🌗 Solar Beta Angle & Eclipse Calculator

Beta angle · eclipse fraction & duration per orbit · full-year evolution with J2 node drift

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Orbit & Date

Results (at date)

Beta angle β
– deg
Eclipse threshold β*
– deg
Eclipse fraction
– %
Eclipse duration
– min
Sunlit time / orbit
– min
Max |β| over year
– deg
Max eclipse over year
– min
Eclipse-free days / year
– d

One-Year Evolution — β (green) & eclipse minutes (blue)

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📖 How to use

  1. Enter the altitude and either i + RAAN (general orbit) or LTAN (sun-synchronous).输入高度，一般轨道填倾角 + 升交点赤经，太阳同步轨道填 LTAN。
  2. Read today's β angle and eclipse duration; the chart sweeps a full year with the node drifting at the J2 rate (or the sun rate for SSO).读取当天的 β 角与阴影时长；曲线按 J2 速率（SSO 按太阳速率）推演升交点，扫描整年。
  3. Power sizing uses the max eclipse (battery) and min sunlit fraction (array); thermal cases use max and min |β|.能源设计取最长阴影（电池）与最短光照比（帆板）；热设计取 |β| 的最大/最小工况。
  4. A dawn-dusk SSO (LTAN ≈ 6 h) keeps |β| high — often eclipse-free for most of the year, ideal for SAR power and simple thermal design.晨昏太阳同步轨道（LTAN ≈ 6 时）β 角常年很大——一年大部分时间无阴影，适合 SAR 供电与简化热设计。

Beta angle and eclipse model

The beta angle is the angle between the sun vector and the orbit plane:

sin β = cos δ_s·sin i·sin(Ω − α_s) + sin δ_s·cos i

with (α_s, δ_s) the sun's right ascension/declination from a low-precision ephemeris. For a circular orbit in a cylindrical Earth shadow, an eclipse occurs when |β| < β* where sin β* = R_E/(R_E+h), and the eclipse fraction is

f_E = (1/π)·acos( √(h²+2·R_E·h) / ((R_E+h)·cos β) )

The year sweep advances Ω at the J2 secular rate (sun rate for SSO) and the sun along the ecliptic. Penumbra and oblateness effects (~±1–2 min) are neglected — adequate for power/thermal sizing.

All computation runs locally in your browser.

β 角与阴影模型

β 角为太阳矢量与轨道面的夹角：

sin β = cos δ_s·sin i·sin(Ω − α_s) + sin δ_s·cos i

其中 (α_s, δ_s) 为低精度星历给出的太阳赤经/赤纬。圆轨道、圆柱形地影假设下，当 |β| < β*（sin β* = R_E/(R_E+h)）时出现阴影，阴影比例为

f_E = (1/π)·acos( √(h²+2·R_E·h) / ((R_E+h)·cos β) )

全年推演中 Ω 按 J2 长期速率（SSO 按太阳速率）推进，太阳沿黄道运动。忽略半影与地球扁率影响（约 ±1–2 分钟），满足能源/热设计精度。

全部计算在你的浏览器本地完成。