Find the radius of the moon and its distance from earth which has a known radius

Using ai requires complete avoidance of the words sun, earth, and moon. I have found that carefully crafting a simple and concise two step query will produce results and formulas that will make it possible for anyone to follow and find the real answer.


Step 1: Find the distance and radius of the sun by copying and pasting this search

There is a symmetrical sphere extended light source shining light in every direction. There is a sphere with a known radius. Any material, such as dust, can be used to visualize a number of light beams hitting the sphere. Every angle of the light beams hitting the sphere and the distances between them can be measured. Find the radius of the light source and its distance from the sphere.


Step 2: Find the distance and radius of the moon by copying and pasting this search

There is a symmetrical sphere extended light source with a known radius shining light in every direction. There is a first sphere with a known radius. The distance from the light source to the first sphere is known. There is a second sphere that can move around the first sphere at a fixed radii of less than the distance to the light source. The two spheres can cast shadows on each other. Find the radius of the second sphere and its distance to the first sphere.