Detecting the Memory Effect from a Massive Black Hole Merger at the Galactic Center through Lunar Ranging

Abstract

A gravitational wave pulse from a major merger of massive black holes at the Galactic center induces a permanent increase in the Earth–Moon separation. For black holes of mass ∼106 M ⊙, the shift in the local gravitational potential is comparable to the Earth–Moon potential, leading to the Moon being perturbed relative to the Earth during the passage of the pulse. The permanent increase in the Earth–Moon separation is a fraction of a millimeter, measurable by lunar ranging for future merger events.