# If a being on a planet experiences infinite expansion of mass, starting from zero, will there come a point that the planet might revolve around him?

A thought experiment that I would like to work into a story. Need to basically know the tipping point of such an event happening.
Assumption: The being is starting from a small size and is still alive & functioning even with the square-cube law in effect

• Does the volume of the being also increase? Because otherwise the being will exert more and more pressure on the ground and will promptly sink to the center of the planet. (And, about "revolving": rotational momentum is a conserved quantity. If the being was initially at rest with respect to the planet then what exactly will make the planet revolve around him?) – AlexP Aug 30 '19 at 14:04
• During its mass increase, the being is going to need to stay away from all other matter or it will end up becoming the core of a new planet. Sometime later, it will become the core of a new star and eventually, after an event horizon emerges around it, a new black hole. No rotation and pretty orbits. Just an accumulating bombardment from everything around it. – Henry Taylor Aug 30 '19 at 14:06
• Where is the mass coming from? You appear to be violating some serious laws of physics. – Carl Witthoft Aug 30 '19 at 14:11
• @AlexP I think you answered your own question - as his mass increases, the center of mass (strictly, center of momentum) moves from the center of the planet towards him, leading to eccentric rotation (from an outside observer) – Carl Witthoft Aug 30 '19 at 14:13
• @CarlWitthoft: Unless their volume increases in proportion with their mass, they will sink to the center of the planet loooong before their mass reaches a significant fraction of the mass of the planet... – AlexP Aug 30 '19 at 14:26

# Assume a spherical cow in a vacuum

Two bodies don't revolve around the centre of mass of one of the bodies, they revolve around the centre of mass of the bodies combined. When two bodies are as significantly different in mass as those of a person and a planet, then the combined centre of mass doesn't deviate much from the centre of mass of the larger body. As the bodies become more equal in mass the common centre moves towards the halfway point between the two centres.

Hence there is no "tipping point", it's a continuous progression from one to the other.

# So what's with the cow?

It's a metaphorical cow, it's a metaphor for there being a fundamental flaw with the model.

In this case the model requires infinite strength in the planet crust (and the person). What will actually happen is that he will reach a certain mass, depending on the thickness of the planetary crust around him, and having exceeded that mass he will break through and slowly sink to the core of the planet. The planet will revolve around him at that point.

• Personally, I'm a fan of the spherical chicken. +1 – A Rogue Ant. Aug 30 '19 at 16:15
• An interesting point along these lines: If all the gas giants were to line up, the sun (and the rest of the solar system) would actually revolve around a barycenter that's outside of the sun itself. – Cort Ammon Aug 30 '19 at 16:33
• Thank you for the answer @Separatrix. I didn't consider the strength of the planet's crust. My assumption was that as the being grows, the gravity around him grows stronger than that of the planet's, making him the center for the planet to revolve around. Also an assumption, that I apparently brushed over was the existense of the planet in vacuum and not in a system. Your cow example seems like a perfect analogy to what I had in mind. Thanks – Sumit Shetty Sep 2 '19 at 14:59
• Oh, great, steal all the points I made in the comments :-) . Well-written explanations. – Carl Witthoft Sep 3 '19 at 17:10
• @CarlWitthoft a mix of you and Alexp, that'll teach you to put half answers in the comments ;) I was actually holding off until I saw whether the question was going to be closed or not – Separatrix Sep 3 '19 at 20:46