Standard Horizon
Receding a distant ship smoke on the horizon?
Because the earth is round, there is observable horizon.
What should be the pressure of atmosphere to make the surface of the earth to appear flat, and horizon disappear?
Refraction index of standard air at sea level is
no = 1.00029
People,
the planar front of constant phase of horizontal ray remains always vertical when the ray bends properly,
right?
If air's refraction gradient enables you to see a little further, it's "flattening" the curvature. Increased pressure & density should increase the refractive index, but will it increase the gradient? Yes, according to the formula used to compute air pressure as a function of altitude and sea-level pressure (it's in the form p = p0 * e ^ (k * g * (h - h0)). But I'd suspect not reliably unless g increases also. One reason being that the pressure increase would expand the atmosphere and air would be lost at the fringes where molecular velocity >= escape velocity.
EDIT: OK, so the wavefront stays vertical, the velocity is proportional to radius R and the refractive index N inversely proportional. Then we need to use the pressure-vs-altitude equation, and the fact that the fractional part of N is proportional to pressure (ref.) to derive the desired SLP. This yields 440000 Pa giving an N value of 1.001259 and a gradient dN/dR of -1.575E-07/m. This gives (dN/N)/dR = 1/R. Of course the gradient is only correct at sea level for the desired flattening effect.
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