Extended body corrections to the inverse square law for spherically symmetric sources

Extended body corrections to the inverse square law for spherically symmetric sources

Mradumay Sadh and Lorenzo Gavassino

The inverse-square law for calculating the irradiation arises as a direct consequence of the conservation of the energy, when spherical symmetry is imposed. The law implies that any spherically-symmetric source can be replaced, without changing the energy flux, by a point-sized source located in the center of symmetry. However, anybody who has seen a sunset knows, that when the center of the Sun moves slightly below the horizon, still a considerable portion of the stellar surface can be visible, irradiating much more than the corresponding point-sized source, which would be hidden under the horizon. This apparent contradiction is immediately solved when one realises that the presence of the planet, whose surface is absorbing part of the photon flux coming from the star, breaks the spherical symmetry, producing violations of the inverse-square in the sunset (or, equivalently, sunrise) region. On exoplanets that are extremely close to their star, this breakdown of the inverse-square law can become very important.

Proceedings of the Polish Astronomical Society, vol. 12, 270-272 (2022)

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