GmM/R for m = 938 MeV/c², M = 2e30 kg and R = 700,000 km is about 1.0 keV
(In retrospect, it’s not surprising they would be the same order of magnitude, as per the virial theorem.)
(In the above I’m implicitly bragging about remembering the mass and radius of the Sun off the top of my head (everyone working in my field knows the proton mass anyway so that’s not bragworthy), but I didn’t learn them last month, so that doesn’t count.)
Huh: Unless I’ve botched something:
kT for T = 15 MK is about 1.3 keV;
GmM/R for m = 938 MeV/c², M = 2e30 kg and R = 700,000 km is about 1.0 keV
(In retrospect, it’s not surprising they would be the same order of magnitude, as per the virial theorem.)
(In the above I’m implicitly bragging about remembering the mass and radius of the Sun off the top of my head (everyone working in my field knows the proton mass anyway so that’s not bragworthy), but I didn’t learn them last month, so that doesn’t count.)