# 牛顿万有引力定律

（更严谨的表达请见下文中的矢量式方程。）

• ${\displaystyle F}$: 两个物体之间的引力
• ${\displaystyle G}$: 万有引力常数
• ${\displaystyle {{m}_{1}}}$: 物体1的质量
• ${\displaystyle {{m}_{2}}}$: 物体2的质量
• ${\displaystyle r}$: 两个物体之间的距离

## 重力加速度

a1为事先已知质点的重力加速度。由牛顿第二定律知${\displaystyle F=m_{1}\ a_{1}}$， 即${\displaystyle a_{1}={\frac {F}{m_{1}}}}$。取代前面方程中的F

${\displaystyle a_{1}=G{\frac {m_{2}}{r^{2}}}}$

## 向量式

${\displaystyle \mathbf {F} _{12}=G{m_{1}m_{2} \over r_{21}^{2}}\,\mathbf {\hat {r}} _{21}}$${\displaystyle \mathbf {F} _{12}=-G{m_{1}m_{2} \over r_{21}^{2}}\,\mathbf {\hat {r}} _{12}}$

${\displaystyle \mathbf {F} _{12}}$: 物体2对物体1的引力
${\displaystyle G}$: 万有引力常数,其值约等于6.67259×10-11 N m2/kg2
${\displaystyle {{m}_{1}}}$${\displaystyle {{m}_{2}}}$: 分别为物体1和物体2的质量
${\displaystyle {r_{21}}}$: 物体2和物体1之间的距离
${\displaystyle \mathbf {\hat {r}} _{21}\equiv {\frac {\mathbf {r} _{2}-\mathbf {r} _{1}}{\vert \mathbf {r} _{2}-\mathbf {r} _{1}\vert }}}$: 物体1物体2的单位向量

${\displaystyle \mathbf {a} _{1}=G{m_{2} \over r_{21}^{2}}\,\mathbf {\hat {r}} _{21}}$

## 重力场

${\displaystyle \mathbf {g} (\mathbf {r} )=G{m_{2} \over r^{2}}\,\mathbf {\hat {r}} }$

${\displaystyle \mathbf {F} (\mathbf {r} )=m\mathbf {g} (\mathbf {r} )}$

## 牛顿理论存在的问题

### 理论问题

• 没有任何征兆表明重力的传送媒介可以被识别出，牛顿自己也对这种无法说明的超距作用感到不满意（参看后文条目“牛顿定律的局限性”）。
• 牛顿的理论需要定义重力可以瞬时传播。因此给出了古典自然时空观的假设，这样亦能使约翰内斯·开普勒所观测到的角动量守恒成立。但是，这与爱因斯坦的狭义相对论理论有直接的冲突，因为狭义相对论定义了速度的极限——真空中的光速——在此速度下信号可以被传送。

### 牛顿定律的局限性

(I have not yet been able to discover the cause of these properties of gravity from phenomena and I feign no hypotheses... It is enough that gravity does really exist and acts according to the laws I have explained, and that it abundantly serves to account for all the motions of celestial bodies. That one body may act upon another at a distance through a vacuum without the mediation of anything else, by and through which their action and force may be conveyed from one another, is to me so great an absurdity that, I believe, no man who has in philosophic matters a competent faculty of thinking could ever fall into it.)