If the satellite was accelerating you would feel a pull. When you are in a car and you accelerate you feel a pull.
No, when the car pushes on a portion of us to accelerate us, we feel that force being transmitted through our body.
Here is a question for you, if you were to be levitated in an incredibly strong magnetic field, which acts on your entire body to levitate it, what would you feel?
You could even consider this for a water droplet or a magnet falling through a metal pipe or a piece of metal being levitated by an induction melter.
If the force acts equally on every part of a homogenous body, so there is no force transmitted through the body, does it feel anything?
What's a geodesic? Oh, the shortest distance between two points.
In general, no.
e.g. consider 2 points on the surface of a sphere at the equator. One is at 0 degrees east, the other is at 10 degrees east.
A geodesic connecting them can either go the short path, passing through 5 degrees east, or the long path, passing through 180 degrees east.
By round earth's own theory, you must admit relativity is bunk or that satellite is traveling a straight line through space-time.
Or we can admit it is travelling along a geodesic through space-time, tracing a curve in space.
Put em all together - these worldlines form a smooth flat bundle of geodesics that fill out a particular region of spacetime
Do they?
Do they actually fill out a region, or did you mean they define a boundary of a region?
If the latter, do they actually form a boundary of an enclosed region, or does it just divide the region?
Or are you saying it fills out a 3D region which defines the boundary between two 4D region?
That congruence is flat by any meaningful definition of the word
Before saying that I would ask if there is a meaningful definition of the word "flat" for non-euclidean (i.e. non-flat) geometry, and what that actually means.
For example, for Euclidean geometry a flat surface is a plane.
One way to define this is with a point and a normal.
Then if you take that point, and any direction perpendicular to that normal, and travel in a straight line, you remain in the plane.
But this is not necessarily the case with non-Euclidean geometry, at least not for the surface you have defined.
Instead, you can take a point on that surface and a normal to the surface, and then find a direction perpendicular to that normal, which in order to remain on the surface it is not a straight line.
e.g. if we take 2D space + time to get 3D space time, we can consider effectively 1 orbital plane of Earth.
So we can consider satellites in this perfect orbit, spaced apart by longitude or time.
Each path would appear as a helix when represented in a flat version of this curved spacetime (where we are representing a 1D line of a 2D surface in 3D space).
By considering all of them, we get a cylinder in this representation in space.
So why then can't we consider a path also along this cylinder which retains the same spatial coordinates and just moves through time.
Locally at the first point we consider, it is going straight still, like something at the peak of a toss, but then it doesn't continue moving along a geodesic.
So does the concept of a flat surface make sense in a non-Euclidean space?
and that flat region surrounds and defines the border area of earth.
Earth is flat. QED.
Far too much of a logical leap.
You had a satellite not Earth. So that would be defining some arbitrary region of space time which Earth is in, not Earth itself.
Why should Earth being inside a flat region make it flat?
Why not more directly consider all points on Earth's surface, which are not following geodesics and therefore Earth is not flat?
So we now have another proof that you can believe its flat and not reject all science.
Yet you can't bring yourself to answer a simple question:
In this hypothetical world of yours, what is the angle sum of a triangle on the surface (ignoring irregularities like mountains)?