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. 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. Alan 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 note the time a star is occulted by a distant mountain peak. The location and elevation of the observer and mountain peak is known.

At the time of occultation, the altitude angle of the star equals that of the mountain peak. Stellarium is used to find the angle to the star, which will be the same as the angle to the mountain peak at the moment the star is occulted. This angle is then compared against the globe and flat Earth predictions for what angle the peak should appear at from the observer's location.

When flat Earthers use CT, they make several mistakes which skew the globe earth prediction (which is gone into more detail below). In reality, the globe's predictive capability for star occultations far exceeds flat Earth, especially as the distance and altitude of the peak increase.

Calculating the FE elevation angle

Once a mountain peak and observer location is selected, the distance between the the two locations is computed using the haversine formula. This is the website Heffron uses, which states the following:

All these formulas are for calculations on the basis of a spherical earth (ignoring ellipsoidal effects) – which is accurate enough* for most purposes… [In fact, the earth is very slightly ellipsoidal; using a spherical model gives errors typically up to 0.3%1 – see notes for further details].

For the flat Earth prediction, the elevation angle of the mountain peak can be calculated using:

$\theta =\arctan \frac{\mathrm{\Delta }h}{d}$

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. No angles are measured whatsoever, which is ironic given the method has theodolite in the name.

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 justify this by pointing out that on a flat Earth, the geometric altitude angle of the star at the observer location would be the same 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.

In addition, flerf proponents of CT insist on toggling off Stellarium's atmosphere simulation, which subsequently removes the effects of refraction. While they don't outright deny the presence of refraction, they seem to think it doesn't affect the time of occultation, believing the occultation will always occur when the geometric angles of the star and peak coincide with each other.

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. This happens after the geometric angles coincide. The reason for this is that atmospheric refraction raises the apparent position of both, but raises the star more since it's light travels through more atmosphere. This is an example of how flerfs misunderstand refraction.

Comparing the predicted angle

Flerf proponents of CT compare the (erroneously) predicted altitude angle of the star in Stellarium at the time of occultation to the (erroneously) calculated elevation angle of the mountain peak for both a flat Earth and globe Earth. For mountain peaks of certain distances and altitudes, flat Earthers can make it seem like the FE prediction is closer if they are able to sufficiently skew the prediction of the star's altitude angle.

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
• Stellarium being accurate whatsoever, given it uses a spherical 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:

• DEBATE: ‪‪@jeranism‬ vs ‪@Witsit‬ - The Celestial Theodolite
• The Fudge Factor for the Celestial Theodolite (feat. ‪@space_audits‬ and ‪@shanestpierre‬ )
• Celestial Theodolite: Why are you using the globe, dawg?
• Astronomical / Celestial Refraction (as applied to the Celestial Theodolite)

Astronomy Live

Astronomy Live conducted his own measurements with a slightly revised method: using planes and weather balloons instead of mountain peaks. He found that the accuracy of the CT's flat Earth prediction decreases as the Δheight and distance values for the mountain peak (or other occulting object) increase.

• He presented his method and data analysis in a debate with Alan.
• His data is available in a Google Drive folder and on GitHub.