But no.

Gravity would act downwards on such a plane

just not true

it would collapse onto that single point

Because every local position has the same mass on the plane

yes but tell me

You have the same mass to your left and right

where would its centre of mass be

It wouldn't matter in this case.

Break it down into a load of squares

it it the exact point

Imagine Minecraft, gravity would act downwards in that case.

Because a sufficiently far object exerts no force on you.

And you have the same mass uniformly radially around you and under you.

The problem with that is there is a centre of gravity somewhere

There's no problem with that at all.

An infinite plane with uniform mass does not exist

There is

Hehe

It doesn't need to be infinite

Just large enough

It does because then a centre of the object can be found

which is its centre of mass

And force would be uniformly downward.

which is where force would be applied from radially

making it crumple in on itslef

g = GM/r2 correct?

Well no.

Because it has uniform gravitational forces at all places expect its boundaries.

Except.

Unlike the earth

In a round sense

as the mass of such size would create such an immense gravity that it collapses in on itself

Which would have more gravitation at different parts in it.

@Monticks ha but no. Again, the radius makes it not matter.

No. You cant wrap your head around the idea that gravity comes from the centre of mass

which is the object is unifrom

It's like saying: gravity exists therefore the universe must collapse.

so your saying , g = GM , then

it is the centre of the object

boy xD