Re: Because of the tilt of the Earth on its axis, the sun tends to wander above

Date: Sun Jun 28 19:39:43 1998
Posted By: Ricky J. Sethi, PhD
Area of science: Astronomy
ID: 898500734.As

Message:

Hi James,

Your question was about the relation of the Moon's orbit to the Earth's equator. The following picture from GRMC should help with our discussion:

Lunar Orbital Plane

The Actual Answer

As the picture shows, the tilt of the moon's orbit from the Earth's equator is 28.5degrees (in the picture, this is the angular difference between the line representing the Earth's equatorial plane and the line representing the Lunar Orbital Plane). Thus, the moon is in a constant orbit that is at an angle of 28.5degrees from the Earth's equator. Since this orbit is "off-center" from the equator, in general, the moon is over the equator only twice: each time it crosses the equatorial plane.

Caution: ramblings ahead!

Similarly, the Sun also "crosses" the equator only twice in its "orbit". But this isn't a very accurate description of what's going on. We know that the Sun is "stationary" and the Earth is the object in orbit around it. So how can we get away with saying the Sun orbits the Earth? Well, it turns out that by making this approximation, or model, we can make predictions much more simply than doing more cumbersome and complicated calculations on what's "really" going on. This is the hallmark of science: using models (or approximations) to represent what's going on and then extrapolating useful data and insights. It's important to remember that this is just a model... and not what's "actually" going on.

So the model that we can use is that of a geo-centric universe. Just one more quick digression: next time you hear about the early scientists who thought that the Earth was the center of the Universe and laugh at how silly they were and how could they ever think such a thing, just remember how well our little exercise works. This simple approximation leads to the correct answer to your question! In fact, many of those early scientists were just as brilliant and insightful as we like to think we are. :)

End of Detour

Okay, back to the subject at hand... this geo-centric universe gives us a Sun that revolves around the Earth along an "orbit" on the celestial sphere (the projection of all the stars on an imaginary sphere that surrounds the Earth). There is a nice description of the celestial sphere at this online cou rse, just in case you thought I made all this up; incidentally, that's also where I got the picture to the left. This "orbit" of the Sun is called the ecliptic. Similarly, the Earth's equator is projected onto the celestial sphere, and this is called the celestial equator. The ecliptic (the "orbit" of the Sun) results from the orbital motion of the Earth. The celestial equator, however, results from the rotation of the Earth (and it's equator) on it's spin axis. All this is pictured and described very nicely at Emory University's online Astro course; the picture on the right was from there.

So what does all this have to do with the motions of the Sun and Moon as seen from the Earth? Well, as you pointed out, the tilt of the Earth gives the ecliptic an angle of 23.5degrees from the celestial equator. And this leads to the Sun's motion above and below the equator (as you also pointed out). The Moon shares this eccentric behaviour (you can think of the Moon's orbit as being 5degrees above the ecliptic (please see picture above) on the celestial sphere) but the cause of it's eccentricity is completely different. The Sun's "orbit" around the Earth is imaginary, as it's the Earth that's doing the orbiting... but the Moon's orbit around the Earth is definitely real! Thus, two seemingly related behaviours have two completely different causes. That's what makes your question a really good one!

I hope that helped,

Rick.

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