Celestial Theodolite

The celestial theodolite (CT) is a proposed method for testing Earth's curvature by recording the time that a star is occulted by a terrestrial object (typically a mountain peak) of known distance and known relative elevation.^[1] The method was created by Mike Heffron. Flerfs claim that the CT produces data that is consistent with a flat Earth and not a globe. Flerfs Space Audits and Shane St. Pierre are notable proponents of CT.

Method

In the original method described by Heffron in Beyond the Null Hypothesis, an observer is to measure the time a star is occulted by a distant mountain peak. The location of the observer and mountain peak is known.

The "predicted" altitude angle angle of the star in Stellarium is then compared with the calculated elevation angle of the mountain peak assuming a flat Earth. The only data that is actually collected is the time of occlusion . This is because if flerfs used an actual theodolite to measure the elevation angle of the mountain peak, it would immediately confirm the globe^[2].

The method eloquently summarised by Roohif:

Basically they record the time that a star is occluded behind a mountain, perform some fuckery in Stellarium to get an angle, then they compare that angle to the raw, flat Earth trig.

Calculating the FE elevation angle

Once a mountain peak and observer location is selected, the haversine formula (which uses spherical geometry) is used to compute the distance between the the two locations. The elevation angle to the mountain peak assuming flat Earth can then be calculated using:

$θ = \arctan \frac{Δ h}{d}$

Where Δh is the difference in elevation between the observer and peak, and d is the horizontal distance between the observer and mountain. It's important to note that in this step, the horizontal distance is assumed to be flat despite having obtained this value under the assumption that earth is spherical.

Timing the occultation of a star

The observer then waits for a star to disappear behind the mountain peak, then notes the exact time of the occultation. That's it for this step. This is all the data that needs to be collected for CT.

Finding the predicted altitude angle of the star

The "predicted" altitude angle of the star at the time of occultation is computed in Stellarium. Flerf proponents of CT do not set the observer location in Stellarium to the actual observer location; they set it to the location of the mountain peak. They claim that this is because on flat Earth, the geometric altitude angle of the star at the observer location is the same as it is at the mountain peak at the time of occultation. While this is true in theory, there are two issues with this:

the geometric angle is different from the apparent angle - flerfs are ignoring the effects of atmospheric refraction
Stellarium doesn't f*cking use flat Earth to predict star angles - the position of the star will obviously be different at the mountain peak

Flerf proponents of CT don't realise that the occultation actually occurs when the apparent angle of the star coincides with the apparent angle of the mountain peak. Both are subject to atmospheric refraction, and in fact, the star is refracted much more due to it's light travelling further through the atmosphere. Flerfs seem to think that the occultation will always occur when the geometric angles coincide with each other, even when accounting for refraction. This is patently false, and it shows how flerfs misunderstand refraction.

List of globe Earth assumptions

The CT method as proposed by flerfs uses several globe Earth assumptions and calculations, including:

The distance between the observer and the mountain (see: haversine formula)
The predicted altitude angle of the star
The amount of astronomical refraction^[3]
Stellarium being accurate whatsoever, given it uses globe earth to make predictions

This list is a confirmation of the First Law of Flerf.

Notable Debunks

Roohif

Roohif has a [currently] 4-part series on YouTube exposing the many problems with CT:

references

[1] ttps://publish.obsidian.md/spaceaudits/99_Old/Celestial-Theodolite/Cel-Theo/Cel-Theo-Concept

[2] ttps://www.youtube.com/watch?v=7oY-4NSRbOs

[3] ttps://www.youtube.com/watch?v=iGH1TMWS8KE

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