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spaceboy0
2010-Jul-13, 07:20 PM
The Equation of time shows the difference between Apparent Solar time and Mean Solar Time due to the earth's elliptical orbit and earth's tilt.

Does the Analemma also apply to planets and stars as viewed from Earth? For example, if the Sun crosses the central meridian 12 minutes late, do also Jupiter and the stars?

Hornblower
2010-Jul-13, 10:49 PM
The Equation of time shows the difference between Apparent Solar time and Mean Solar Time due to the earth's elliptical orbit and earth's tilt.

Does the Analemma also apply to planets and stars as viewed from Earth? For example, if the Sun crosses the central meridian 12 minutes late, do also Jupiter and the stars?

The stars are virtually unaffected by this. They are so far away that the Earth's motion has little effect on their apparent positions, so they will remain in step with a constant rate clock within a small fraction of a second at most. Of course that clock must be adjusted to show sidereal time rather than mean solar time. A mean solar clock will show each star transiting about 4 minutes earlier each day.

The meridian transit times of the planets would be tied to that of the Sun, but disentangling the analemma effect from the orbital motions of the planets would be rather complicated. We would find that any given planet's equation of time would be out of phase with the Sun's equation by an amount that depends on the difference in ecliptic longitude at the moment. For example, suppose the planet is on the ecliptic 90 degrees from the Sun. At a time of the year when the Sun is late, the planet will be early, and vice versa.

Clear as mud? It is fairly straightforward to demonstrate visually on a globe or a suitable chart, but it can be a pain in the neck to verbalize intelligibly.

grant hutchison
2010-Jul-13, 10:58 PM
The sun is only "late" or "early" when compared to the Mean Sun, which is how our clocks measure time: we don't want the variability associated with the real sun, so we mean out the variation.
The stars cross the meridian in synch with the Earth's rotation, so they have their own timetable, independent of the sun; it's pretty precise, but varies in the long term with the precession of Earth's rotation axis.
Jupiter's apparent motion in the observer's sky is a complex combination of the orbital motion of Jupiter and Earth, together with the Earth's rotation.

So only the sun has an analemma like the sun's analemma, because only the sun oscillates around a mean position relative to our clocks. The stars can produce rather simple 25,800-year "analemmata" (circles) as their apparent position changes with precession. The planets and the moon can sketch similar (but non-recurring) figures in the sky when plotted relative to some appropriate mean value, such as their synodic period.

Grant Hutchison