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标准重力参数

天体 (km3s-2)
太阳 132,712,440,018
水星 22,032
金星 324,859
地球 398,600
火星 42,828
谷神星 63
木星 126,686,534
土星 37,931,187
天王星 5,793,947
海王星 6,836,529
冥王星 1,001

太空动力学上,一个天体的标准重力参数 万有引力常数 和它质量

标准重力参数的单位是 km3s-2

细小物件环绕主天体

假设

基于太空动力学标准假设,得出:

  • 是次天体的质量,
  • 是主天体的质量,

而整个系统的标准重力参数就是主天体标准重力参数。

圆轨道

  • 是轨道的半径
  • 是轨道速率,
  • 角速度
  • 轨道周期

椭圆轨道

以下这条恒等式概括了椭圆轨道:

对于所有的抛物线轨道都是常数,等于

对于椭圆和双曲线轨道,是半长轴的二倍乘以比较轨道能量的绝对值。

两个物体互相环绕

在更加一般的情况下,其中物体并不一定是一个大一个小,我们定义:

  • 向量为一个物体相对于另一个的位置;
  • ,在椭圆轨道的情况下,还要定义半长轴
  • (两个的值之和)

其中:

  • 是两个物体的质量。

那么:

  • 对于圆轨道,
  • 对于椭圆轨道a的单位是AU,T的单位是年,M是相对于太阳的总质量,我们得出
  • 对于抛物线轨道是常数,等于
  • 对于椭圆和双曲线轨道,是半长轴的二倍乘以比较轨道能量的绝对值,后者定义为系统的总能量除以约化质量

地球的标准重力参数称为地心引力常数,等于398 600.441 8 ± 0.000 8 km3s-2。所以误差是1比500 000 000,比的误差都要小很多(1比7000)。

太阳的标准重力参数称为日心引力常数,等于1.32712440018×1020 m3s-2

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标准重力参数
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