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Telstar was a series of communication satellites first launched in 1962. The body of the satellite is roughly spherical, with much of the outer surface covered in solar cells. This gives the advantage of generating electrical power no matter which direction is oriented toward the sun. The disadvantage is that few of the cells are at the ideal perpendicular angle to the incident sunlight, and half of the cells generate no electricity as they are on the dark side of the satellite.

In contrast, most solar cells used on spacecraft today are on flat panels that are automatically oriented to the ideal angle of incident sunlight.

How does the power output of such a spherical solar cell configuration compare to a flat panel with the same area of cells? Surely the sphere generates less power than the flat panel, but by what percent? I would accept either an "ideal" answer using calculus (e.g. with an ideal sphere completely covered in cell material) or an "actual" answer using published values.

Some assumptions to make the comparison valid: Notice that the cells covered only a fraction of Telstar's surface. Therefore, the comparison should be with a flat panel with the same area of cells, not the whole surface area of the sphere. Include all cells (oblique, on the dark side) as part of the cell area. Because solar technology has improved over the decades, assume that the same types of cells are being used in both designs.

Telstar

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