Neutron stars, sugar cubes, and squeezed humans
June 3rd, 2010
The wikipedia article on Neutron star says the following,
'The density of a neutron star is approximately equivalent to the mass of the entire human population compressed to the size of a sugar cube.'
I hope we can all agree that whoever came up with the idea of measuring the density of stars in the units of compressed human beings was a great visionary. Too bad for him, then, that wikipedia shackles his imagination by demanding facts. In this case, the above statement is followed by a superscript saying 'citation needed.' When someone has come up with such a great idea, I thought it's my moral duty to carry on his legacy and provide some concreteness to his ideas by doing some small calculations.
The problem we want to solve is to calculate approximately how many human beings need to be compressed to the size of a sugar cube in order to have the same density as that of a neutron star. A neutron star has a density 3 E^17 kg/m^3. One sugar cube, according to Yahoo answers, is half an inch (1.27 cm) long per side. Which makes the volume of the sugar cube to be 2.05 E^-6 m^3. If the sugar cube has the density of a neutron star, the total mass it should contain is 615 billion kg. Taking the average weight of a human to be about 80 kg, about 7.7 billion people are needed to be squeezed together in order to attain the astronomical densities we are talking about - which is not too different from the current population of the world.
If we are only talking about order of magnitude approximations, the wikipedia comment is acceptable. But we can go further. The current population of the world is about 6.8 billion and growing at about 1.1% which means that the magic figure of 7.7 billion will be reached sometime near 2021. At around that time, with the assumption of an average weight of 80 kg, the wikipedia statement would be truer than it is today. But then the assumption of 80 kg is obviously on shaky grounds. With so many kids who invariably fail at tipping the weighing machine beyond the 30 kg mark, our noble aim is but a mirage. For all these underweight human beings, it is upon McDonalds and Burger King to maintain the required balance. If it was not for these noble institutions, humanity would still be decades away from the day when sugar cubes, neutron stars and squeezed humans could be spoken of in one single sentence.
Anyway, I hope this little calculation added to our understanding of neutron stars. I think the citation that the wikipedia article required has finally been found :).