Quantum Effects on all Lagrangian Points and Prospects to Measure Them in the Earth-Moon System

TL;DR

This paper investigates tiny quantum corrections to the Earth-Moon system's Lagrangian points, explores their measurable effects via laser ranging, and discusses the existence of displaced solar sail orbits due to these quantum effects.

Contribution

It provides the first detailed analysis of quantum corrections to Lagrangian points and their potential measurability in the Earth-Moon system, including effects on solar sail orbits.

Findings

Quantum corrections cause millimeter-level shifts in Lagrangian points.

Quantum effects modify the algebraic equations governing libration points.

Displaced periodic solar sail orbits exist due to quantum corrections.

Abstract

The one-loop long distance quantum corrections to the Newtonian potential imply tiny but observable effects in the restricted three-body problem of celestial mechanics, i.e., both at the Lagrangian points of stable equilibrium and at those of unstable equilibrium the Newtonian values of planetoid's coordinates are changed by a few millimetres in the Earth-Moon system. First, we find that the equations governing the position of both noncollinear and collinear quantum libration points are algebraic fifth degree and ninth degree equations, respectively. Second, we discuss the prospects to measure, with the help of laser ranging, the above departure from the equilateral triangle picture, which is a challenging task. On the other hand, a modern version of the planetoid is the solar sail, and much progress has been made, in recent years, on the displaced periodic orbits of solar sails at all libration points. By taking into account the quantum corrections to the Newtonian potential, displaced periodic orbits of the solar sail at libration points are again found to exist.