Testing the Strong Equivalence Principle with spacecraft ranging towards the nearby Lagrangian points

Abstract

General relativity is supported by great experimental evidence. Yet there is a lot of interest in precisely setting its limits with on going and future experiments. A question to answer is about the validity of the Strong Equivalence Principle. Ground experiments and Lunar Laser Ranging have provided the best upper limit on the Nordtvedt parameter $\sigma [\eta ]=4.4\times 10^{-4}$. With the future planetary mission BepiColombo, this parameter will be further improved by at least an order of magnitude. In this paper we envisage yet another possible testing environment with spacecraft ranging towards the nearby Sun-Earth collinear Lagrangian points. Neglecting errors in planetary masses and ephemerides, we forecast $\sigma [\eta ]=6.4(2.0)\times 10^{-4}$ (5 yr integration time) via ranging towards $L_1$ in a realistic (optimistic) scenario depending on current (future) range capabilities and knowledge of the Earth's ephemerides. A combined measurement, $L_1$+$L_2$, gives instead $4.8(1.7)\times 10^{-4}$. In the optimistic scenario a single measurement of one year would be enough to reach $\approx 3\times 10^{-4}$. All figures are comparable with Lunar Laser Ranging, but worse than BepiColombo. Performances could be much improved if data were integrated over time and over the number of satellites flying around either of the two Lagrangian points. We point out that some systematics (gravitational perturbations of other planets or figure effects) are much more in control compared to other experiments. We do not advocate a specific mission to constrain the Strong Equivalence Principle, but we do suggest analysing ranging data of present and future spacecrafts flying around $L_1$/$L_2$ (one key mission is, for instance, LISA Pathfinder). This spacecraft ranging would be a new and complementary probe to constrain the Strong Equivalence Principle in space.

8 pages, 2 figures, 2 tables

References in corpus (8)

• The Confrontation between General Relativity and Experiment
• Testing Einstein's Equivalence Principle with Fast Radio Bursts
• Constraints on frequency-dependent violations of Shapiro delay from GW150914
• Space-based tests of gravity with laser ranging
• On Testing the Equivalence Principle with Extragalactic Bursts
• Measuring test mass acceleration noise in space-based gravitational wave astronomy
• Historical Reflections on the Work of IAU Commission 4 (Ephemerides)
• Derivative of the light frequency shift as a measure of spacetime curvature for gravitational wave detection

Cited by in corpus (4)

• First search for ultralight dark matter with a space-based gravitational-wave antenna: LISA Pathfinder
• Constraining the Nordtvedt parameter with the BepiColombo Radioscience experiment
• Detection principle of gravitational wave detectors
• Space tests of the strong equivalence principle: BepiColombo and the Sun-Earth Lagrangian points opportunity