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Energy production in stars

Authors: Bethe, H. A.;
Abstract

FROM TIME IMMEMORIAL people must have been curious to know what keeps the sun shining. The first scientific attempt at an explanation was by Helmholtz about one hundred years ago, and was based on the force most familiar to physicists at the time, gravitation. When a gram of matter falls to the sun's surface it gets a potential energy Epot = −GM/R = −1.91×1015 erg/gm (1) where M = 1.99×1033 gm is the sun's mass, R = 6.96×1010 cm its radius, and G = 6.67×10−8 the gravitational constant. A similar energy was set free when the sun was assembled from intersellar gas or dust in the dim past; actually somewhat more, because most of the sun's material is located closer to its center, and therefore has a numerically larger potential energy. One-half of the energy set free is transformed into kinetic energy according to the well-known virial theorem of mechanics. This will permit us later to estimate the temperature in the sun. The other half of the potential energy is radiated away. We know that at present the sun radiates ε = 1.96 erg/gm sec (2) Therefore, if gravitation supplies the energy, there is enough energy available to supply the radiation for about 1015 sec which is about 30 million years.

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Keywords

Radiative transfer in astronomy and astrophysics, Quantum theory, Astrophysics

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
448
Top 1%
Top 0.1%
Top 10%
bronze