Satellite Nadir Angle and Slant Range Calculator

2025

The angles and distances between a satellite and a ground station are easy enough to calculate with trig, but I made this calculator to save me the trouble of re-deriving the equations every time.

Diagram from here

I think the most intuitive way of solving this problem is to start with the law of sines:

sin(α)Re=sin(β)d=sin(90+ϵ)RE+a

If you are trying to calculate the satellite nadir angle α from elevation angle ε and altitude a, you can observe that:

α=arcsin(REsin(90+ϵ)RE+a)

Once you have that, you can calculate β easily from:

β=90ϵα

And you can plug β back into the law of sines relationship to determine d:

d=Resin(β)sin(α)

Calculator








Assumptions