Mass-Energy

 I have talked repeatedly about “mass-energy”, most often in the context of “concentrations of mass-energy”, for more than a decade.  When doing so, I have assumed every time that energy within a given volume has the same gravitational effect as the equivalent mass within the same given volume.

 

For example, the gravitational effect of the Sun on the Earth would be precisely the same if mass of the Sun were expressed in mass (kg) or energy (J).

 

Now you might immediately question this, because the Sun is radiating huge amounts of energy every second, 3.86×10²⁶J, and this implies that it would therefore be losing mass at rate of m=E/c²=4.29×10⁹kg per second.  This seems like crazy talk, until you look at what the experts at Stanford say: “that the Sun loses mass 4.289×10¹²g every second to energy”.

 

This makes me a little more confident in my assumption.

 

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Of course, it’s not simply the case that the Sun has a certain amount of energy just sitting there when it’s not escaping at the rate mentioned above.  A continual process of fusion is generating that energy, from mass.  However, it should be noted that, while it takes eight minutes for energy (in the form of a photon) to reach the Earth from the Sun, it takes that energy 100,000 years to bubble up from the core to the surface.  This implies that there is 60×60×24×365.24×100,000×3.86×10²⁶J=1.22×10³⁹J worth of energy in the process of bubbling up to the surface of the Sun from the core, equivalent to 1.35×10²⁰kg, which might sound like a lot but is a very small fraction of the entire mass (about 0.15 billionths).