Kelvin Helmholtz principle

The theory put forward by Kelvin and Helmholtz in the late 1800s

Kelvin Helmholtz mechanism (English: Kelvin–Helmholtz mechanism ）Yes astronomy Event, occurred at fixed star or planet When the surface is cool. As a result of cooling, the pressure of stars and planets is reduced and compensated by contraction. This compression relatively heats the core of the star/planet. This process Jupiter and Saturn , and the core temperature is not high enough to cause nuclear fusion Of Brown dwarf It is very obvious. It is estimated that Jupiter is able to release more than sunlight It absorbs more energy, and Saturn releases 2.5 times more energy than it absorbs from the sun.

Chinese name: Kelvin Helmholtz principle
Foreign name: Kelvin–Helmholtz mechanism

Presenter: Kelvin, Helmholtz
Proposed time: 1800

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This mechanism was originally developed by Kelvin and Helmholtz It was proposed in the late 1800s to explain sunlight Energy source. We know that the total energy generated by the Kelvin Helmholtz mechanism is far less than the energy released by the sun.

Energy generated by Kelvin Helmholtz contraction

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Theoretically, it was deduced that Gravitational potential energy yes sunlight Energy source. Calculate how much energy is released by solar energy in this process (assuming density It is a concentric spherical shell close to the ideal. The gravitational potential energy is the result of integration for all spherical shells, from the center to the outermost radius.

from Newtonian mechanics It is known that the form of gravitational potential energy is:

{\displaystyle U=-{\frac {Gm_ {1}m_ {2}}{r}}}

Here G is Universal gravitational constant , the two masses are respectively the mass of each layer of spherical shell with radius r and thickness dr, which is an integral from 0 to the radius of all spherical shells. The result of this statement (conversion) is:

{\displaystyle U=-G\int _{0}^{R}{\frac {m(r)4\pi r^{2}\rho }{r}}\,dr}

Here R is the radius of the outermost layer of the sphere, and m (r) is the total mass within the radius of r. Let m (r) be expressed in terms of volume and density to meet the conditions for integration:

{\displaystyle U=-G\int _{0}^{R}{\frac {4\pi r^{3}\rho 4\pi r^{2}\rho }{3r}}\,dr=-{\frac {16}{15}}G\pi ^{2}\rho ^ {2}R ^{5}}

After calculating the total mass of the sphere, the final answer is:

{\displaystyle U=-{\frac {3M^ {2}G }{5R}}}

It doesn't matter whether the density is consistent here. We can add the known solar mass and radius, and then divide by the known sun luminosity , get a rough order of magnitude and estimate the life span of the sun. Note that another estimate is added here, because the energy output of the sun does not always remain constant.

{ displaystyle { frac {U} {L_ { bigot}}} approve { frac {2.3 times 10 ^ {41}} {4 times 10 ^ {26}}} approve 18220650 }

Here { displaystyle {L_ { bigot}}} is the brightness of the sun. Although the result is better than that such as Electromagnetic energy Other physical methods can output energy continuously for a longer time. This method is still contrary to the known geological and biological evidence, which shows that the earth has a history of billions of years. Finally, I found out thermonuclear Energy can supply and maintain the energy output of stars for a long time.

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