Einstein made the revolutionary suggestion that gravity is not a force like other forces, but is a consequence of the fact that space-time is not flat, as had been previously assumed: it is curved, or “warped,” by the distribution of mass and energy in it. Bodies like the earth are not made to move on curved orbits by a force called gravity; instead, they follow the nearest thing to a straight path in a curved space, which is called a geodesic. A geodesic is the shortest (or longest) path between two nearby points. For example, the surface of the earth is a two-dimensional curved space. A geodesic on the earth is called a great circle, and is the shortest route between two points(Fig. 2.8). As the geodesic is the shortest path between any two airports, this is the route an airline navigator will tell the pilot to fly along. In general relativity, bodies always follow straight lines in four-dimensional space-time, but they nevertheless appear to us to move along curved paths in our three-dimensional space. (This is rather like watching an airplane flying over hilly ground. Although it follows a straight line in three-dimensional space, its shadow follows a curved path on the two-dimensional ground.)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 circular orbit in three-dimensional space.
In fact, the orbits of the planets predicted by general relativity are almost exactly the same as those predicted by the Newtonian theory of gravity. However, in the case of Mercury, which, being the nearest planet to the sun, feels the strongest gravitational effects, and has a rather elongated orbit, general relativity predicts that the long axis of the ellipse should rotate about the sun at a rate of about one degree in ten thousand years. Small though this effect is, it had been noticed before1915 and served as one of the first confirmations of Einstein’s theory. 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.
Geodesic 測地線
愛因斯坦提出了革命性的思想，即引力不像其他種類的力，而只不過是時空不是平坦的這一事實的後果。正如早先他假定的那樣，時空是由於在它中間的質量和能量的分佈而變彎曲或“翹曲”的。像地球這樣的物體並非由於稱為引力的力使之沿著彎曲軌道運動，而是它沿著彎曲空間中最接近於直線的稱之為測地線的軌跡運動。一根測地線是兩鄰近點之間最短（或最長）的路徑。例如，地球的表面是一彎曲的二維空間。地球上的測地線稱為大圓，是兩點之間最近的路（圖2.8）。由於測地線是兩個機場之間的最短程，這正是領航員叫飛行員飛行的航線。在廣義相對論中，物體總是沿著四維時空的直線走。儘管如此，在我們的三維空間看起來它是沿著彎曲的途徑（這正如同看一架在非常多山的地面上空飛行的飛機。雖然它沿著三維空間的直線飛，在二維的地面上它的影子卻是沿著一條彎曲的路徑）。
太陽的質量引起時空的彎曲，使得在四維的時空中地球雖然沿著直線的軌跡，它卻讓我們在三維空間中看起來是沿著一個圓周運動。事實上，廣義相對論預言的行星軌道幾乎和牛頓引力理論所預言的完全一致。然而，對於水星，這顆離太陽最近、受到引力效應最強、並具有被拉得相當長的軌道的行星，廣義相對論預言其軌道橢圓的長軸繞著太陽以大約每1萬年1度的速率進動。這個效應雖然小，但在1915年前即被人們注意到了，並被作為愛因斯坦理論的第一個驗證。近年來，其他行星的和牛頓理論預言的甚至更小的軌道偏差也已被雷達測量到，並且發現和廣義相對論的預言相符。
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