 In 1916, the same year that Einstein published his general relativity paper, Carl Schwarzschild published his exact solution for space around a large, non-rotating mass. His metric is now called Schwarzschild metric, and it works quite well for slowly rotating masses like the Earth and the Sun and the planets in our solar system. We'll use this metric for the first three tests. Let's take a look at what our space-time curvature looks like with this metric. If we draw the circumference of the Earth's orbit, we get a length that is 2 pi times our distance from the Sun. If we existed in flat Euclidean space, we would calculate the circumference of an orbit one kilometer closer to the Sun and see that the distance between the orbits is one kilometer. But because of our positive curvature, if we were to measure the circumference with a radius that is one kilometer shorter than the first, we'd find that it is less than 2 pi times the shorter radius, which means that the distance between the circumferences would be greater than the one kilometer difference in the radii, but only a little. We can repeat this process all the way to the surface of the Sun. With each successive radius, the difference between the orbits would increasingly diverge from the Euclidean numbers. If we were to telescope this picture, you'd see the standard diagrams that are used to help explain general relativity, but diagrams like this are misleading in two ways. First, they represent an external curvature into another dimension, when in fact we are talking about intrinsic curvature. There is no evidence for the existence of a fourth spatial dimension. Second, it looks like you need a downward force on the object to get it to drop into the hole. That would be gravity, but that's what the lines were supposed to represent. So we'll avoid using this technique. For over a half a century before Einstein's time, it was known that there was something odd about the orbit of Mercury. The elliptical path it carves around the Sun shifts with each orbit, leaving its perihelion or closest point to the Sun 56 arc seconds forward on each pass. Newtonian equations accounted for all but around a half an arc second per year. And of course, they couldn't take into consideration the effects of curved space because the idea that space wasn't flat hadn't been considered yet. With Schwarzschild's metric, Einstein came up with the exact number to cover the mysterious half an arc second. He had passed the first test of his new theory.