Modeling the Celestial Dome: A Mathematical Perspective on Flat Earth Theory

In the study of celestial movements and star patterns, both the spherical and flat Earth models utilize a concept known as the celestial sphere. This imaginary sphere, which encircles the Earth, serves as a canvas where all celestial bodies are projected. The spherical model interprets this sphere as surrounding a globe, while the flat Earth theory proposes a dome-like firmament above a flat plane. This article delves into how the celestial dome can be mathematically modeled within the flat Earth framework, offering insights into the interpretation of celestial coordinates and star movements.

Understanding Celestial Coordinates

Right Ascension (RA) and Declination (DEC) are two critical coordinates in astronomy, akin to longitude and latitude on Earth. These coordinates allow astronomers to pinpoint the location of stars and celestial bodies. Interestingly, the flat Earth model incorporates these coordinates under a dome-like firmament, mimicking the celestial sphere used in traditional spherical astronomy. This suggests that the mechanism for locating celestial bodies using RA and DEC remains fundamentally consistent across both models.

Observing Celestial Phenomena

Both the globe and flat Earth models account for observable phenomena such as the decreasing altitude of Polaris, the North Star, as one moves southward. For every 69 miles traveled south, Polaris’s altitude decreases by approximately one degree, disappearing entirely beyond the equator. Conversely, in the southern hemisphere, stars rotate around a central point, becoming visible only south of the equator. These observations are attributed to the Earth’s curvature in the globe model and to movement across a flat Earth under a rotating dome in the flat Earth model.

Mathematical Derivation of the Dome

To quantify these observations, we can derive a mathematical equation for the dome structure posited by flat Earth theory. This equation models the dome as a parabolic shape peaking at a specific height and intercepting the flat Earth at its edges. The formula used is:

where:

• ( y ) is the height of the dome above the flat Earth at any point ( x ),
• ( R ) is the radius (or height) of the dome at its highest point, directly above the center of the flat Earth plane.

Let’s break down how this formula is developed:

1. Defining the Peak of the Dome: The highest point of the dome, or the vertex of the parabola, is at ( R ). Here, ( R ) is derived from the relationship ( R = D x V ), where ( D ) and ( V ) are constants based on observations or predefined parameters. In our example, ( D = 69.07 ) and ( V = 90 ), giving ( R = 6216.3 ) mi.
2. Calculating the Spread of the Dome: The x-intercepts of the parabola (where the dome meets the flat Earth) are crucial for understanding the breadth of the dome. Setting ( y = 0 ) in the equation and solving for ( x ) provides the intercepts: x = +/- 2R
   This calculation shows that the dome extends ( +/- 12432.6 ) mi from the center, covering the flat Earth symmetrically.

Observations

Conclusion

This mathematical exploration into the flat Earth’s celestial dome provides a structured way to visualize how celestial phenomena like star trails and the visibility of celestial poles can be interpreted under a different model. By translating observational data into mathematical terms, we bridge the gap between conceptual models and observable reality, demonstrating the flexibility and adaptability of mathematical tools in explaining natural phenomena, regardless of the underlying model of the Earth.