INTRODUCTION

TO THE

(ALLEGEDLY

SPHEROIDAL)

EARTH

CALCULATORS

Purpose of the (Allegedly Spheroidal) Earth Calculators

The purpose of the (allegedly spheroidal) earth calculators is to demonstrate to readers carrying out and and analyzing measurable planar earth field observations in their own respective regions (or further abroad), the fallacy of the (allegedly spheroidal) earth and hence, the heliocentric paradigm. To that end, readers are encouraged to acquire high quality cameras and other optical equipment to document such observations. (Obviously, professional photographers, film makers, and surveyors will already have a plethora of equipment at their disposal.)

In the case of radar or radio freqency (RF) observations, e.g., radars or radio frequency tranceivers in contact with aircraft or radio frequency transmitters, the equipment involved typically operates in highly regulated, specialized circumstances, being outside the purview of most people. The exception to this of course, would be the licensed amateur radio operators, typically referred to as “hams” (a pejorative term stemming from nineteenth century telegraphy).

Readers are strongly advised to discuss such observations with people who have to work in safety critical, real-world industries or environments where errors are unacceptable; for example, those who work in civil enginering, aviation, shipping, and telecommunications. Discussions with others (including academics) adhering to the existing heliocentric paradigm but not otherwise responsible in the aforesaid safety-critical fields, however, are unlikely to be productive.

Overview of the (Allegedly Spheroidal) Earth Calculators

Five refraction-specific calculators are available to readers as follows:

(Allegedly Spheroidal) Earth Calculator I: w/o Tropo[spheric] Refraction

(Allegedly Spheroidal) Earth Calculator II: w/ Mean Tropo[spheric] Optical Refraction

(Allegedly Spheroidal) Earth Calulator III: w/ Maximum Tropo[spheric] Optical Refraction

(Allegedly Spheroidal) Earth Calculator IV: w/ Mean Tropo[spheric] Radar (or RF) Refraction

(Allegedly Spheroidal) Earth Calculator V: w/ Maximum Tropo[spheric] Radar (or RF) Refraction

Each calculator is essentially stand-alone, enabling the reader to calculate (under specific refraction conditions) both (a) the distance from the observer to the observer’s horizon, and (b) the distance of the subject of observaton below and normal to the observer’s horizon line of sight.

Planar Earth Field Observations

The following procedure is recommended for optical field work:

STEP 1. Determine a suitable location from which to observe the distant (i.e., ≥ 20 miles) island, promontory, marine or shoreline structure, marine vessel, land-based structure at elevation, or mountain (i.e., the subject of observation). Skies can be clear, cloudy, or even overcast as long as atmospheric visibility is high. In many cases, the atmosphere will be very clear 12–24 hours before the arrival of a low pressure system. Hence, it is advisable to monitor both atmospheric visibilty and weather fronts prior to carrying out field observations.

STEP 2. Obtain the geographical coordinates for both the observer \(P_{1}(φ_{1},λ_{1})\) and subject of observation \(P_{2}(φ_{2},λ_{2})\) locations, where \(φ\) and \(λ\) refer to latitude and longitude respectively. Obviously, the observer coordinates (and in some cases, the observer elevation \(H_1\) can be obtained on-site using either your vehicle or mobile device GPS app. Both the observer and subject of observation coordinates and elevations \(P_{1}(φ_{1},λ_{1},H_{1})\) and \(P_{2}(φ_{2},λ_{2},H_{2})\) respectively, are available at high resolution from online topographical maps.1

STEP 3. Calculate the (allegedly) curvilinear distance \(s\) between the observer \(P_{1}(φ_{1},λ_{1})\) and subject of observation \(P_{2}(φ_{2},λ_{2})\) locations. (The (allegedly) curvilinear distance \(s\) between \(P_{1}(φ_{1},λ_{1})\) and \(P_{2}(φ_{2},λ_{2})\) can be calculated using Karney’s algorithm for solving the inverse geodetic problem for an ellipsoid of revolution.2,3 Specifically, use Karney’s Online geodesic calculations using the GeodSolve4 utility.5)

STEP 4. Document the subject of observation by photograph or video using a high quality digital camera or video recorder with high zoom capability. (Most digital cameras will document the location of the observer for each photograph.)

Paradigmatic Conclusions

From the above Planar Earth Field Observations, enter the observer and subject of observation elevations \(H_{1}\) and \(H_{2}\) respectively, and the calculated (allegedly) curvilinear distance \(s\), in the appropriate fields provided in the (Allegedly Spheroidal) Earth Calculator I: w/o Tropo[spheric] Refraction, the (Allegedly Spheroidal) Earth Calculator II: w/ Mean Tropo[spheric] Optical Refraction, and the (Allegedly Spheroidal) Earth Calculator III: w/ Maximum Tropo[spheric] Optical Refraction. Record the calculated values for the (alleged) distances \(d_{n(K = 1)}\),6 (i.e., w/o tropo[spheric] refraction); \(d_{n(K = 7/6)}\), (i.e., w/ mean tropo[spheric] optical refraction); and \(d_{n(K = 5/4)}\), (i.e., w/ maximum tropo[spheric] optical refraction) of the subject of observation (i.e., the highest elevation of the island, promontory, or mountain, or the top of the marine or shoreline structure, or marine vessel, or the top of the land structure at elevation) below the (alleged) spheroidal earth horizon—more specifically, (allegedly) below and normal to the observer’s or optical instrument’s (alleged) horizon line of sight.7

The reader will notice that \(d_{n(K)}\) decreases with increasing refraction, i.e., \(d_{n(K = 1)}\) > \(d_{n(K = 7/6)}\) > \(d_{n(K = 5/4)}\). Hence, in fairness to the currently accepted (heliocentric) model, maximum tropo[spheric] optical refraction will always be assumed prior to making any paradigmatic conclusions. That being established, if the calculated (alleged) distance \(d_{n(K = 5/4)}\), (i.e., w/ maximum tropo[spheric] optical refraction) indicates that the subject of observation should be substantially below the observer’s (alleged) horizon line of sight when in fact, the subject of observation is clearly visible to the observer, and if said observation can be repeated, then it follows that the observer has scientifically demonstrated that the large-scale structure of the earth’s surface is not spheroidal but planar, i.e., that the earth is flat.

Reader, the foregoing procedure applied to a sufficient number of suitable locations worldwide—documented, and reported accordingly—will effect a paradigm change.


— FINIS —


  1. See for example, https://en-ca.topographic-map.com.↩️
  2. C.F.F. Karney, Geodesics on an ellipsoid of revolution, arXiv:102.1215 (Feb. 2011). See https://geographiclib.sourceforge.io.↩️
  3. It should be noted that the inverse problem output also includes the determination of the forward azimuth for each position, however, that determination is irrelevant to the immediate argument.↩️
  4. See https://geographiclib.sourceforge.io/html/GeodSolve.1.html.↩️

  5. See https://geographiclib.sourceforge.io/cgi-bin/GeodSolve.↩️

  6. A general depiction of the (alleged) distance \(d_{n(K)}\) (although not formally identified as \(d_{n(K)}\)) can be seen in Figure 1 on the (Allegedly Spheroidal) Earth Mensuration web page, represented as the line from \(P_{2}(φ_{2},λ_{2})\) (Mean sea level position of island, promontory, structure, or marine vessel) to \(P_{intersection}\) (Alleged intersection of line from mean sea level position of island, promontory, structure or marine vessel, normal to alleged line of sight ray of observer or optical instrument). Obviously, in the case of radar or radio frequency (RF) observations, \(P_{2}(φ_{2},λ_{2})\) is the mean sea level (MSL) or geodetic reference point for an aircraft or radio frequency transmitter with \(P_{intersection}\) being the alleged interesection of the line from \(P_{2}(φ_{2},λ_{2})\) normal to the alleged line of sight ray from the radar or radio frequency transceiver.↩️

  7. Analyses and technical references in support of expression for \(d_{n(K)}\) as well as for expressions for the (alleged) linear (i.e., line of sight) distance \(d_{h(K)}\) to the (alleged) spheroidal earth horizon, and the (alleged and allegedly curvilinear) surface (i.e., geodesic) distance \(s_{h(K)}\)) to the (alleged) spheroidal earth horizon, are included on web pages listed under the CURVATURE and REFRACTION folders.↩️



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DATE 2021-SEP-03