A rounding error in Randall's work. According to Wikipedia, the moon's mass is 7.3477e22 kg, and the electron's mass is 9.10938215[45]e-32 kg, so the ratio is 8.066e52 electrons per moon. That makes an unimaginable result eight times as unimaginable.Neil_Boekend wrote:The electron moon:

An electron weighs approximately 10^{-30}kg (rest mass)

The moon weighs approximately 10^{23}kg

-> Total: 10^{53}electrons (article said 10^{52}which is likely to be a rounding error either in my work or Randall's. I don't care which, it's close enough.)

An interesting aspect of this is that we (or at least, Wikipedia) know the mass of the electron 200 times more accurately than we know the mass of the Earth or the Moon. Presumably, that is because to estimate the masses more accurately we need to measure the gravitational constant more accurately, and that is difficult.

I wonder if we could send a known test mass far out into the solar system (where the tidal forces from Sun and Jupiter are small), and orbit a small object around it, measuring positions and shapes with laser interferometers and computing the gravitational constant from that. This would be very important if we subsequently replace the moon with electrons - an experiment we can only perform once, hence we should do it accurately.