Can you prove that the Earth isn't a hollow sphere?
Yes, easily, using data collected by our own forum members. I'll use two examples.
1) The propagation of seismic waves.
On the old forum, midtskogen showed a recording of an earthquake which took place in New Zealand, from his station in Norway. A key observation in this recording is the lack of direct shear waves.
Shear waves are not visible from stations located more than about 120° from the earthquake center, because they cannot penetrate through the liquid outer core of the Earth.
Another observation is to use the arrival time of the first vibration as a function of distance across the surface of the Earth. If we live on the inside of a hollow sphere, then this arrival time should grow linearly with that distance, because the fastest path the earthquake waves can possibly take is through the surface.
But what we actually observe that the delay grows more slowly with increasing distance:
So, how does one reconcile these observations with a hollow Earth model?
2) The strength and direction of local gravitational field.
On the solid Earth, your local gravity points downward with a strength within a few tenths of a percent of 9.81m/s[sup]2[/sup]. How would gravity work on the inside of a hollow Earth?
If you propose the gravity is due to the distribution of matter, then you have a problem.
The gravitational field inside of a hollow sphere is everywhere equal to zero! We would all be weightless.
If you propose the gravity is an apparent force due to the Earth's rotation, then you still have a problem. You cannot make the local apparent gravity be equal to g everywhere, or everywhere pointing downward with respect to your horizon.
Let's compute the formulas. If standing at a latitude \theta on the inside of a hollow sphere with radius R, spinning with angular velocity \omega, then you experience a
centrifugal acceleration of:
a = \omega^2 Rcos\theta, in a direction which is away from the axis of rotation and at an angle 90 - \theta degrees from your local horizon. (Oh wait, there is no horizon on the inside of a hollow Earth).
Okay, make that \theta degrees from nadir.
So at my location at 48°N, I should experience a gravitational force only 67% as strong as at the equator, and pointed 48° from nadir. Midtskogen at 60°N should feel a force with 50% of the equatorial value, and at 60° from nadir.
Needless to say, this is very inconsistent with reality. But I'll let midtskogen correct me if he happens to feel like he's standing on a 60° slope at 0.5g.
Now let's look at the nine so-called evidences for the hollow Earth.
"Some early modern maps have inversed latitude and longitude"
This is not evidence. A sphere has the same geometry whether you are on the inside or the outside, and you can attach coordinates to it in any way you want.
"Modern polyconic maps show more accurate sizes and shapes"
Also not evidence, for the same reason. Any projection of a curved surface onto two dimensions will work the same way whether the features you are mapping are on the inside or the outside of that surface.
"19th century balloon observations (that is, without an intervening medium) gave the impression of a conclave surface"
So we were on the inside of a hollow until the 20th century, and then suddenly it switched? I like this conspiracy.
"4,000 foot plumb lines reportedly were farther away from each other at the bottom of a mine shaft"
Or we can cite the greater distance at the tops of the towers of the
Verrazano-Narrows Bridge as a better established and contradictory example.
Furthermore, if this claim is true and we conclude it is because we're on the inside of a sphere and gravity is pulling them outwards, then we run into that above problem of explaining how gravity works.
"A laser shot between two posts (over water) seems to curve downwards"
Sure: atmospheric refraction. Works just as well on being on the outside of a sphere as on the inside. So this is not evidence.
"An old rectilineator experiment indicates a conclave surface (the experiment has been criticized here)"
Ok.
"Radar and radio wave horizons cannot be explained on a convex ball"
Sure they can. Every experienced HAM radio operator is familiar the role of the ionosphere on radio wave propagation.
"Ships disappearing below the horizon are an optical illusion"
AKA: "When faced with observations that are incompatible with your world view, declare them to be illusions." Like stars, the Moon, and satellites.
"Light bends upwards, which allows for the rising/setting illusion of the sun and moon"
Atmospheric refraction again. This isn't evidence of being on the inside of a hollow Earth.
So this list of nine evidences is really just a list of claims which are either wrong, dubious, or otherwise compatible with being on the outside of a sphere.