How do I calculate how far a planet is using geometry
Using parallax
To make this session as fun and useful as possible, I would love to know how you feel about triangles.
I know basic math, but trigonometry is brand new to me.
It is completely fine if trigonometry is brand new to you! We do not need any complex formulas to understand how this works—at its heart, measuring space distances is just a clever game of perspective.
What is Parallax?
To see this geometry in action right now, hold one of your thumbs out at arm's length. Close your left eye and look at your thumb with only your right eye, aligning it with an object on the wall behind it. Now, switch eyes: close your right eye and open your left.
Your thumb suddenly appears to jump to the side!
Your thumb did not actually move. Instead, what you are seeing is —the apparent shift in an object's position against a distant background, caused entirely by a change in your viewpoint.
A top-down view of binocular parallax showing how a single thumb projects to different positions on a background wall depending on which eye is used.
The physical distance between your two eyes is called the baseline. If you know the length of this baseline, and you can measure the angle of that apparent 'jump,' you have actually sketched out a giant triangle in space.
Calculating the distance to the object is simply a matter of solving for the height of that triangle.