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Astronomy/Celestial Coordinate Conversions


Dear Mr. Seligman,

When looking at a sky map that shows both galactic coordinates and the plane of the ecliptic, one can see that each line of galactic longitude intersects the plane of the ecliptic at one point.  Is there a formula that can calculate the positions of these points?

For instance: Suppose I have a line of galactic longitude: 90.5 degrees, or 47.2 degrees, or whatever I specify.  It intersects the plane of the ecliptic at one precise point.  That precise point has a precise galactic longitude, already given, and a precise galactic latitude, unknown.  That is what I want to know how to calculate.

Of course I can make eyeball guesses looking at a map, but I am thinking that this must be calculable using trigonometry and constants representing the angular relations between the different coordinate systems, but I have been unable to find the math.  Would you happen to know a formula, or where I might find one?  



Here is a link to a detailed discussion of how to use spherical trigonometry to convert from ecliptic to galactic coordinates, or the reverse:

For your problem, you want to choose a galactic longitude and find the galactic latitude for the point where the Ecliptic latitude is zero (the intersection point of the galactic longitude line with the Ecliptic). That is quite a different thing from choosing a specific galactic latitude and longitude and converting it to Ecliptic coordinates; so I still need to give the matter more thought. But I presumed you might want to see how the "simpler" calculation could be done.


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Courtney Seligman


I can answer almost any question about astronomy and related sciences, such as physics and geology. I will not answer questions about astrology and similar pseudo-scientific rubbish.


I have been a professor of astronomy for over 40 years, and am working on an online text/encyclopedia of astronomy, and an online catalog of NGC/IC objects.

Astronomical Journal, Publications of the Astronomical Society of the Pacific (too long ago to be really relevant, but you could search for Courtney Seligman on Google Scholar)

I received a BA in astronomy and physics and a MA in astronomy, both from UCLA. I was working on my doctoral dissertation when I started teaching, and discovered that I preferred teaching to research.

Awards and Honors
(too long ago to be relevant, but Phi Beta Kappa and Sigma Xi still keep trying to get me to become a paying member)

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