What is the formula to calculate the parallax angle?

Question

The images were rendered in Blender. The two images were rendered 20 meters apart, side by side. The focal length is 50 mm if that matters. What is the formula to calculate the parallax angle θ as shown in the diagram?

This is similar to a previous question. How is the parallax angle actually measured?

The setup here is identical to how astronomers would calculate distances to stars. This should be much easier though.

I've not been able to find an equation that relates the foreground (the star) with the background (galaxies) to give you the angle. In this simulated case, the stars are indeed infinitely far away which is ideal.

Please try to relate that bright star near the center to the tip of the pyramid. See how it changes and how you would calculate the parallax angle from that change. In this case, the angle would have been 79.813°.

I would really appreciate this if you would show the formula and actually plug in the numbers and work it out so I can really understand it. Thank you!

Answer 1

You are missing a vital piece of information, a datum which defines an angular separation.

Suppose that I wanted to find the angular width of the Moon.
I would set the telescope cross wire on the left side and then measure the angle through which the telescope has to be rotated to have the cross wires set on the right side of the Moon. The measured angle is the angular width of the Moon.

If during my observations I took a photograph of the Moon that photograph by itself would not enable me to find the angular width of the Moon.

In your photographs there are many "fixed" stars including the one that you have highlighted. In order to find the angle between the tops of the pyramids you need to know the angular separation between at least two of the fixed stars.