[bbojan]

Because all masses accelerate at equal rates in a gravitational field either:

1) Inertial mass and gravitational mass are exactly equal without an explanation why

or

2) The acceleration is just an effect of a curvature of space.

Imagine two bodies thrown exactly Northward on a sphere. Although their paths are parallel they would approach each other, as if there was an acceleration. This acceleration would be the same whatever their mass is.

[BobaFloutist]

>Imagine two bodies thrown exactly Northward on a sphere. Although their paths are parallel they would approach each other, as if there was an acceleration. This acceleration would be the same whatever their mass is.

The thing that always confuses me is how the distortion explains their behavior when stationary.

Sure, sure, "stationary" doesn't exist and everything is a matter of reference frames etc etc etc, but still, if you and I are both standing still on a sphere, there's nothing drawing us towards each other. Why are we drawn together from rest?

[AceyMan]

They would be converging at a fixed rate (dx/dt = 0), aka , not accelerating. This is unlike what we see in the presence of gravity.

I like the observation, tho, so if there is a way to 'save it' do let us know.

[jfyi]

I am just trying to understand this and not make any claim, so bear with me.

Let's say we have a cylinder with a hemispherical top instead of a sphere.

Say the two objects were thrown directly from the base of the cylinder towards what would be the equivalent of north on the hemisphere. Relative to each other they would be moving perfectly parallel and the distance between them would not be changing.

Once they reach the hemispherical section they would still be moving parallel to one another at the same speed but the distance between them would start to shrink, wouldn't this be the equivalent of acceleration due to gravity? Movement towards each other started at 0 and increased, right?