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# [sci.astro] Time (Astronomy Frequently Asked Questions) (3/9)Section - C.10 Why isn't the earliest Sunrise (and latest Sunset) on the longest day of the year?

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```Author: Steve Willner <willner@cfa183.harvard.edu>

This phenomenon is called the "equation of time."  This is just a
fancy name for the fact that the Sun's speed along the Earth's equator
is not constant.  In other words, if you were to measure the Sun's
position at exactly noon every day, you would see not only the
familiar north-south change that goes with the seasons but also an
east-west change in the Sun's position.  A graphical representation of
both positional changes is the analemma, that funny figure 8 that most
globes stick in the middle of the Pacific ocean.

The short explanation of the equation of time is that it has two
causes.  The slightly larger effect comes from the obliquity of the
ecliptic---the Earth's equator is tilted with respect to the orbital
plane.  Constant speed along the ecliptic---which is how the "mean
sun" moves---translates to varying speed in right ascension (along the
equator).  This gives the overall figure 8 shape of the analemma.
Almost as large is the fact that the Earth's orbit is not circular,
and the Sun's angular speed along the ecliptic is therefore not
constant.  This gives the inequality between the two lobes of the
figure 8.

Some additional discussion, with illustrations, is provided by Nick
Strobel at <URL:http://www.astronomynotes.com/nakedeye/s9.htm>, though
<URL:http://www.astronomynotes.com/nakedeye/s7.htm>.  Mattthias
Reinsch provides an analytic expression for determining the number of
days between the winter solstice and the day of the latest sunrise for
Northern Hemisphere observers,
<URL:http://arXiv.org/abs/astro-ph/?0201074>.

The Earth's analemma will change with time as the Earth's orbital
parameters change.  This is described by Bernard Oliver (1972 July,
_Sky and Telescope_, pp. 20--22)

An article by David Harvey (1982 March, _Sky and Telescope_,
pp. 237--239) shows the analemmas of all nine planets.  A simulation
of the Martian analemma is at
<URL:http://apod.gsfc.nasa.gov/apod/ap030626.html>, and illustrations
of other planetary analemmas is at <URL:http://www.analemma.com/>.

```

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Top Document: [sci.astro] Time (Astronomy Frequently Asked Questions) (3/9)
Previous Document: C.09 What is the Green Flash (or Green Ray)?
Next Document: C.11 How do I calculate the phase of the moon?

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