What would happen if ...

What would happen if … the Earth-Moon system stopped spinning and rotating?

 

Note, I don’t mean orbiting, I just mean if they stopped rotating around the common centre of mass and stopped spinning on their axes.

 

Well, as I understand it, you’d have two large masses (and a few others that are small enough or unstable enough as to not refer to as satellites, plus some actual human made satellites) that will approach the common centre of mass at an acceleration given by that mass.  It would look like the moon smashes into the Earth (although in reality they are smashing into each other).

 

Eventually, the combined Earth-Moon system would become more spherical (not entirely spherical, because there would still be some effect due to orbiting the Sun).  And the density of the system would be far increased, because we no longer have the system filling a volume about the radius of the orbit of the moon around the common centre of mass, just one that is a little bit bigger than the Earth.  (Note that the moon is 60% as dense as the Earth but even so, assuming no compression of the combined mass, the resultant system would have a radius that is about 0.7% greater than we currently have.  The moon orbits at about 400,000km, but once the moon crashes into and merges with the Earth, the radius would become about 6250km, so the density of the entire system increases massively – from about 2 grams per cubic metre to about 6 tonnes per cubic metre.)

 

From this little thought experiment, I conclude that a non-rotating system is denser than a rotating system of the same mass.

 

Is there any reason why I should not conclude that non-rotating black hole is denser than any black hole (of the same mass) that is rotating?

 

And, for a given mass, is there anything that is denser than a non-rotating black hole?

 

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Note that it is quite common for people to note that black holes vary in density and that there are objects that are denser than a black hole (as defined by the mass of the black hole divided by the volume enclosed by its radius).  For example, the supermassive black hole at the centre of our galaxy is calculated to be about 8.0×10³⁶ kg, its radius is calculated to be 1.2×10¹⁰ m, giving a notional density of about 10⁶ kg/m³.  Compare that with the density of a white dwarf that has the size of the Earth, at about 10⁹ kg/m³, or a neutron star, at about 10¹⁷ kg/m³.

 

Our supermassive black hole is, however, a relatively little one at about 4 million solar masses.  They extend up to billions of solar masses (although above 5 billion solar mass black holes are sometimes referred to as ultramassive black holes).  A black hole on the border of becoming ultramassive, at 4.5 billion solar masses, with a radius of about 1.3×10¹³m, would have a density equivalent to that of water.