The first three rungs of the cosmological distance ladder

It is straightforward to determine the size of the Earth and the distance to the Moon without using a telescope. The methods have been known since the third century BCE. However, few astronomers have done this measurement from data they have taken. We use a gnomon to determine the latitude and longitude of South Bend, Indiana, and College Station, Texas, and determine the value of the radius of the Earth to be $Rearth=6290$ km, only 1.4% smaller than the known value. We use the method of Aristarchus and the size of the Earth’s shadow during the lunar eclipse of June 15, 2011 to estimate the distance to the Moon to be $62.3Rearth$⁠, 3.3% greater than the known 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. We use simultaneous observations of asteroid 1996 HW1 obtained with small telescopes in Socorro, New Mexico, and Ojai, California, to obtain a value of the Astronomical Unit of (⁠$1.59±0.19)×108$ km, about 6% too large. The data and methods presented here can easily become part of an introductory astronomy laboratory class.