Stellar aberration with non perpendicular starlight

[Jean-C]

Homework Statement

So the problem is the following : we observe the stellar aberration of a star which isn't on the zenith, so that the star forms an angle theta with the ecliptic plane of the Earth. With such a position, the star will describe an ellipse instead of a circle (typical movement for a star at zenith). This is due to the fact that the starlight isn't always perpendicular to the speed vector of the Earth. The task is to find the value of theta knowing that the minor axis value is 36''. We consider Earth speed to be constant.

Homework Equations

tan(alpha)=v/c when the Earth speed and starlight speed are perpendicular (v is Earth speed)
2*alpha is the axis related to that angle

The Attempt at a Solution

I've tried different methods but I can't find a way to solve the value of theta. What I know is that the major axis is 2*alpha : when the Earth is nearest to be sun and at the furthest, the speed of Earth and starlight are perpendicular, so we can apply the equation written higher. But for the positions 1/4 of a period later, the starlight and Earth speed aren't perpendicular. One of the speed forms an angle theta with starlight, the angle we are looking for (the other position forms an angle 180-theta, which gives the same sin value).

This is where I block : I can't find a way to link the value of the minor axis to theta, since the above equations apply only when Earth speed and starlight form a right triangle...

 

[mfb]

Did you draw a sketch? You can use the reference frame of the distant star, and a telescope moving in some direction not perpendicular to the starlight hitting the telescope. Where does the starlight end up?

 

[Jean-C]

I had a sketch drawn, but redrew it just in case and found out what I was missing! Thanks for your reply!