Note on the Central Differential Equation in the Relativity Theory of Gravitation
Note on the Central Differential Equation in the Relativity Theory of Gravitation
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关于引力相对论中中心微分方程的注记
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通讯作者：
A. R. Forsyth
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作者：
A. R. Forsyth
爱因斯坦的引力相对论中的临界方程以如下形式给出：（du /d2）2 + u2 = c2 - 1/h2 + 2 mu /h2 + 2 mu 3，其中m是太阳的质量，u是运动物体到太阳的距离的倒数，h2 = ma（1-e2），c2 - 1 = - m / a a是“轨道长半轴”，单位为天文单位，e是轨道的“偏心率”。上述方程可以精确积分，所涉及的函数是椭圆函数而不是圆函数;而且太阳系的近似很容易得到，因为椭圆函数的模很小。
The critical equation in Prof. Einstein’s relativity theory of gravitation is given in the form ( du / dϕ )2 + u 2 = c 2 — 1/ h 2 + 2 mu / h 2 + 2 mu 3, where m is the mass of the sun, u is the reciprocal of the distance of the moving body from the sun, h 2 = ma (1— e 2), c 2 — 1 = — m / a , a is the “major semi-axis of the orbit,” the units being astronomical, and e is the “excentricity” of the orbit. The foregoing equation can be integrated exactly, the functions involved being elliptic and not circular; and the approximations for the solar system are easily obtained, because the modulus of the elliptic functions is small.