# A millionth of the sun's mass is heat and light

#### marcus

Gold Member
Dearly Missed
By mass I mean the inertia of an object at rest.

The idea emerged in a recent PF that one could somehow separate the sun's mass into a "material component" and an "energy component". One of the posters, Instanton, questioned whether there was a good operational definition of the material component----which at first sight would be the sum of the rest masses of all the particles.

Anyway, the sun's rest mass (or, since "rest" is redundant in contemporary physics language, simply the sun's mass) is known to be 2E30 kg. The fraction of this that is heat (thermal motion) is given in a standard Astrophysics handbook, "Allen's A. Q." and likewise the fraction of the mass that is internal radiation.

It is perhaps good to imagine the core of the sun concretely and to realize that it is densely pervaded by Xray light. The core is at 15 million kelvin----corresponding to Xrays mostly over 1000 eevee. This is already less than the gamma directly resulting from fusion---this is just the thermal light corresponding to that temperature. The whole sun is soaked full of light and this internal light contributes (slightly) to its mass, measured at rest.

But not a heck of a lot! The heat and light in the sun contribute only a little over a millionth of its mass---if the handbook figures in "Allen's Astrophysical Quantities" are correct.

But the mass contributed by these things is nevertheless part of what holds earth in its orbit, so they perhaps deserve our consideration all the same.

The mass contributed by translational motion of the component particles of matter is 3.0E24 kilograms (3 trillion trillion)
and the mass contributed by internal light is 3.1E23 kilograms.
That makes the two combined 3.3E24 kilograms---somewhat over a millionth of the total 2E30 kg.

this is just a rough ballpark estimate of the fraction contributed by these things----and far from a complete analysis. A more detailed attempt to analyze the sun's mass would account for the negative contribution of gravitational binding energy. Even a stone cold star is not equal in mass to the sum of the rest masses of its particles!

Thought some here might be interested in this bit of trivia as to how the sun's mass breaks down. When I say mass, I mean, as always, its rest mass (there are still people around PF who use the deprecated "relativistic mass" concept).

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"A millionth of the sun's mass is heat and light"

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