The moon is a giant nuclear pile
Here goes. If anyone is kind enough to fix my formatting, I'll be grateful. The moon has mass around 1 x10^23 kg, and radius 1.75 x10^6m. Earth has radius 1.3 x10^7m.
At 3.84 x10^8m distance, earth covers 0.0338 rad angular distance from the moon. (theta = arcsin (radius/distance)).
This means it covers 0.00564 of the moon's night sky (areafrac = 1-cos(pi x theta)). And the sky is only half the angular area that the moon would send radiation to.
So for every watt received at the atmosphere of earth, the moon would have to emit 2 / arcfrac watts = 354.6 W.
In real life we receive 1.73 x10^14 watts of solar energy at the surface, with about 50% having been reflected into space. So earth received 3.46x10^14W total.
That means the moon would have to emit 354.6 x 3.46 x10^14W = 1.227 x10^17W, or 3.869 x10^24 J in a year.
A kg of uranium emits about 8.2 x10^13 J/kg when fissioned. 921
So the burn rate of uranium is 3.869 x10^24 / 8.2 x10^13 = 4.72 x10^10 kg per year.
If this moon lasts 10^12 years, it has mass mass 9.44 x10^22 kg. This is pretty darned close to the real life mass of the moon.
This means that this moon of pure uranium, density 19000 g/m^3, has volume 4.97 x10^18 m^3. That gives it a radius of 1.06 x10^6, about half that of the real moon (which makes sense, uranium is roughly 6 times denser than moon rock).
In other words, the moon looks and acts very much like the moon does now, but it's a bit smaller and is as bright as the sun.
Now, of course, that moon will explode (right, physics crowd? I'm only a chemist / programmer).
But that's with it lasting 10^12 years. Shorten that lifespan by a factor of up to 1000 and substitute in inert moon rock. Now the moon lasts for a billion years. And it looks and acts just like the sun does now.
This assumes that with some proportion of U-235 between pure and 1 in 1000, the moon becomes a stable nuclear pile. And that's where I use my hands; I either hand wave the problem away, or I hand away the problem to a physicist.
Alternatively, the ratio could be even lower, but the life of the sun is then shorter.
PS What the heck are gamma rays and xrays? You're making things up, nothing to see here. 921