THE SOUTHWORTH PLANETARIUM
207-780-4249 www.usm.maine.edu/planet
70 Falmouth Street Portland, Maine 04103
43.6667° N, 70.2667° W
Founded January 1970
"Indonesian authorities advised tourists to observe the
total solar eclipse in the Komodo National Park so that when it went
dark, they'd be in striking distance when the Dragons panicked."
THE DAILY ASTRONOMER
Wednesday, March 9, 2016
The Equation of Time
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You might find it helpful to read today's article on the planetarium web-site.
http://usm.maine.edu/planet/da-7-december-2015
Each day, we post a new "Daily Astronomer" to this page and we often
include illustrations or graphs. Go to this page to see the
"Equation of Time" graph.
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We often say -and, we truly shouldn't- that the Sun rises in the east,
attains its highest altitude when crossing the meridian in the due
south, and then sets in the west. In fact, Earth is spinning on its
axis and the Sun merely appears to rise and set. It is an example of
a Ptolemaic illusion, harkening back to the geocentric days when Earth
seemed fixed in the cosmic center. Astronomy has humbled us
somewhat and so we now know that we revolve around the Sun, not vice
versa.
We also say -and, here again, we shouldn't- the the Sun crosses the
meridian at high noon. Though this is true on occasion, most of the
time the Sun does no such thing. Generally, the Sun will either be
just east or just west of the meridian at noon time. It will be
lagging behind or moving ahead of the "proper" noon position.
Therefore, to know precisely when the Sun reaches its highest point
due south, we need the "Equation of Time." Here, the term
"equation" denotes a corrective factor as opposed to a mathematical
formula.
Astronomical almanacs often include an "Equation of Time" graph or
value table so we can predict precisely when the Sun will reach the
meridian, a point called "upper culmination." Inputting this
correction is a simple matter of addition or subtraction. For
instance, on the 1st day of January, the equation of time is -3.5
minutes, meaning that the Sun will cross the meridian 3.5 minutes
after civil noon. Or, one could say that the Sun lags behind "noon"
by 3.5 minutes. Around mid February, this equation reaches a local
maximum of about 14.5 minutes. Around mid April, the equation of
time equals zero, meaning that the Sun crosses the meridian at noon
sharp. Then, the Sun starts to move ahead, so that one must
introduce a positive factor: Around May 2, the equation of time is 3
minutes, meaning that the Sun reaches upper culmination at 11:57 a.m.
The Sun will already be three minutes beyond the meridian by noon
time. The equation of time becomes zero again around mid June and
again in early September and, once more around Christmas. Between
these dates, the equation of time will be alternately positive and
negative.
This equation of time factor is necessary because Earth is titled on
its axis by 23.5 degrees, so the Sun's will be north of the celestial
equator during half of the year and south of it during the other half.
The angle its apparent path, the ecliptic, makes relative to the
celestial equator will also vary. Also, Earth's orbit is slightly
elongated, so its distance from the Sun varies from its closest point,
perihelion, to its most distant point, aphelion. Consequently, the
Sun's "speed" along the ecliptic also changes because Earth moves most
quickly around the Sun when it is closest to it and slowest when it is
farthest away.
If Earth's axis weren't tilted and if its orbit were perfectly
circular, an equation of time wouldn't be necessary, as the Sun would
cross the meridian at noon every day. But, then, again, what fun
would that be?
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