Earths attraction

[rov1200]

Having heard about the new ring millions of miles from Saturn how many miles from the Earth would you have to travel before any attraction is lost and does it depend on the mass?

[Jumbuck]

attractive force between 2 objects = (G x M1 x M2) / (R^2)

where G is the gravitational constant, M1 and M2 are the two masses and R is the distance betwen the 2 objects.

So it's never 0 but the gravitational attraction from other celestial bodies will soon swamp any pull that the Earth exerts..

[jake-the-peg]

Jumbucks formula is Newton's handiwork which lasted unchallenged 300 years.

It's an "inverse square" so if you double the distance the force diminishes by half tripple it , the force diminishes by 1/9th etc. etc.

99.9% of things could be explained by this. However there were some oddities.

Einstein came up with General relativity about a century ago and explained these - Things like the orbit of Mercury which couldn't be explained by Newton's formula.

But still we have the inverse square law.

Of course though there's a problem

In this theory two grains of sand a light year apart should exert a gravitational force on each other - two atoms should.

Does this really make sense?

This is all based on observation and creating formulae that fit what we see. But we don't have instruments to measure forces that small nor the ability to set up the experiments even if we did.

So we do not know if it's realistic to extend what we see at medium ranges and masses to huge distances and tiny masses.

So far it's served us well but cracks are begining to show in the form of Dark Energy and Dark Matter which might turn out to be failings in our understanding of Gravity.

We think that in theory Gravity might come in waves and there might be a particle called the Graviton that transmits the force.

If that's true then things might change in answers to some of these questions but the experiments to find these things are right on the very edge of our technical capability and so far have not turned up anything.

But I don't think the story of Gravity is done and dusted. There are a few Nobel Prizes left in that field left for the taking but whether it'll be another 50 years or another 300 years I really wouldn't like to say.

[Jumbuck]

No-one has yet come up with the ultimate equation which will apply to the entire cosmos - even General Relativity is just an approximation which applies to a larger scale than Newton's laws. But the OP was about things on the scale of the Solar System, and Newton's laws are good enough to be used by NASA when it comes to planetary space missions (when they don't mix up imperial and metric units).

[Seafarer1966]

Nnnnnnghhhhh......my brain is exploding

[rov1200]

Thanks for your very good answers. The amazing thing to me using Newtons Inverse Square Law is that the mass contained within the particles in the ring millions of miles from Saturn is extremely small and multiplying that mass near to zero would produce an answer close to zero. Yet it still produces an eliptical ring and formation that can be seen.

Like you say Jake we don't yet know it all and maybe Newton's Law holds true only under certain circumstances.

[Jumbuck]

hmmmmmmmmm brains...

[jake-the-peg]

Depends of the mission I guess.

I know that GPS satellites have to adjust for General Relativity.

I'd imagine the Hinode Sun mission might have had to as well.