Determining the instantaneous distance to the moon by direct triangulation

Abstract

Details of a method for obtaining the instantaneous distance from the earth to the moon to within 5% by direct triangulation are described. Line of sight unit vectors are calculated based on azimuth and zenith angle measurements of the moon made simultaneously with ordinary surveying theodolites from two known points on the surface of the earth. These unit vectors and the baseline distance between the two observation points, typically several thousand kilometres apart, are used to compute the earth–moon distance. Recommendations for college and high school physics classes are included.

An experiment to measure the instantaneous distance to the Moon

“…Past work required the use of lunar and solar eclipses to perform low-precision measurements of the distance to the Moon. [7][8][9][10] Lough 11 determined this distance by measuring the horizontal coordinates of the Moon at two points on the Earth's surface using theodolites, while Cenadelli 12 set up an international campaign to image the Moon from Italy and South Africa and derive its parallax. Their results agree with those of more precise methods to within a few percent.…”

“…Their results agree with those of more precise methods to within a few percent. The experiments of Lough 11 and Cenadelli 12 have the advantage of a simple theoretical framework, but their drawback is that a large effort must be exerted to coordinate observations at two locations on Earth.…”