Spacecraft Eclipse Duration Calculator
Calculate the maximum eclipse duration for any orbit and beta angle. Drives battery sizing, depth-of-discharge, and survival mode timeline.
What It Does
The Eclipse Duration Calculator returns the maximum umbra eclipse time for an orbit at a given beta angle. Input altitude, inclination, and beta angle (or date), and the calculator returns the eclipse fraction of the orbit period in seconds and as a percentage. It supports both circular and elliptical orbits and accounts for the geometric umbra cone (atmospheric refraction not modeled, appropriate for thermal and power sizing, not for star tracker operations).
Key Features
- Maximum umbra eclipse duration from orbit elements and beta angle
- Eclipse percentage of orbit period (key input for battery DOD calculations)
- Support for elliptical orbits with eclipse-near-perigee handling
- Annual eclipse envelope from orbit elements and date range
Why It Matters
Eclipse duration directly sizes the spacecraft battery. A LEO satellite spends roughly 35 minutes per 90-minute orbit in eclipse, which means batteries must support full bus loads for that duration with margin for end-of-life capacity loss. Underestimating eclipse duration means undersized batteries that brown out at solstice; overestimating means kilograms of unused mass that could have been payload. The calculator gives the worst-case eclipse for the worst-case beta angle so battery sizing has the right anchor.
Calculator
T = 2π√(a³/μ), eclipse fraction = (1/π)·acos( √(1 − (R/r)²) / cos β )
Inputs
Result
What this does not model. Circular orbit and a cylindrical umbra. Penumbra is not modelled, so this is the umbral worst case used for battery sizing rather than the value a star tracker would see.
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Included in every plan
The aerospace pack ships 127 calculators, and there are 478 across all 20 industry packs. Plans start at $14.99/month.