the rotational rate of the Earth?
What are the other issues that need to be accounted for?
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You are correct, the rotation of the earth about the sun means that the time
between successive "high noon"s is different from the time it takes for the
earth to make a full 360° rotation about its axis.

Here is a previous answer from the ask-a-scientist archive:

"The time it takes the Earth to rotate once about its axis is a little
shorter than the 24-hour "solar" day we're accustomed to.  A "solar" day is
defined as the average time from high noon to high noon, that is, the
interval between the times when the Sun is highest in the sky.  Because the
Earth orbits the Sun, by the time it completes one revolution, the location
on the earth closest to the sun has shifted a bit.  The Earth then needs to
rotate a little more to make it line up again.   The time for one true
rotation is the interval between the times that a distant star is highest in
the sky, "fixed star to fixed star."  This interval is known as a "sidereal"
day, which is 23 hours, 56 minutes, 4.06 seconds."

As you see, your calculation of the length of a sidereal day is right on.

The reason a "leap year" is necessary is that the time between successive
high noons (24 hours) does not divide evenly into the time it takes for the
earth to revolve once around the sun.

Centripetal forces, ocean tides, etc. are already taken into account with
the rotational speed of the earth.  The ocean interacting with the gravity
of the sun and the moon (tides) can potentially act as a drag on the
rotation of the earth, gradually slowing it down.  This effect will
necessarily be small, because the mass of the oceans is such a small
fraction of the mass of the earth and because tidal motions are such a small
fraction of the momentum of the earth.  Over great periods of time, however,
they may change the earth's rotational velocity.

Richard E. Barrans Jr., Ph.D.
Assistant Director
PG Research Foundation, Darien, Illinois
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John,
As compared to distant stars rather than the sun, the Earth rotates once in
0.997 days, or (0.997)*(24hrs).  This is only three-tenths of one percent
different from exactly 24 hours.  The time required to orbit the Sun once is
365.25 days.  Variation from this quantity requires a century to pass for it
to matter.  Neither of these quantities is exact.  Slight alterations from
time to time due to other planets, comets and such do occur.  Uncertainties
are extremely small:  too small to notice in most circumstances.

As for things to study, tides operate on the 24hr system because tides are
oriented by the sun.  What must be considered much more than Earth orbit
with tides is position of the moon.  The moon affects tides almost as much
as the sun.  With satellites, the effects of the Moon significantly
overpower any variations due to variation of Earth rotation.

Dr. Ken Mellendorf
Illinois Central College
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As you have correctly noted, what the "obvious" answer is, is not always
correct, or is correct to only a certainty accuracy/precision depending upon
how many interactions/effects one wants to incorporate into the analysis of
whatever the problem at hand might be. A good example of this is the
question you raise, "What is THE rotational rate of the earth?" The short
answer is, "There is no single rate!" A recent citation:

http://home2.planetinternet.be/ballaux/

illustrates the point very well. Nothing in life (and especially astronomy)
is easy.

Vince Calder
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