[Paper Review] Sunsets, tall buildings and the Earth's radius

P. K. Aravind|ArXiv.org|Dec 20, 2008

Historical Geography and Cartography3 references3 citations

TL;DR

This paper presents a method to determine the Earth's radius using repeated observations of the sunset from different heights on a tall building, leveraging the time delay between sunsets at various elevations. It also shows how these observations can estimate atmospheric refraction at the horizon at certain latitudes.

ABSTRACT

It is shown how repeated observations of the sunset from various points up a tall building can be used to determine the Earth's radius. The same observations can also be used, at some latitudes, to deduce an approximate value for the amount of atmospheric refraction at the horizon.

Motivation & Objective

• To develop a practical, classroom-friendly method for estimating the Earth's radius using observable phenomena.
• To address the challenge of measuring Earth's curvature with accessible tools and minimal equipment.
• To explore the role of atmospheric refraction in sunset observations and its quantifiable impact.
• To provide a pedagogical tool for teaching geometric and observational principles in physics education.

Proposed method

• Observing the sunset from multiple elevations on a tall building to measure time differences between successive sunsets.
• Using the time delay between sunsets at different heights to calculate the Earth's radius via geometric reasoning.
• Applying trigonometric relationships between height, angular displacement, and Earth's curvature.
• Incorporating atmospheric refraction effects by comparing observed sunset times with theoretical predictions.
• Using latitude-dependent corrections to estimate the amount of refraction at the horizon.
• Validating results through theoretical modeling and comparison with known values of Earth's radius and refraction.

Experimental results

Research questions

• RQ1 Can the Earth's radius be estimated using only repeated sunset observations from varying heights on a tall building?
• RQ2 How does atmospheric refraction influence the observed timing of sunsets at different elevations?
• RQ3 What is the relationship between height above ground and the time delay between successive sunsets?
• RQ4 At which latitudes can this method also yield an estimate of atmospheric refraction?
• RQ5 How accurate is this method compared to standard geodetic measurements?

Key findings

• The method enables a reliable estimation of the Earth's radius using only a stopwatch and observations from a tall building.
• Time delays between sunsets at different elevations are proportional to the square of the height, consistent with spherical Earth geometry.
• The observed time differences align with theoretical predictions when Earth's radius is approximately 6,370 km.
• At certain latitudes, the same data can be used to estimate atmospheric refraction at the horizon, yielding values consistent with known atmospheric models.
• The technique is robust and suitable for educational demonstrations in physics and earth science classrooms.
• Corrections for atmospheric refraction improve the accuracy of the Earth radius estimate, especially at low elevations.