The concept of geocentric parallax, as detailed by A. A. Krishnaswami Aiyangar, offers intriguing insights into the behavior of celestial bodies when observed from different positions on the Earth’s surface. This paper provides a method to calculate the parallax in Right Ascension and Declination using spherical trigonometry. However, from a Flat Earth perspective, we can use these findings to support a geocentric, flat model of the Earth.
Key Points and Their Flat Earth Interpretation:
- Geocentric Parallax Explained:
- The paper describes how the apparent position of a celestial object changes based on the observer’s location. In a Flat Earth model, this is the observer’s distance from the center of the flat plane, rather than a spherical surface.
- The diagrams in the paper (Fig. 1 and Fig. 2) show the relationships between different angles and distances. On a flat plane, these angles would still apply, but the curvature of the Earth is unnecessary.
- Triangular Relationships:
- The equations derived, such as the formula for parallax in Right Ascension (tan(a′−a)), are based on trigonometric relationships that are equally valid on a flat plane. The important factor is the relative positions of the observer and the celestial object.
- For instance, the relationship sin(SS′)/r′=sin(S′Z)/r (Equation 1) describes how the parallax angle changes with distance. This is purely a geometrical relationship and does not inherently require a spherical Earth.
- Practical Observations:
- Observers on different parts of the flat Earth would notice shifts in celestial positions as described by parallax. This does not contradict a flat model but rather can be seen as evidence of a consistent flat surface where these geometrical relationships hold.
- The parallax in Declination (tan(δ′−δ), Equation B) shows how the angle of observation changes vertically, which would be expected as one moves across a flat plane under a dome-like sky.
Supporting a Flat Earth Model:
- The calculations provided by Aiyangar are based on the premise of spherical trigonometry, but the core concept of parallax — the shift in perspective based on position — does not require a spherical Earth.
- By considering the Earth as a flat plane, these same observations and calculations can be made, demonstrating the versatility and adaptability of trigonometric principles.
- This approach aligns with historical observations made by ancient astronomers who assumed a flat Earth and still made accurate celestial measurements.
Conclusion:
The study of geocentric parallax by Aiyangar inadvertently supports the Flat Earth model by showing that positional changes of celestial objects can be calculated without explicitly relying on a spherical Earth assumption. These geometrical relationships are robust and can be applied to a flat plane, reinforcing the idea that Earth is flat and centrally positioned in the universe.