Calculating Angle Between Ecliptic and Horizon for Observer at 18 Degrees North

[Frank Einstein]

Homework Statement

Which is the angle between the ecliptic and the horizon in the moment that the point of Aries is hiding for an observer whose position is 18 degrees north?

2. Homework Equations
None

The Attempt at a Solution

The first thing I have tried to is to do a drawing of the situation: here it is: http://postimg.org/image/dh3xkvipv/

Then I went to the software stellarium and I put the observer exactly at 18 degrees north; found a star with zero right ascension and I went forward in time until the star had height zero; then, I measured the difference between the north and the ecliptic and I got about 84 degrees: http://postimg.org/image/vs1i12dwp/.

If I calculate 90-23.5+18 I get 84.5, which is similat to the 84 that I got with the approximate calculus at stellarium, but I don't know how to justify it.

Can anyone thell me if there is a way to calculate the angle between the ecliptic and the horizon in the moment that the point of Aries is hiding for an observer whose position is known?

Thanks for reading.

 

[gneill]

I think if you make a sketch where you're looking edge-on at the intersection of the ecliptic and equatorial planes (so the planes appear as two crossed lines and you the observer are looking on from the first point of Aries), and you center their intersection in the center of a circle representing the Earth in profile, then you should be able to convince yourself that Aries first "hides" for all points on the circle to the right of the N-S line of the Earth.

 

[Frank Einstein]

I agree with you; I have made that with stellarium, is the second link; what I don't know is how to prove that the angle between the horizon and the ecliptic is 84.5 degrees

 

[gneill]

If, on the same diagram, you draw in the line of latitude for 18° it will be a line parallel to the line representing the equatorial plane. Draw a line from the center of the Earth circle to where that latitude line intersects the circle, and construct a perpendicular to that line there (it will be tangent to the circle). See any angles and triangles that might be of use?

 

[Frank Einstein]

Yeah, I will try with that, thank you very much.