Gravitational energy

The gravitational energy is in astrophysics the term for the potential energy that is released during the contraction of celestial bodies. In addition to nuclear fusion, it is the source of high-energy radiation from stars and galaxies. It only plays a marginal role for light or very extensive celestial bodies.

appraisal

According to Newton's law of gravitation , the gravitational energy is of the order of magnitude:

(1) ${\displaystyle E_{\mathrm {G} }\sim {\frac {GM^{2}}{R}}}$

With:

G : gravitational constant ,

M : total mass

R : characteristic radius of the collapsed system

When a very spacious gas cloud contracts to a star the size of the sun, an energy of approx. 10 ⁴¹  J is available. Sometimes it heats up the body, sometimes it is emitted as thermal energy and via neutrinos.

For comparison:

• An oxyhydrogen mixture of the mass of the sun produces an energy of approx. 10 ³³  J.
• The helium burning the sun delivers an energy of 10 ⁴⁵  J.
• The rotational energy of a rapidly rotating neutron star is of the order of 10 ⁴⁰  J.

Homogeneous full sphere

For the important case of a homogeneous full sphere, the gravitational energy is calculated

${\displaystyle E_{\mathrm {G} }={\frac {3GM^{2}}{5R}}}$

(for a detailed calculation, see article binding energy )

Observations

Transport processes that are necessary to maintain a nuclear fusion limit the maximum radiation power in stars. Many astronomical observations can therefore not be explained by this reaction process.

A star collapse of a sun-like structure to a neutron star reduces the radius to 16 km. According to the rough estimate (1), energy on the order of 10 ⁴⁶  J is emitted within a short time .

The release of gravitational energy can explain the lighting up of supernovae or gamma-ray flashes, as well as the high radiation power of active galactic nuclei .

The accretion is based on the same effect. For example, X-ray binary stars draw their energy from the contraction of a cloud of matter around a neutron star .

See also

• Gravitational binding energy

Individual evidence

1. ↑ Chandrasekhar, p. 1939, An Introduction to the Study of Stellar Structure (Chicago: U. of Chicago; reprinted in New York: Dover), section 9, eqs. 90-92, p. 51 (Dover edition).
2. ^ Lang, KR 1980: Astrophysical Formulas (Berlin: Springer Verlag), p. 272.