Author: Steven Alonzo, B.Sc. in Geocentric Cosmology
Published: April 29th, 2024
Accepted: April 14th, 2024
DOI: 10.7434/j.gcosmog.2024.04.001
Abstract
This study evaluates the practicality of determining the Moon’s distance from Earth using trigonometric and parallax methods, employing real observation angles and a baseline distance typical of Earth-based measurements. The results underscore the extreme precision required in angle measurements, rendering these methods impractical for accurate lunar distance calculations without advanced technological aids.
Introduction
Accurately measuring celestial distances is a fundamental challenge in astronomy. While trigonometric and parallax methods are theoretically sound, their application to lunar distance measurements using conventional Earth-based observations proves highly problematic due to the precision required in angle measurements.
Methods
- Trigonometric Method: Calculating lunar distance by creating a triangle with the baseline between two observers and the Moon, and measuring the angles at each observer’s location.
- Parallax Method: Determining distance based on the apparent angular displacement of the Moon as observed from two different points on Earth.
Observational Data
The baseline used for observations was 4746 km, and the initial angles measured were:
- Angle 1: 50°
- Angle 2: 80°
These angles resulted in:
- Trigonometric Distance: 4673.90 km
- Parallax Distance: 17712.31 km
To match the officially accepted lunar distance of 384,000 km:
- Parallax Method Required Angles:
- Angle 1: 5.82°
- Angle 2: 4.40°
- Trigonometric Method Required Angles:
- Angle 1: 90.35°
- Angle 2: 88.94°
Results and Analysis
The disparity between the angles used in real observations and those required to accurately reflect the Moon’s distance illustrates the infeasibility of these methods for precise measurements. The trigonometric method, in particular, requires near-perpendicular angles relative to the baseline, which are impractical to achieve consistently with accuracy.
Conclusion
The findings confirm that conventional trigonometric and parallax methods, while theoretically valid, are impractical for precise lunar distance measurements due to the extreme sensitivity to angle accuracy. Instead, modern methods such as laser ranging and radar, which do not rely on such precise angle measurements, are necessary to achieve reliable and accurate celestial distance determinations.
Recommendations
Further research should focus on enhancing the precision of angle-measurement instruments if these methods are to be used in practical scenarios, or alternatively, prioritize the development and application of more reliable distance-measurement technologies.