# Verification of the equivalence principle in orbit

## PTB provides test masses with sub-micrometer manufacturing tolerances for a space mission

PTBnews 2.2023
02.05.2023
Especially interesting for

fundamental research in physics

Using four test masses in the form of hollow cylinders from PTB, the space mission MICROSCOPE was able to verify the equivalence principle with unprecedented precision.

The test masses usually consist of a platinum-rhodium alloy. Only the outer test mass in the heterogeneous configuration was made of titanium.

Since the times of Galileo Galilei and Isaac Newton, the equivalence principle has been considered one of the fundamentals of physics. The definition of the weak equivalence principle states that only the mass of a body determines how a homogeneous gravitational field will act on it, regardless of the body's shape, the chemical elements it is composed of, or its location at any given time. Gravitational and inertial forces are therefore equivalent. Their effect cannot be experimentally differentiated. Even Albert Einstein considered this a possible basic principle of a theory of gravitation, and these considerations led him to the general theory of relativity.

Mathematically, the equivalence principle is represented by the Eötvös ratio η. With respect to two different masses, it describes the difference of their gravitational accelerations divided by their sum. If the equivalence principle is fulfilled, the result is η = 0. Even small deviations from this value would indicate a violation of the equivalence principle. In order to be able to detect or exclude such a violation, scientists have long been working to measure the Eötvös ratio with ever greater accuracy.

Initially, conventional mechanical (torsion) pendulums were used (Isaac Newton, Friedrich W. Bessel: η < 10−3, Loránd Eötvös: η < 10−9). During the Apollo missions, mirrors were placed on the moon to determine the Eötvös ratio using the photon propagation time on the Earth-Moon-Earth route (Irwin Shapiro: η < 10−12). The most accurate measurements to date, with η < 10–13, were carried out by a group led by the gravitational physicist Eric G. Adelberger.

To be able to determine an even lower upper limit for the Eötvös ratio, the space mission MICROSCOPE was initiated. Experiments with accelerometers were carried out on board a microsatellite from the Myriade series to measure the acceleration of test masses in the gravitational field of the Earth. A total of four test masses in the form of hollow cylinders were manufactured by the Scientific Instrumentation Department at PTB. By extensively enhancing the applied manufacturing and measurement methods, it was possible to achieve the sub-micrometer manufacturing tolerances needed to attain the required measurement accuracy.

In the so-called heterogeneous configuration, an accelerometer was equipped with two test masses made of dissimilar materials and used to verify the equivalence principle. Systematic and instrument-specific influences were eliminated by means of a second accelerometer that was fitted with two test masses of identical material (i.e., homogeneous configuration). In this way, it was possible to measure the upper limit of the Eötvös ratio with unprecedented precision: η < 1.5 · 10−15

### Contact

Daniel Hagedorn
Department 5.5, Scientific Instrumentation
Phone: +49 531 592-5540
daniel.hagedorn(at)ptb.de

### Scientific publication

P. Touboul, G. Metris, M. Rodrigues, D. Hagedorn, F. Löffler et. al.: MICROSCOPE Mission: Final results of the test of the equivalence principle. Physical Review Letters 129, 1–8 (2022)