[syhprum (OP)]

The simple view of the force of gravity between two bodies is that it varies according to their masses and the square of the distance between them
The Planck system of units lays down minimum units of space and time does anything similar apply to force ,is there any distance when the force falls to zero ? 

[Bogie_smiles]

I think that the consensus is that gravity is quantum, i.e., quantized. The professional scientific community is looking for a quantum solution. There is no distance where the inverse square law produces zero force, and Mach’s principle is based on the idea that gravity has an infinite reach.
https://en.m.wikipedia.org/wiki/Mach%27s_principle

[mad aetherist]

My reading of 1905 & 1916 etc stuff suggests that the consensus of everyone whose name ends in Einstein & begins with Albert is that gravity is not quantized.

[Bogie_smiles]

Maybe someone like @PmbPhy or @alancalverd or one of the GR vs gravity experts on the moderating staff could weigh in?

[syhprum (OP)]

Assuming gravity to travel at c if the expansion of the universe after the BB was faster than c the gravity of the original mass of the universe would not have caught up with us yet which could be the reason why we are still expanding 

[evan_au]

Light is quantised, but there is no minimum energy of a photon. There is no maximum range for a photon (within its light cone) - the expansion of the universe merely reduces the energy of the photon towards zero.

If (as many modern physicists believe), gravity also turns out to be quantised,there would be no minimum energy of a graviton. Similarly, there would no maximum range for a graviton (within its light cone) - the expansion of the universe merely reduces the energy of the graviton towards zero.

[Colin2B]

The Planck system of units lays down minimum units of space and time does anything similar apply to force ,is there any distance when the force falls to zero ? 

To add to what @evan_au is saying, planck units don’t give a minimum. For example, planck impedance is about 30Ω and planck mass is 2.18 x 10^-8. Clearly, there are things much smaller than these values.

[set fair]

...is there any distance when the force falls to zero ?

In deep space dark energy may be said to overwhelm gravity, resulting in negative gravity. This might be two conflicting forces, alternatively dark energy might concievably curve space in the opposite way that gravity does.

Satelites are effectively in zero gravity, they are held in orbit by earth's gravity but are in freefall. We don't feel the sun's gravity because we and the earth are in freefall. Try working how much you would way if the earth were replace by a giant non rotating ball 93 million miles in diameter... it's a very easy sum.

[set fair]

Oops way should be weigh. diameter should be radius.

[yor_on]

Not sure I agree Collin.

" "Planck scale" is the magnitudes of space, time, energy and other units, beyond (or below) which the predictions of the Standard Model, quantum field theory and general relativity are no longer reconcilable, and quantum effects of gravity are expected to dominate. This region may be characterized by energies around 1.22×1019 GeV (the Planck energy), time intervals around 5.39×10−44 s (the Planck time) and lengths around 1.62×10−35 m (the Planck length). At the Planck scale, current models are not expected to be a useful guide to the cosmos, and physicists no longer have any scientific model whatsoever to suggest how the physical universe behaves. " https://en.wikipedia.org/wiki/Planck_impedance

In some ways I think of this as basic 'building blocks', creating a universe. I also suspect that at some point measuring becomes a meaningless occupation. We can't measure Planck scale as far as I know. And going beyond seems to create singularities. https://rantonels.github.io/is-the-planck-length-the-minimum-possible-length/

[TimBandTech]

It's a divergent world of human theories at this point I think. Most recently the claim of observation of the Higgs boson, which somehow delivers mass ought to factor in, but I agree that the relativistic claim is to split mass and gravity so that curvature of space explains the attractive force. The quauntum gravity people claim that emergent spacetime is a part of their theory, but is the Higgs? I don't think so, otherwise we should hear of such interpretations. To what degree are momentum and gravity related? Through mass they are.
Pretty sure the positive side of all this is that there are open problems still. Dismantling existing theories i.e. breaking them is a valid pursuit. Generally you'll want to recover at lest some of their parts in your own construction. We are Shakespear's monkeys in this way. Learn to work out variations. Maybe one will be strong.

Staying within Newtonian gravity as the OP seems to be doing, it's the reciprocal of the distance squared. Far more interesting is that at zero distance this force blows up. Along the way atomic theory overrides gravity, but I'm not really convinced. Most of atomic theory is a curve fitters paradise. All the way down from there the experimntalists are running the show. When will pure theory derive the atom, the electron or the quark? Because it fits into a pretty table; that's not really enough. Somehow that Higgs was predicted some time ago.  The complexities of the pile are such that a few flips of it may settle out to a new theory that provides a better interpretation.

[evan_au]

more interesting is that at zero distance this force (Newtonian gravity) blows up.

This is true at the center of a black hole - but this is shrouded behind the event horizon.

However, for the normal matter around us, gravity does not "blow up".
- Most matter in the universe is hydrogen, with a density far less than the 150g/cm³ found at the center of the Sun
- The uranium nucleus approaches the density of a neutron star at around 10¹⁴ g/cm³, but even this is not enough to "approach infinity"

[Colin2B]

Not sure I agree Collin.

Well, I’m not sure you disagree either 

planck impedance is about 30Ω and planck mass is 2.18 x 10^-8. Clearly, there are things much smaller than these values.

Would you say that there are no values smaller than Planck impedance and Planck mass?
What I was pointing out was that a sweeping statement about planck units being a system that lays down minimum units, cannot be true.
I agree that much of it comes down to measurement at the small end, but when you say “we can't measure Planck scale as far as I know.” it’s worth remembering that a speed of 1 Planck length per Planck time is the speed of light in a vacuum, and we can measure that.
When I first saw the Hologramata article last yr, I remember thinking that it was a very good explanation of the issues. When he talks about minimum length, it is not in the classical sense that most people seem assume it is when based on articles in the pop press and wiki.