Light rays too must follow geodesics in space-time. In recent years, the even smaller deviations of the orbits of the other planets from the Newtonian predictions have been measured by radar and found to agree with the predictions of general relativity. Small though this effect is, it had been noticed ( see Chapter 3) long before 1915, and it served as one of the first confirmations of Einstein’s theory. General relativity predicts that the long axis of the ellipse should rotate about the sun at a rate of about one degree per ten thousand years. The largest deviation is in the orbit of Mercury, which, being the planet nearest to the sun, feels the strongest gravitational effects and has a rather elongated elliptical orbit. Projected onto the two-dimensional globe, the path of a spacecraft flying along a straight line in spaceĪctually, although they are derived differently, the orbits of the planets predicted by general relativity are almost exactly the same as those predicted by the Newtonian theory of gravity. Though the phenomenon is harder to picture, the mass of the sun curves space-time in such a way that although the earth follows a straight path in four-dimensional space-time, it appears to us to move along a nearly circular orbit in three-dimensional space. Project its path down onto the two-dimensional surface of the earth and you find that it follows a semicircle, tracing a line of longitude over the northern hemisphere. Or imagine a spaceship flying in a straight line through space, passing directly over the North Pole. The plane might be moving in a straight line through three-dimensional space, but remove the third dimension-height-and you find that its shadow follows a curved path on the hilly two-dimensional ground. This is rather like watching an airplane flying over hilly ground. In the presence of matter, four-dimensional space-time is distorted, causing the paths of bodies in three-dimensional space to curve in a manner that in the old Newtonian theory was explained by the effects of gravitational attraction. In the absence of matter, these geodesics in four-dimensional space-time correspond to straight lines in threedimensional space. In general relativity, bodies always follow geodesics in four-dimensional space-time. Distances on the Globe - The shortest distance between two points on the globe is along a great circle, which does not correspond to a straight line if you are looking at a flat map When you move "straight" east, you are not really moving straight, at least not straight in the sense of the most direct path, the geodesic. The appearance of these two paths on a map, in which the surface of the globe has been distorted (flattened out), is deceiving. But you can get there in 3,605 miles if you fly along a great circle, heading first northeast, then gradually turning east, and then southeast. For instance, you could fly from New York to Madrid by following your compass for 3,707 miles almost straight east, along their common line of latitude. (The term "great circle" comes from the fact that these are the largest circles you can draw on the globe.) As the geodesic is the shortest path between two airports, this is the route an airline navigator will tell the pilot to fly along. So is any other circle on the globe whose center coincides with the center of the earth. A geodesic on the earth is called a great circle. The surface of the earth is a two-dimensional curved space. Technically speaking, a geodesic is defined as the shortest (or longest) path between two nearby points.Ī geometric plane is an example of a two-dimensional flat space, on which the geodesics are lines. Bodies such as the earth are not made to move on curved orbits bv a force called gravity instead they move in curved orbits because they follow the nearest thing to a straight path in a curved space, which is called a geodesic. In general relativity, space-time is curved, or "warped," by the distribution of mass and energy in it. Einstein's theory of General Relativity is based on the revolutionary suggestion that gravity is not a force like other forces but a consequence of the fact that space-time is not flat, as had been previously assumed.
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