Flat Earth Challenges

I offer Flat Earthers several straight-forward challenges:

#1 Simply produce a flat map that is both area and distance accurate.  This should be very straight-forward on a flat Earth.

Initial checks should be to Measure distance from Nuuk to New York (2984.16km) to Johannesburg (12834.99km) to Prague (8556.58km) back to Nuuk (4076.04km) and area of Greenland(836300 mi²), Africa (11.67 million mi²), New Zealand(103483 mi²), & Texas (268820 mi²)

If your flat map distorts any of these more than a fraction (for allowable measurement error) then it is wrong, period.

Furthermore, you can show that the values we observe on Earth only work on a spheroid - thanks to Gaussian curvature which proves you cannot flatten a spheroid into a flat map without distortions & tearing.

Please Note: the highly distorted equidistant projections are known to fail this test.

Distances only work to the center point and areas are distorted increasingly the further from center you get.

#2 show me your equations which explain the fact that we observe two (2) celestial poles (points in the sky around which all the stars appear from Earth to rotate) and accounts for the motions of all the major bodies (sun, moon, naked-eye-visible planets, and the stars where we have measured parallax such as Barnard's star, etc).

And Please Note (as they often get this wrong): there is no such thing as an exact North or South pole star - I'm NOT talking about the stars, I'm talking about the point in the sky around which they appear to rotate.  Hint: Polaris is not that point, it is just pretty close.

Bonus points, explain why that celestial point moves in agreement with the axial precession of Earth's axis - which you claim isn't spinning.

#3 set up an experiment where you simultaneously measure the angle of the suns shadow off an object 5 meters tall that is plumb from at least 5 points along the same longitude line (or within ~3 degrees).  1 must be very near the equator, 1 as far North as you can get it, the remainder in between but not too close, spread out.

Taking all the permutations of angles compute the "distance to the sun" and show that all the values agree.  If they diverge then the flat earth model is disproved.

If they fit an exponential (which they do) then that matches the spherical model (in other words, the further north you go, the shadows will get longer at an exponential rate)

Psst, we all already know this from Eratosthenes.

#4 Given the standard 'spherical Earth' values for Earth mass (5.972 × 10^24 kg), equatorial radius (3,959 mi), and rotational rate (once every 24 hours), calculate the effective equatorial centrifugal acceleration at the Equator and PROVE that this would spin us off into space; that is, overcome Gravity at MSL which is ~9.807 m/s²

Hint: you are pitting ~0.0339 m/s² against 9.807 m/s² -- GO!

The profound innumeracy of the Flat Earth movement renders this one all but moot but I like to see them try to do the math because it's SO hard (rω²).