Hello! I am posting this because I saw some discussion regarding the process of wrapping images around a sphere.
I created this program about three years ago, It uses a 528 Poly sphere to display a space background, Earth and Moon.
I have since upgraded to a 2,208 poly sphere (which has a much 'rounder' appearance due to more polys) for projects I'm currently working on, but this is a very good starting point for those looking for more understanding. Please see the included .pdf that describes how the Equirectangular Projections are converted into Polar Compressed map projections and then mapped onto the sphere.
The models are fully rotatable and scalable with many options. the Earth, Moon and distance between them is to scale making it hard to always get both in view at the same time...so I added an 'Exaggerate' option for both of them, check it out !
This program is also useful as a 360 Panoramic Viewer when you replace the space background with other images. After the initial posting I will add other planets and images that have already been prepared as Polar Compressed Projections. BE SURE to download and try the image "Dragon Rock Projection24.jpg' found in a separate post below!!! Awesome.