To me, the speed of light is actually really slow - meaning, if you think classically you assume c infinite (at which point, as far as I understand, relativity theory essentially behaves like classical physics).
Learning that information travels way slower than the universe expands is quite unnerving. Similarly, learning that earth's fate could be determined already since hundreds of thousands of years through a hypernova directed at it - that we'll only know about when it hits us and wipes out our atmosphere. Well... light speed is far too slow for my taste ;).
Edit: It still doesn't answer my first question though: If you have something really energy dense like a neutron star - what fraction of gravity does energy make out then? 1E-3? 1E-10? 1/2? I'd find that interesting to know. According to wiki, neutron stars fall in temperature within years of creation from up to 1E12 K to 1E6 K. Six orders of magnitude. Depending on how much this decreases gravity I could imagine this effect alone influencing stellar orbits (I assume that a supernova would still allow other stars in a multi star system to continue existing). Has such a thing ever been measured?
Sorry.. there's just a whole can of worms opened about this in my head right now. Need to find an astro physicist to shake down :D.
Watch that youtube link in my sibling comment first, but I actually wanted to take a crack at an answer. What's the change in mass, ∆m, as the star cools? We'll assume the mass of the neutron star is 1.5 solar masses.
E = mc^2
∆m = ∆E/c^2
So really, what's ∆E? A hyper hand-wavy estimate:
∆E = Q = mc∆T (c being specific heat)
Specific heat by mass is really hard to predict, but by moles it is fairly constant, well within an order of magnitude. So we'll discuss mass in moles.
m = neutron star moles
m = (mass of neutron star / mass of neutron) / Avogadro's #
m = 2.9580163e33 mol
c = 24 J / (mol * K)
∆T = 1e12 K - 1e6 K
Substituting that back into the original, as a neutron star cools:
∆m = 7.0991681e45 J / c^2 = 7.89888982e28 kg
Which is like 2.6% of the mass of the original star, so a pretty solid chunk. But that number is pulled out of my ass—I am not a physicist.
But there are even more weird effects going on, due to the warping of gravity the mass of neutron stars can be up to 20% less than you'd expect based on its baryonic (neutron) constituents (questions 4 and 7):
About your last equation, wouldn't J/m^2/s^2 come out as kg? 7.9E2 would be very low then, no?
I wonder how much energy is stored electromagnetically and through nuclear forces though. These things are supposed to have extremely strong EM fields and I imagine every piled up nucleus like a little atomic spring that has been depressed as much as possible. Wouldn't most of the stored energy be in there?
Learning that information travels way slower than the universe expands is quite unnerving. Similarly, learning that earth's fate could be determined already since hundreds of thousands of years through a hypernova directed at it - that we'll only know about when it hits us and wipes out our atmosphere. Well... light speed is far too slow for my taste ;).
Edit: It still doesn't answer my first question though: If you have something really energy dense like a neutron star - what fraction of gravity does energy make out then? 1E-3? 1E-10? 1/2? I'd find that interesting to know. According to wiki, neutron stars fall in temperature within years of creation from up to 1E12 K to 1E6 K. Six orders of magnitude. Depending on how much this decreases gravity I could imagine this effect alone influencing stellar orbits (I assume that a supernova would still allow other stars in a multi star system to continue existing). Has such a thing ever been measured?
Sorry.. there's just a whole can of worms opened about this in my head right now. Need to find an astro physicist to shake down :D.