A proposed mathematical model of thermal variations on the HartRAO Lunar Laser Ranging telescope for enhanced test of Earth-Moon system dynamics

Abstract

A new geodetic observatory at Matjiesfontein will house a 1-metre aperture Lunar Laser Ranging (LLR) optical telescope to acquire millimetre Earth-Moon distance measurements. Large optical telescopes utilised for laser ranging observations of Earth-Moon distance, with sub-centimetre level accuracy can suffer from structural deformations induced by thermal variations, wind loadings and/or gravitational forces. These variables need to be measured to enable correction of the resulting pointing errors. This paper presents the proposed locations of temperature sensors on the composite structure of the Hartebeesthoek Radio Astronomy Observatory (HartRAO) LLR 1-metre optical telescope. Furthermore, we describe a mathematical model for (i) obtaining thermal measurements from a network of temperature sensors, (ii) interpolating the temperatures across the telescope composite structure, and (iii) predicting thermally-induced structural deformations. Currently, the available thermal simulation results of the LLR telescope tube assembly indicate isotherms with gradients of about 1°C followed by thermal deformations that vary between 2.9 μm and 40.7 μm along the optical tube axes. The physical implementation of the above mathematical model is part of the next phase of this research work coupled with experiments to derive thermally-induced pointing errors. The errors will be incorporated into the steering control software to compensate for thermally-induced misalignment of the telescope axes.