Value chain · CLM-0895
In plain terms
Twice a year, for about six weeks around each equinox, a satellite in geostationary orbit passes through the Earth's shadow once a night, for up to about seventy minutes. Keeping two gigawatts flowing through that would need roughly two and a third gigawatt-hours of batteries. The 1978 design carried about a two-hundredth of that, and only to keep its transmitter tubes warm. Over a year the shadow costs about one per cent of the time.
The claim as recorded
A geostationary satellite passes through the Earth's shadow once a night for at most about 70 minutes at equinox, so sustaining 2 GW of output through one maximum eclipse would require about 2.3 GWh of on-board storage - about 190 times the 12.186 MWh the 1978 reference design carried, which that design provided for klystron cathode heaters only and explicitly not for bulk power. The eclipses come in two seasons, one around each equinox, each lasting about 44 days in full shadow (umbra) and about 47 days counting partial shadow (penumbra). Summed over both seasons the interruption is about 77 hours of umbra a year, about 0.88 per cent of the year, or about 88 hours (1.0 per cent) including penumbra (CALC-140).
Evidence behind this: Own arithmetic over physical constants and two held inputs, the geostationary radius and the Earth's tilt, compared against held figures (CALC-140).
Scope and limits
THREE FIGURES HERE ARE APPROXIMATIONS AND ARE LABELLED RATHER THAN TIDIED. 69.6 minutes treats the Sun as a point, so the shadow is a cylinder of the Earth's radius. With the Sun's real size the umbra lasts at most 67.5 minutes and any shadow at most 71.7 minutes, which is the 72 minutes most held sources give; the storage for one longest eclipse is then 2.25 to 2.39 GWh, still about 2.3 (CALC-140). The half-maximum average is this record's own rough. The 44-day season is the umbra season of CALC-140 (43.98 days; 45.4 with the Sun as a point, 46.9 counting penumbra). The 51 hours (0.58 per cent) in support, from that rough and a 44-day season, is therefore an ORDER-OF-MAGNITUDE figure, superseded in the claim by the geometric figures below, and none of these is a capacity-factor derivation. THE 190-FOLD COMPARISON IS NOT A CRITICISM OF THE 1978 DESIGN, which never proposed to ride through eclipse - CLM-0211 states plainly that its storage is for cathode heaters. It measures the distance between what was carried and what full output would need. Separately, and left for a reader to put together rather than asserted here: the register holds an economics record, CLM-0177, fixing capacity factor at 1 with no allowance for eclipse or any availability term. That record is not contradicted by this one - it is unexamined by it. The annual total in support is low. CALC-140 gives about 77 h of umbra (0.88 per cent of the year) and about 88 h including penumbra (1.0 per cent), because the mean daily eclipse over a season is about 0.78 of the maximum, not half. Weighting each minute by the share of the Sun's disc that is hidden gives 82.5 h (0.94 per cent), the closest of these to the energy lost. Most held sources give seasons of 42 to 47 days and a longest eclipse of 69 to 72 minutes. The 1978 reference report gives about 75 minutes, with no working, and a 1979 Boeing report and the 1981 OTA study give seasons of 31 days, about two thirds of the geometric length (CALC-140). None of these figures adds the time to shut down and restart.
What it assumes
A satellite on the equatorial plane at equinox, the geometric worst case. That an SPS would be expected to sustain output through eclipse at all, which no held source states as a requirement.
Where it comes from
This is the project's own working, shown in full:
Earth angular radius from GEO = asin(6378.137/42164) = 8.7005 degrees; shadow crossing with the Sun as a point, at 15 degrees per hour = 2 x 8.7005/15 = 1.1601 h = 69.6 min. 2 GW x 1.1601 h = 2.3201 GWh; 2.3201 GWh / 12.186 MWh = 190.4. Annual: two seasons of about 44 days, averaging about half the maximum, gives 2 x 44 x 34.8 min = 3,062 min = 51.0 h = 0.582 per cent of 8,766 h. CLM-0211 supplies the 12.186 MWh and states it is for klystron cathode heater power during occultation, not bulk storage. CALC-140, from the geometry and from a year simulated in 5 s steps, with the Sun's real size: umbra at most 67.5 min, seasons of 43.98 days (44 eclipses), 77.4 h a year (0.883 per cent); any shadow at most 71.7 min, seasons of 46.89 days (47 eclipses), 87.7 h (1.00 per cent); the Sun as a point, 69.6 min, 45.43 days, 82.4 h (0.940 per cent).
Basis: GWh of storage, and hours per year
Related records
- Answers question
- QST-021 not published in this release
Cite this
energyaperture.com/c/clm-0895
CLM-0895, Energy Aperture, as of 2026-09.
Connected records
Other published records linked to this one. A list, not a judgement.
- Cited in articles