I've recently become aware of a supposed well known fact, that actually seems quite wrong. It is said in many places that the difference between the Tropical Year and the Sidereal Year is about 20 minutes. Here are some examples on Wikipedia, but I've seen this in astronomy and science textbooks:

and

But if this were to actually happen, if we were to really have 20 extra minutes when the sun reaches the same place at the vernal equinox for the completion of a tropical year, then we would be cycling through the zodiac 5 full degrees each year and not 50 arcseconds.

I believe the incorrect equation is being used. The difference in the tropical and sidereal year is not 20 minutes. This is clearly not happening. Precession through the zodiac at the vernal equinox would be only 72 years(because 20 minutes covers 5 full degrees of the sky) if this were happening. The difference is only 50 arcseconds per year, which in real time is only 3.3 seconds.

To say this: "One sidereal year is roughly equal to 1 + 1/26000 or 1.0000385 tropical years." is not correct. It's 1 year plus 1/2600 of the angle of the sky, which is 50 arcseconds of angle.

This is very interesting!

Mark

http://en.wikipedia.org/wiki/Axial_precession_(astronomy)#Effects"Thus, the tropical year, measuring the cycle of seasons (for example, the time from solstice to solstice, or equinox to equinox), is about 20 minutes shorter than the sidereal year, which is measured by the Sun's apparent position relative to the stars. Note that 20 minutes per year is approximately equivalent to one year per 25,771.5 years, so after one full cycle of 25,771.5 years the positions of the seasons relative to the orbit are "back where they started".

and

http://en.wikipedia.org/wiki/Sidereal_year" [Broken]A sidereal year is the time taken by the Earth to orbit the Sun once with respect to the fixed stars. Hence it is also the time taken for the Sun to return to the same position with respect to the fixed stars after apparently travelling once around the ecliptic. It was equal to 365.256363004 days[1] at noon 1 January 2000 (J2000.0). This is 20m24.5128s longer than the mean tropical year at J2000.0.[1]

But if this were to actually happen, if we were to really have 20 extra minutes when the sun reaches the same place at the vernal equinox for the completion of a tropical year, then we would be cycling through the zodiac 5 full degrees each year and not 50 arcseconds.

I believe the incorrect equation is being used. The difference in the tropical and sidereal year is not 20 minutes. This is clearly not happening. Precession through the zodiac at the vernal equinox would be only 72 years(because 20 minutes covers 5 full degrees of the sky) if this were happening. The difference is only 50 arcseconds per year, which in real time is only 3.3 seconds.

To say this: "One sidereal year is roughly equal to 1 + 1/26000 or 1.0000385 tropical years." is not correct. It's 1 year plus 1/2600 of the angle of the sky, which is 50 arcseconds of angle.

__We've been lumping in the precession measure with the measure for the spin of the earth in a year__.__They are independent movements.__The stars do not shift 20 minutes(5 degrees) compared to the sun at vernal equinox every year.This is very interesting!

Mark

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