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The application of physical theory to celestial systems such as stars, planets, galaxies, supernovae, and black holes. Astrophysics proper is concerned with explaining phenomena more so than making observations, the latter falling under the purview of astronomy.

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Does a star's emitted energy equal the work of its gravitational field?

No, a star's source of energy is nuclear reactions, not gravitational collapse. Lord Kelvin estimated the age of the sun on the assumption that its only source of energy was gravitational potential en …
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