TLE to something useful?

Hello bloggers! How are you all doing today? I’m a little bit frustrated. Right now I’m trying to experiment with what I’ve been learning in diff geo. What I want to do is take statelier reentry data and make it into a curve of its position and platitude with respect to time. That way I can get its equation. You see, when a satellite or comet falls towards Earth it’s free falling and the only force excreted on it is gravity (if we ignore winds, which we can do if we go high enough in the atmosphere). And according to general relativity gravity isn’t a force at all but a shape. The gravity around earth is shaped a certain way and that makes things like balls and satellites travel towards the earth. I’ve included a picture of what I think the gravity around Earth looks like (this is only a slice). I’m managed to secure some satellite reentry data but it’s come in the form of a two line element (TLE) which I guess is standard for NASA. But I want longitude, latitude and altitude from this data. I’m having an impossibly hard time making the jump from Right Ascension to a longitude and altitude or whatever it supposed to be. Does anyone know how to do that? Or know anyone who would know?

Back in Black!

Wow. So my little world counter up there in the right corner has exploded with little red dots, so I think it might be beneficial for me to start this thing up again! Since I left the blog I've been hard at work trying to unravel the secrets of the universe. I've spent most of this summer teaching myself differential geometry. (The study of diff geo actually starts in kindergarten. Basically it's all about shapes, but the formal version is more concerned with their equations rather than their names.) And I have made a sincere effort to teach myself general relativity as well, but that hasn't gone so well, mainly because every time I start to read it all I want to do is throw the book across the room! General relativity (GR) is about the least formal, least elegant physical theory I have ever laid eyes on! I like the concepts: mass bending space, acceleration and gravity being the same thing, light bending, black holes and all that good stuff; but the math is positively atrocious! After reading all the formalized elegant diff geo it just makes me want to go throw up. Honestly I feel like GR needs to be redone! Now a question for you: has anyone ever tried to reformulate GR into a more mathematically elegant setup? If not I'm very tempted to try it!