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The (alleged) diurnal rotation of the earth about its (alleged) axis is categorically disproven just by considering a direct (non-stop), north → south flight such as Avianca Flight 21¹ from New York (STD 07:10 AM EST) to Bogotá (STA 12:05 AM EST) — a de facto repeatable experiment. The approximately 5 hour flight from New York, specifically, (JFK) John F. Kennedy International Airport, located at coordinates N40°38.40' / W73°46.42',² to Bogotá, specifically, (UIO) El Nuevo Dorado International Airport, located at coordinates N4°42.10' / W74°8.82',³ is essentially a north → south flight more or less along the (W) 74^th meridian (obviously with certain deviations in accordance with flight plan requirements), the average outbound heading being approximately 181° (S).

Now the (west → east) linear or tangential velocity \(v_{t(φ\,=\, 0°)}\) of a point on the equator (i.e., the latitude, \(φ=0°\)) of the (allegedly) rotating earth is simply,

\[v_{t(φ\,=\,0°)}=v_{t(equator)}=ωa,\]

where, using World Geodetic System 1984 (WGS 84)⁴ parameters,

\(ω\) is the (alleged) Nominal Mean Angular Velocity of the Earth \(=7.292115\times10^{-5}\,\textrm{rad s}^{-1}\),⁵ and \(a\) is the (alleged) Semi-major Axis (Equatorial Radius of the Earth) \(=6378137.0\;\textrm{m}\)⁶ (or in \(\textrm{km}\)) \(6.3781370\times10^3\; \textrm{km}\).

Hence (to the nearest \(\textrm{km hr}^{-1}\)),

\[v_{t (φ\,=\,0°)}\\ =7.292115\times10^{-5}\,\textrm{rad s}^{-1}\\ \times 3600\;\textrm{s hr}^{-1}\\ \times6.3781370\times10^3\;\textrm{km}\\ =\color{brown}{1,674\;\textrm{km hr}^{-1}}.\]

For any other latitude north or south of the equator, the (alleged) tangential velocity of the earth is obviously less than that at the equator in proportion to the decreasing radii of the correspondingly decreasing circumferences. If the (allegedly) spheroidal earth were perfectly spherical, then at any given degree of latitude \(φ\) north or south of the equator, the (alleged) tangential velocity \(v_{t(φ)}\) would be:

\[v_{t(φ)}=v_{t(equator)}\textrm{cos}\,φ.\]

But because the current paradigm alleges the earth to be spheroidal or ellipsoidal, the (alleged) latitudinal radii are based on an ellipsoid of revolution (specifically, the WGS84 ellipsoid) rather than a sphere and hence, must be calculated accordingly. Critical to accurately calculating the (alleged) tangential velocity of the earth at any degree of latitude is the determination of the ellipsoidal radius \(R\,\) for the latitude in question. The ellipsoidal radius for any particular latitude \(φ\) is determined by transferring a point on that latitude to its correspoinding point on an auxiliary sphere, the latitude on the auxiliary sphere being the reduced (or parametric) latitude \(β\), given by the following equation from C.F.F. Karney⁷ (the source of which he attributes to Legendre^8,9):

\[\textrm{tan}\,β=(1-f)\,\textrm{tan}\,φ,\]

where \(f\) is the (alleged) Flattening Factor of the Earth defined by its reciprocal \(1/f=298.257223563\).¹⁰

Hence,

\[β=\textrm{tan}\,^{-1} [(1-f)\,\textrm{tan}\,φ].\]

Figure 1 illustrates the reduced or parametric latitude \(β\) on the auxiliary sphere for latitude \(φ\) on the ellipsoid. Point \(P(φ,λ)\) (at latidude \(φ\) on the ellipsoid) is mapped to point \(P′(β,λ)\) (at reduced latidude \(β\) on the auxiliary sphere), preserving the radius \(R\) of the ellipsoid at latidude \(φ\). Hence, the magnitude of radius \(R\) at latidude \(φ\) on the ellipsoid is simply:

\[R=a\,\textrm{cos}\,β.\]

Figure 1. The reduced or parametric latitude \(β\) on the auxiliary sphere of latitude \(φ\) on an ellipsoid (adapted from the National Geospatial-Intelligence Agency¹¹ and C.F.F. Karney¹²).

Therefore, the (alleged) tangential velocity \(v_{t(φ)}\) for any particular latitude \(φ\) on the (alleged) terrestrial ellipsoid is,

\[v_{t(φ)}=ωa\,\textrm{cos}\,β,\]

or in terms of \(φ\),

\[v_{t(φ)}=\]

\[ωa\,\textrm{cos}\,\{\textrm{tan}\,^{-1}[(1-f)\,\textrm{tan}\,φ]\}.\]

So getting back to Avianca Flight AV21 and substituting the WGS 84 numerical values for the constants \(ω\), \(a\), and \(f\) in the above equation, the (alleged) west → east tangential velocity of the earth at New York (JFK) at latitude N40°38.40' (i.e., 40.6400°N) with \(\textrm{tan}\, 40.6400°=\,0.8583\), is (to the nearest \(\textrm{km hr}^{-1}\)): \[v_{t(φ\,=\,40.6400°\textrm{N})}\\=\color{brown}{1,272\;\textrm{km hr}^{-1}}.\]

In a similar manner, the (alleged) west → east tangential velocity of the earth at Bogotá (BOG) at latitude N4°42.10' (i.e., 4.7017°N) with \(\textrm{tan}\, 4.7017°=\,0.0822\), is (to the nearest \(\textrm{km hr}^{-1}\)): \[v_{t(φ\,=\,4.7017°\textrm{N})}\\=\color{brown}{1,669\;\textrm{km hr}^{-1}}.\]

Hence, the departure runway at JFK (and consequently, Avianca Flight AV21 at departure) has a west → east tangential velocity (allegedly but based upon the current paradigm) of \(\color{brown}{397\;\textrm{km hr}^{-1}}\) less than that of the arrival runway at BOG. If in fact the earth were a rotating spheroid, Avianca Flight AV21 would have to land on a runway that is moving \(\color{brown}{397\;\textrm{km hr}^{-1}}\) eastward relative to the aircraft. Whereas (as previously mentioned) the average outbound heading for Avianca Flight AV21 is approximately 181° (i.e., almost due south), the aircraft would not have adjusted for the eastward velocity component, thereby physically precluding a landing at the arrival runway at BOG.

But it gets better. After flying almost due south for about \(5\; \textrm{hours}\) at an (alleged) west → east tangential velocity of \(\color{brown}{397\; \textrm{km hr}^{-1}}\) less than that of the arrival runway at BOG, Avianca Flight AV21 would soon realize that their destination (i.e., the arrival runway at BOG) was \(\color{brown}{1,985\; \textrm{km}}\), (i.e., \(5\;\textrm{hr} \times 397\;\textrm{km hr}^{-1}\)) east of the aircraft’s position — now flying over the Pacific Ocean about \(\color{brown}{625\; \textrm{km}}\) north-northwest (NNW) of the Galápagos Islands.

But of course, this does happen because the earth is a stationary plane as pointed out in aviation technical documents. Such documents must absolutely reflect real world conditions as they exist (not as some would have the public believe), an example of which is a NASA document that derives a linear model for aircraft dynamical analysis.^13,14 The document SUMMARY states:

This report documents the derivation and definition of a linear aircraft model for a rigid aircraft of constant mass flying over a flat, nonrotating earth [emphasis added]. The derivation makes no assumptions of reference trajectory or vehicle symmetry. The linear system equations are derived and evaluated along a general trajectory and include both aircraft dynamics and observation variables.¹⁵

In its CONCLUDING REMARKS, the document states:

This report derives and defines a set of linearized system matrices for a rigid body aircraft of constant mass, flying in a stationary atmosphere over a flat, nonrotating earth [emphasis again added]. Both generalized and standard linear system equations are derived from nonlinear six-degree-of-freedom equations of motion and a large collection of nonlinear observation (measurement) equations.

This derivation of a linear model is general and makes no assumptions on either the reference (nominal) trajectory about which the model is linearized or the symmetry of the vehicle mass and aerodynamic properties.¹⁶

While some would argue that the flat,¹⁷ nonrotating earth conditions are actually simplifying assumptions, it is contrariwise argued that aircraft range (even on short flights) would necessitate accounting for earth curvature and rotation if such factors did indeed exist. Additionally, it is difficult to believe that NASA’s budget would preclude the marshalling of sufficient technical resources to generate a necessarily more complicated analysis involving earth curvature and rotation parameters if such parameters were necessary to model reality.

But the reader need not be too concerned with such technical matters. One only has to visit an amusement park merry-go-round to fully understand the underlying concept of a stationary earth. From the perspective of tangential velocity, a rotating disk (i.e., the merry-go-round) is conceptually equivalent to a rotating sphere or spheroid (i.e., the (allegedly) spheroidal, rotating earth).¹⁸ Have one person stand near the center of the merry-go-round (where the tangential velocity is low) and another person stand near its periphery (where the tangential velocity is much higher). Have the person near the center attempt to throw a soccer ball to the person near the periphery. Assuming counterclockwise rotation of the merry-go-round (relative to the person near the center facing outward—conceptually equivalent to the (allegedly) counterclockwise rotation of the earth relative to Avianca Flight AV21 from New York flying south), unless the person near the center throws the soccer ball sufficiently counterclockwise of the person near the periphery, the soccer ball will exit the merry-go-round somewhat clockwise of the person near the periphery, just as Avianca Flight AV21 (originating in New York and therefore nearer to the (so-called) North Pole or rotational axis of the (allegedly) spheroidal, rotating earth) would be over the Pacific Ocean approximately \(\color{brown}{625\; \textrm{km}}\) NNW of the Galápagos Islands upon reaching the latitude of Bogotá (i.e., clockwise of the airport at Bogotá located just under 5° from the equator and therefore close to the periphery or maximum rotational radius of the (allegedly) spheroidal, rotating earth).

Reader, this is just basic dynamics. It is that simple. Obviously, our educational system (not to mention our popular culture) needs an existential review.

— FINIS —

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1. https://www.flightradar24.com/data/flights/av21.↩️

2. https://skyvector.com/airport/JFK/John-F-Kennedy-International-Airport.↩️

3. https://skyvector.com/airport/SKBO/Santafe-De-Bogota-Eldorado-Airport.↩️

4. National Geospatial-Intelligence Agency (NGA) Standardization Document (Office of Geomatics), Department of Defense World Geodetic System 1984: Its Definition and Relationships with Local Geodetic Systems (NGA.STND.0036_1.0.0_WGS84), Version 1.0.0, 2014-07-08.↩️

5. Ibid., p. 3-4, Table B.1 WGS 84 Defining Parameters.↩️

6. Ibid. While the (alleged) Semi-major Axis (Equatorial Radius of the Earth) \(a\) is one of the four defining parameters, the (alleged) Semi-minor Axis (Polar Radius of the Earth) \(b\) (\(=6356752.3142\;\textrm{m}\,\)) is a derived constant (see p. 3-9, Table 3.5 Ellipsoid Derived Geometric Constants).↩️

7. C.F.F. Karney, Geodesics on an ellipsoid of revolution, arXiv:102.1215 (Feb. 2011), p. 2. Equation (8) (https://geographiclib.sourceforge.io).↩️

8. Legendre, A.M., “Analyse des triangles tracés sur la surface d’un sphéroide,” in Mémoires de la classe des sciences mathématiques et physiques de l’Institut Nationale de France, Premier semestre de 1806 (Paris: Baudouin, Imprimeur de l’Institut, Juillet M. DCCC. VI), pp. 130–161 (http://books.google.com/books?id=-d0EAAAAQAAJ&pg=PA130-IA4). Legendre’s flattening equation is presented on p. 136 as follows: \[\textrm{tang.}\ λ'=\dfrac{b}{a}⋅\textrm{tang.}\ λ,\] where \(λ\) is the true latitude (la latitude vraie), \(λ'\) is the reduced latitude (la latitude réduite), \(a\) is the radius of the equator (le rayon de l'équateur), and \(b\) is the (minor) semi-axis (le demi-axe). See pp. 134-137.↩️

9. The current version of Legendre’s equation uses the factor \(1-f\) instead of \(b/a\), where \(f\) is called the flattening expressed as: \[f=\dfrac{a-b}{a}.\] See for example, Wolfgang Torge and Jürgen Müller, Geodesy, Fourth Edition (Berlin: De Gruyter, 2012), p. 91, Equation (4.1a).↩️

10. NGA.STND.0036_1.0.0_WGS84, op. cit., p. 3-4, Table B.1 WGS 84 Defining Parameters.↩️

11. NGA.STND.0036_1.0.0_WGS84, op. cit., p. 4-2, Figure 4.1 Ellipsoidal Coordinates.↩️

12. C.F.F. Karney, op. cit., p. 4-2, “Fig. 15 The construction for the reduced latitude. [...].”↩️

13. Eugene L. Duke, Robert F. Antoniewicz, and Keith D. Krambeer (Ames Research Center, Dryden Flight Research Facility, Edwards, California), Derivation and Definition of a Linear Aircraft Model (NASA Reference Publication 1207) (National Aeronautics and Space Administration, Scientific and Technical Information Division, August 1988).↩️

14. While the (alleged) extraterrestrial exploits of NASA are (and should be) under historical scrutiny in terms of scientific and engineering feasibility as well as financial traceability, the agency is nonetheless (for other reasons) necessarily involved in conventional technological deployments that can only be properly managed under a rubric of technical excellence.↩️

15. Ibid., p. 1.↩️

16. Ibid., p. 30.↩️

17. See Spheroidal Earth Refuted: Experimental Proof of a Planar Earth.↩️

18. The essential concept being that for both a disk and a sphere (or spheroid) rotating at a constant angular velocity, the tangential velocity is directly and exclusively proportional to the radial distance from the rotational axis.↩️

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