# What force is needed to overcome expansion?

1. Jun 20, 2015

### rede96

As I understand it gravitationally bound objects don’t move apart with expansion. So I was wondering, assuming constant acceleration of expansion, what is the minimum gravitational force required to keep objects from moving apart?

2. Jun 20, 2015

### RyanH42

Are you talking about static universe model.

3. Jun 20, 2015

### rede96

I'm not really well up on current models as I am just an interested layman. So was wondering if we assume the current Hubble constant of 70 m/s per mega parsec

4. Jun 20, 2015

### RyanH42

Albert Einstein added a positive cosmological constant to his equations of general relativity to counteract the attractive effects of gravity on ordinary matter, which would otherwise cause a spatially finite universe to either collapse or expand forever.This is the property of static universe.If you need numbers I cant help you.

5. Jun 20, 2015

### rede96

Ok, thanks for that. I was probably thinking more practically than that. I read that expansion does not apply any forces to objects. So if this was the case then it seemed that any force at all attracting / binding two objects would be enough for it to stop them receding with expansion. But that assumes a constant rate of acceleration.

6. Jun 20, 2015

### rootone

In a system of objects which are gravitationally bound they will in general remain gravitationally bound and not significantly affected by cosmic scale expansion.
I can imagine however that there could be edge cases where a very loosely bound object can become detached.
After all, the extent of an objects gravitational field is infinite, (is it not?), - although it becomes insignificantly weak far from the object.
So there is no place in the universe where gravity is totally absent, just extremely weak, and weak enough so that expansion could dissociate for example a tiny outlying galaxy from a loosely bound cluster.
This is not a theory, it just seems to me as if it could be possible, but probably someone can present me with impenitrable math which refutes the possibility, and I will happily take their word for it.

7. Jun 20, 2015

### wabbit

There's a distinction between unaccelerated expansion, which as I understand it has no effect whatsoever, and a cosmological constant (leading to accelerated expansion) which is similar to a tiny repulsive force proportional to distance - the latter doesn't prevent the formation of gravitationally bound systems up to the scale of say galaxy superclusters, but it becomes significant at cosmological distances. I am not sure of this but if my recollection is correct, the distance at which this repulsion balances gravity is roughly of the same order as the Hubble radius.

8. Jun 20, 2015

### Chalnoth

Depends upon how massive the objects are and how far apart they are.

Read up on Jeans Instability if you want an in-depth analysis on how this works:
https://en.wikipedia.org/wiki/Jeans_instability