🌍 J2 Perturbations Calculator

Nodal regression · apsidal rotation · nodal period · critical inclination & SSO checks

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Inputs

Secular Rates (J2)

Nodal regression Ω̇
– °/day
Apsidal rotation ω̇
– °/day
Mean anomaly drift ΔṀ
– °/day
Node full turn
– days
Perigee full turn
– days
Keplerian period
– min
Nodal period
– min
Anomalistic period
– min
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📖 How to use

  1. Enter perigee/apogee altitude and inclination — the J2 secular rates update live.输入近/远地点高度与倾角——J2 长期变化率实时更新。
  2. Ω̇ < 0 for prograde orbits (node drifts west), Ω̇ > 0 for retrograde; +0.9856°/day means sun-synchronous.顺行轨道 Ω̇ < 0（升交点西退），逆行轨道 Ω̇ > 0；等于 +0.9856°/天 即太阳同步。
  3. At the critical inclination 63.43° (or 116.57°) the perigee stops rotating — the basis of Molniya/Tundra orbits and frozen-perigee designs.在临界倾角 63.43°（或 116.57°）处近地点停转——这是闪电/苔原轨道与冻结轨道设计的基础。
  4. Use the nodal period (not the Keplerian one) when designing repeat ground tracks — the Repeat Ground Track tool does this automatically.设计回归轨道时应使用交点周期而非开普勒周期——回归轨道工具已自动处理。

J2 secular rates

With p = a(1−e²), n = √(μ/a³) and k = (3/2)·J₂·n·(R_E/p)²:

Node: Ω̇ = −k·cos i

Perigee: ω̇ = (k/2)·(4 − 5·sin²i) — zero at i = 63.43° / 116.57°

Mean anomaly: Ṁ = n + (k/2)·√(1−e²)·(2 − 3·sin²i)

Nodal (draconitic) period T_node = 2π/(Ṁ + ω̇); anomalistic period T_anom = 2π/Ṁ. These first-order secular rates capture the dominant oblateness effect; higher zonal harmonics, drag and luni-solar terms matter for precision work but rarely change a design trade.

All computation runs locally in your browser.

J2 长期变化率

令 p = a(1−e²)，n = √(μ/a³)，k = (3/2)·J₂·n·(R_E/p)²：

升交点: Ω̇ = −k·cos i

近地点: ω̇ = (k/2)·(4 − 5·sin²i) —— 在 i = 63.43° / 116.57° 处为零

平近点角: Ṁ = n + (k/2)·√(1−e²)·(2 − 3·sin²i)

交点周期 T_node = 2π/(Ṁ + ω̇)；近点周期 T_anom = 2π/Ṁ。一阶长期项已涵盖扁率的主导影响；高阶带谐、大气阻力与日月摄动对精密工作重要，但很少改变总体设计权衡。

全部计算在你的浏览器本地完成。