GEOPOTENTIAL SURFACE CORRECTIONS TO LARGE-APERTURE LIQUID MIRROR TELESCOPES

An exact derivation of the formula for the shape of a liquid mirror on the surface of the Earth is shown to contain a parabolic term that ar ises from the effects of curvature of the Earth's gravitational equipo tential surface. The term is independent of the angular rare of rotati on of the liquid mirror container and has as its consequence an extens ion of the focal length of the mirror beyond that expressed by the cla ssical formula. An expansion up to terms of order rho(5), where rho is the distance from the axis of rotation, is shown to contain only term s whose relative magnitude is rho(2)/4R(c)ircle plus(2), where R(circl e plus) is the radius of the Earth. Our results demonstrate that, even when geopotential curvature effects are considered, liquid mirrors ar e excellent paraboloids.