The First Three Rungs of the Cosmological Distance Ladder

TL;DR

This paper demonstrates how amateur astronomers can determine fundamental astronomical distances and Earth's size using simple, historical methods and small telescopes, providing educational value and practical insights.

Contribution

It applies classical astronomical techniques to real data, estimating Earth's radius, lunar distance, and the astronomical unit with accessible methods and small instruments.

Findings

Earth's radius estimated at 6290 km, 1.4% below true value.

Lunar distance estimated at 62.3 Earth radii, 3.3% above true value.

Astronomical unit estimated at 1.59 x 10^8 km, 6% above true value.

Abstract

It is straightforward to determine the size of the Earth and the distance to the Moon without making use of a telescope. The methods have been known since the 3rd century BC. However, few amateur or professional astronomers have worked this out from data they themselves have taken. Here we use a gnomon to determine the latitude and longitude of South Bend, Indiana, and College Station, Texas, and determine a value of the radius of the Earth of 6290 km, only 1.4 percent smaller than the true value. We use the method of Aristarchus and the size of the Earth's shadow during the lunar eclipse of 2011 June 15 to derive an estimate of the distance to the Moon (62.3 R_Earth), some 3.3 percent greater than the true mean value. We use measurements of the angular motion of the Moon against the background stars over the course of two nights, using a simple cross staff device, to estimate the Moon's distance at perigee and apogee. Finally, we use simultaneous CCD observations of asteroid 1996 HW1 obtained with small telescopes in Socorro, New Mexico, and Ojai, California, to derive a value of the Astronomical Unit of (1.59 +/- 0.19) X 10^8 km, about 6 percent too large. The data and methods presented here can easily become part of a beginning astronomy lab class.