The Analemma and Time Equation.

Assuming you mean the variation in day length over the seasons...

It's due to the angle of the earth's axis. eg. the axis on which the earth spins isn't perpendicular to the plane of orbit.

So at one side of our orbit the North pole is slopesd away from the sun and has virtually constant night, when the orbit takes the earth round the other side the N pole is now tilted towards the sun...so constant day.

The eccentricity of the Earth's orbit doesn't make much difference.

Extending this discussion a little: the reason for going over to 'atomic time' as an international time standard is that, at the levels of precision and accuracy now required by some users, the position of the earth relative to the 'fixed stars' is now so variable that a time standard based upon day lengths is inadequate. The time standard is now based on a stated number of vibrations of an electron in the caesium atom.

A trip to the http://www.google.co.uk/search?hl=en&q=Greenwich+Observatory&btnG=Google+Search&meta=, which lies at 0 deg longitude, will explain a lot more (usual disclaimer applies - the only connection is as a satisfied customer).

Thanks for the input you guys. Your great.

What has me confused is the "rate" at which the length of the day changes thoughout the year. Kinda like a kid on a swing?

Perhaps it is instructive to think about how the day seems at the poles. In winter the sun circles below the horizon and it is night all the time. In summer the sun circles above the horizon; keeping at the same height above the horizon all day and so it is always day. Often going to extreems makes it easier to understand a phenomena. The sun's north-south excursions of the sun over a year is of course due to the tilt of the earths rotational axis or in other words the axis not being perpendicular to the orbital plane.

Now if you consider the day as the time from local noon to noon then its slight variation is due to the eccentricity of the earth's orbit; and it is very slight. The earth is at the nearest point to the sun in the begining of January and farthest six months later. So you can check the duration of the noon to noon time at these times to see this.

Ha!!! ou got it spot on!!!

EXACTLY like a kid on a swing!!!!

It's all 'Simple Harmonic Motion'...(or close enough for jazz) back to the A level Physics!

Sin wave...flatter (slow rate of change) at the top & bottom mid summer & mid winter... most rapid rate of change of day length in Spring & Autumn arond the Equinox.. ( or 'night of the dark horses' )

I am referring to the time between sunrise and sunset. The "rate" at which this time changes is not constant. By that I mean, it does not change by a fixed amount each day but accelerates then slows, then accelerates than slows. Like a kid on a swing.

Please explain this to me. I have misinterpreted this phenomena terribly. My imagination wants to lead me down and entirely different path. Involving not only the orbital inclination relative to the suns equator but also that of the galactic plane and including a magnetic oscillation caused by interaction between the Solar and Geo fields.

There are two source not accounted for that I'm aware of:

1) you are dealing with a sphere so spherical geometry applies to the solar footprint. So it is not a linear progression.

2) the Earth wobbles like a toy top only not so pronounced.

literally 2 bits from Brad

Thank You Brad. I appreciate you taking the time for a response.

1. How does the spherical geometry affect the "rate of change" of the "solar footprint.?" Maybe if there were some pictures or something that I could look at.

2. Are you talking about precession or nutation?

I'm a bit More primitive in my visualization, take a globe in the sun tilt its axis of rotation to approximate the Earths and spin.

Summer solstice and winter solstice are the only times the axis aligns with the sun the rest of the time it is at a tangent to the angle of rotation.

The effect on timing is what Del refers to. The progression is quarterly.

The wobble and drifting poles are a another matter.

The trick to understanding it is to simplify...

Forget everything except the angle of inclination of the axis and you wil be 99% right!

If you look at rate of change of the slope of a sine wave ... it flattens out to zero at the top and bottom... it is steepest where it crosses tzero.

"Given the small eccentricity of Earth's orbit, how is the "rate of change" in the "length of day" explained?"

The Analemma is a graphical representation of the Equation of time, i.e. the time that the sun is ahead or behind local mean time.

The Analemma Provides extensive information about the analemma.

See a new thread, "Sunrise and Sunset"

A guest in Forum Thread: Why elliptical ? described all the details I copied here.

The Earth's orbit is defined by five facts:

• Earth's Rotation: The Earth rotates around its axis, taking 23 hours, 56 minutes, and 4.091 seconds to line up relative to the stars (Sidereal day), and 24 hours plus or minus 20 seconds to line up relative to the sun (Solar day). The solar day varies because the Earth is closer to the sun at some times of the year than others, which affects its rotation;
• Moon's orbit: The moon revolves around the Earth approximately every month. As the moon passes over a section of the Earth, its gravity raises the water in the seas, causing the tides.
• Earth's Revolution: The Earth revolves around the sun approximately 365.24 days, or one year. The Earth revolves in an elliptical path, so it is closer to the sun at some times of the year than others; the Earth moves faster when it is closer to the sun, reflecting Kepler's laws of planetary motion;
• Axial tilt: The Earth is tilted on its axis approximately 23.5 degrees relative to its orbit around the sun. Because of this tilt and the Earth's orbit around the sun, the Earth's northern hemisphere is tilted toward the sun from March 21 to September 21, and the southern hemisphere is tilted toward the sun from September 21 to March 21. This is what causes the seasons.
• Precession: It takes 365.2421 days for the Earth to revolve far enough to line up with the sun(the tropical year), and 365.2425 days for the Earth to revolve far enough to line up with the background stars (the sidereal year). This phenomenon, called equinox precession, causes the sun to appear to us to move a little bit relative to the stars every year in a 24,000 year cycle called the Great Year, which was the basis of the Zodiac.

To bad we can't give credit to whom we don't know = Guest?

Add to this the pole wobble from by Brett Gladman, Cornell University http://www.astrosociety.org/education/publications/tnl/29/season6.html

This influence depends on the fact the Earth isn't exactly a sphere. Since the Earth rotates quickly (1,000 miles an hour at the equator), centrifugal force causes the equator to bulge out and the poles to flatten by a small amount; the same thing happens to a water balloon when you spin it rapidly. The Moon's gravity yanks on the bulging equator. This wouldn't matter if the Moon orbit was aligned with the Earth's equator. But the Moon does not orbit exactly in the Earth's equatorial plane -- it's inclined by about 5 degrees -- and consequently it tries to change the tilt of the Earth.

The Earth's spin resists this change. The tug-of-war between spin and Moon causes the Earth's axis to precess, or wobble. It's the same effect that makes a spinning top wobble: Gravity wants to make the top fall over, and it would if it weren't spinning, but rotation stabilizes the top -- and the result is that the spin axis precesses. In the case of the Earth, the spin axis completes precesses once every 26,000 years.

Brad

Thanks for all the great replies everybody. You have given me a lot of meat to pull off the bone. It will take me awhile to digest it all. It ain't easy being a middle aged tyro.

Thanks again!

Gavilan.