Equilibrium and Stability of Orbiting Liquid Mirror Telescopes

Liquid mirror telescopes (LMTs) have recently been proposed as a potential alternative to rigid mirror telescopes, promising easier deployment and lower mass. Under microgravity (low Bond number) conditions, LMTs could exploit the natural formation of spherical liquid interfaces to achieve significantly large rapertures than rigid telescopes. However, the equilibrium and stability of large-scale liquid interfaces under orbital perturbations remain insufficiently characterized, leaving this microgravity precondition unconfirmed. This paper investigates the effects of key environmental factors on the shape of LMT surfaces by adopting NASA’s 50-m Fluidic Telescope (FLUTE) as a case study. A static equilibrium model is formulated and solved numerically under a range of external effects. Inertial acceleration thresholds are derived that (i) define the boundary of the capillary-dominated regime and (ii) indicate the onset of mirror deformations incompatible with optical requirements. Two candidates for reflective liquids, Galinstan and 1-ethyl-3-methylimidazolium ethylsulfate, are analyzed, with Galinstan exhibiting greater resistance to deformation. Results indicate that external perturbations lead to substantial deformations of the liquid interface, exceeding optical limits for visible light at apertures below one meter and at apertures of about 2.9 m for far IR (10−4 m). Although the thin-film dynamics of the telescope will likely mitigate these effects over long time scales, an active liquid control strategy is required to meet optical specifications and might be needed for initial formation of the interface.