If I’m following this correctly, the idea is that because satellites can be said to be traveling in a straight line through curved spacetime, then it follows that the surface of the earth is “flat”, only curved in spacetime.

Problems I see with this are:

1. Satellites can only be in a stable circular orbit at a precise speed for any given altitude, yet we always perceive the Earth’s curvature the same regardless of velocity wrt the Earth’s surface, including stationary.

I'm not sure why this is a problem, or perhaps I'm missing something in the "wrt". Can you expand on this?

wrt = with respect to

I probably should have said relative to. Although that was still not quite right, as orbital speed isn’t relative to rotation on surface anyway. What can I say- there was some booze involved in that post.

Anyway, the basic point is unchanged. The curved path of an orbiting object is entirely dependent on it’s speed. You only get an orbit going by at the right speed, depending on altitude.

By that’s not how things are when we look at the surface of the earth. The curve is the same, no matter how fast we go.

2. It falls apart if you apply this line of thinking to other planets and moons (which we can and do put objects into orbit around). The moon for example has a much weaker gravitational field than the Earth, being much smaller. Yet if we’re saying the curvature is due to to spacetime distortion, if should require a stronger field to have a tighter curve.

They are large enough to support their own mass and orbits. The field is the same relation. Smaller objects typically orbit small bodies.

But we can achieve an equivalent orbit around the moon to Earth at much lower velocity, so the moon’s field (I’m avoiding the G word) must be weaker.

But if the surface is only curved because of a distortion in spacetime, it should require a stronger field than the earth, because it’s more tightly curved.

Any correlation between orbits curved by spacetime and the surface curved by spacetime is in the wrong direction than your hypothesis suggests.

3. But why stop there? If we’re saying something that appears spherical is actually flat, only curved by spacetime, should we then apply this to all spherical objects? Is a football (soccer ball) really also flat?

To your actual question: Is the football flat? No, various forces are keeping it in its shape, gravity not one of them in the sense we are talking - though understand that it would apply just as easily at smaller scales - its just might not productive to worry about the frame of reference of an electron (or perhaps it might...). This is perhaps where the argument "its just a slight deviation due to the force" might be noteworthy, not in the pseudoforce that apparently bends objects in circles around round bodies.

To a more interesting point - Take the path of all soccer balls as they are kicked or as they are stationary; at their apex they are traveling a straight line through spacetime as they are not suffering from acceleration. Taking its apex, one can extrapolate by noting its felt acceleration where it might be if it was not suffering from this affliction. This path would be tangent to the apex, and flat at a constant altitude, much like the orbit. Taking the space of all these solutions, we end up with a space consisting of spaces of planes comprised of these points.

I was being a bit facetious with the football comment. Sorry.