OT: I'm confused about gravity

[Bill Wright]

I always sort of assumed without thinking about it that gravity would simply obey the inverse square law. But as I sit here on the planet the mass of the said celestial body is not all below me. It occupies a near hemisphere as viewed from here, with little mass around the edges and more and more mass towards the straight down direction. So a significant part of the gravitational force is in opposition (moments of a force and all that? Please remember I was cheated of a science education because the school decided I could write bollocks more convincingly than any other child, so they made me do Arts). So as I rise up in my thought-experiment space vehicle, the angles of the components of the Earth's gravitational pull come together, work more in concert than when I was on the ground, and thus become stronger in effect, so the inverse square law would not give the correct result?...?

Bill

[newshound]

It's a bit complicated for a non-homogeneous planet, but IIRC at the surface of a homogeneous spherical one the gravitational effect is exactly the same as if all the mass were concentrated at the centre of mass (i.e. the centre).

If you go down a vertical mine shaft, the gravitational force declines because all the material in the shell "outside" your position turns out to cancel itself out.

At the point where 90% of the mass is nearer the centre than you are, the "M" term is down to 90%, but of course the "R" term is lower too so the "g" is higher (but not as high as at the surface).

[Fredxx]

How I understand it gravity is a vector in that it provides a force with a direction.

Forces from either side of you cancel out, the exception is if you are close to a mountain, where the direction of force is distorted such it will not quite pass through the centre of the Earth.

[Bill Wright]

I can't see how it could be. I can see that the sum of the forces would be downwards, but the matter that's off to the side isn't going to pull you down is it?

If you're near a mountain there's a slight sideways pull.

And gravity varies anyway from place to place.

Those rules must also apply when you are above the surface. No reason why different rules of physics should apply depending on whether you're above or below the surface.

Bill

[Bill Wright]

So when you're out in space the forces that were on either side of you when you were on the ground won't cancel out any more because they'll be in almost the same direction. So the inverse square law won't work without modification.

the exception is if you are

So when you're out in space the forces affecting you from the mountain when you were on the ground will add to the forces frpom the rest of the planet. So the inverse square law if used to calculate the force at a point in space based on the force when you're near the mountain won't work without modification.

Bill

[newshound]

But two forces pulling sideways in opposite directions have a net force downwards.

Not homogeneous

Because the earth isn't homogeneous

The rules aren't different. It's all about the net effect when you use calculus to sum up all the infinitesimal forces.

GIYF.

[The Natural Philosopher]

The long answer is that you have to sum the effect of every single molecule in the earth

The short answer is, that what this gives you is the same result as if all the earths mass was concentrataed at its center (of gravity).

[Indy Jess John]

There is no such thing as gravity. The Earth sucks ;-)

Jim

[Jim]

Reminds me of a Tom Waits lyric "Don't you know there ain't no devil, there's just God when he's drunk."

[dennis]

They seldom pass through the centre of the Earth as the moon, sun and everything else affects it.

[harry]

You are lighter at midday. And when the moon is high in the sky. The planets also have and effect.

This is why the orbits of artificial satellites are peturbed and need constant adjustment.

[NY]

I remember from my O level physics that the gravitational force between two objects is

(G m1 m2) / r^2

where G is the universal gravitational constant.

So gravitational force *is* an inverse square law.

I shall refrain from comment about whether they were right :-)

However I was a victim of a similar "we know best" policy at my school. There were two forms in each year, and the A form (supposedly the cleverer form) had to do Latin and German, whereas the B form did Biology and Ancient History. I asked whether I could do German and Biology, but this was strictly forbidden - it was either/or, based on which form we'd been put into.

I'd like to have done Biology, and I'm frustrated that I missed out.

[Tim Watts]

It does if you're dealing with a distance point mass.

If you're not, then you need to consider all the "point masses" (ie this becomes a problem of intergral calculus).

ie you have to work out all the forces between you and every part of the other body -

each of which acts with a certain magnitude in a certain direction (straight down, mostly down with a bit sideways, etc)

then you add them all up using vector addition:

(x1,y1,z1) + (x2,y2,z2) = (x1+x2, y1+y2, z1+z2)

From that ^^^ you can see if you have mostly z negative (eg down), any

+x and +y will cancel equivalently sized -x and -y forces.

As it happens, there are some shortcuts in special cases of spheres:

[Tim Watts]

^^ point objects

So you can't necessarily blindly apply that to a pyramid sitting on the surface of a cuboid planet off centre. You'd have to work that one out.

But is happens with spherical objects of uniform density that you are outside of can be treated as point objects with all the mass concentrated at the centre. Happy special case...

I wanted to do a computing O-Level - but that was "something modern we don't believe in" (in 1986!!!!)

[Bill Wright]

So in a tug-of-war why doesn't the little flag on the rope go down to the ground?

Two forces pulling sideways (or up and down or any which way as long as they're opposite) cancel out. Two forces pulling sideways and opposite but down a bit will exert a downward force, but it will be weaker than if they were both pulling directly down.

Bill

[Max Demian]

Things below the Moon's orbit (sublunary) move in straight lines towards the centre of the Earth and decay. Things from the Moon's orbit outward move in circles and are eternal. At least that's what people used to think.

[Bill Wright]

I prefer common sense to fancy maths. Maths never worked for me. The answers were always wrong.

Bill

[Bill Wright]

Do you mean 32ft/sec/sec?

Bill

[Bill Wright]

How do the molecules know which way to pull? Do they discuss it?

So are you saying that the molecules in my G & T are trying to drag my ceiling lamp past them and onwards to the centre of the earth?

Bill

[Roland Perry]

Paging Isaac Newton, who is credited with inventing gravity.