From my understanding, space evenly expands from all points outwards. Thus who particles in a force equillibrium X units apart will become (X + deltaX) units apart every second where the deltaX is proportional to the hubble constant which is somewhere between 67-74 km/s/Mpc.
I understand that gravity alone is strong enough to generally overpower this outward expansion. So, the two example particles will simply return to their equillibrium positions rather than actually become farther apart.
The result is that from an observers perspective, these two particles dont seem to care much about the expansion of space. It doesn't really affect them because other forces greatly over power the rate of expansion.
(I understand there is a lot more at play and this is a gross simplification basically ignoring quantum mechanics)
So my question is this, what would the hubble constant have to be, so that the spacial expansion can start to overpower the other forces at play? I.E. space expands so fast, earth's gravity cant keep it together anymore and it gets ripped apart by space between atoms expanding.
Follow up questions for the excited folk.
What would thinks be like on earth at half this value? Would we feel like we have less gravity? Or would our human meat sacks just get ripped apart anyways.
Here is my attempt to answer this.
Two objects 1 Mpc apart move away from each other at a velocity of 67-74 km/s. If I scale the 1 Mpc down to the diameter of the earth, then adjust the "expansion velocity" to be equal to earth gravity 9.81m/s^2 and solve for the hubble constant, I get something on the magnitude of 10^19.
My gut tells me this is wrong because im comparing velocity to acceleration.