Ok now that I’ve gotten that out of my system, back to black holes. There are a lot of different equations that I’ve not talked about here. They can get very complicated very fast and if I shared then it would be super confusing. But when you get an understanding of a certain number of equations it turns out that you can predict orbits around a black hole. And not just a black hole, one of the most famous applications of general relativity was an orbital prediction in our own solar system. Or bits in our own solar system?! you say. No! We already know those from Kepler and Newton, you say. But no! They are not quite right. I have a graphs here with two curved lines. They are both potential energy lines. Reading them is easy if you think about it right way. If you imagine putting a marble at the intersection of the straight line (the amount of energy in the system) and the potential energy curve and then letting it go then it’s going to go back and forth like a pendulum. But if we look at the horizontal axis we see that it is something corresponding to an orbital radius. From this we get a familiar looking orbit (the last picture). Now the first curve is what Newton and Kepler came up with, and the second curve is what general relativity predicts. You will notice there is a slight difference. When we get near the vertical axis the Newtonian curve just keeps going up. But when we get near the vertical axis in the general relativity curve we see that there is this sharp slope and the object falls off into the black hole. But the thing is that it doesn’t have to be a black hole. It can be any planet or star, including our own. Now, you say, what does this have to do with our own solar system? Well I shall explain that tomorrow!
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