# How to test the equivalence principle in space? The Microscope mission

The goal of the Microscope mission is to test the equivalence principle to a precision two orders of magnitude better than is achieved on ground, more precisely 10-15 or one part in 1 000 000 000 000 000.

Members of the mission like to say that this is the difference of weight of a 500 000 ton tanker when a 0.5 milligram drosophilia fly lands on the deck. In order to do so, one needs to compare the free
fall of two objects of different composition (see why here). But the two objects must feel exactly the same gravitational field, and thus be placed at the same point in space. In the Microscope set up, they are two coaxial cylinders of different material – one is made of titanium and the other one of a platinum-rhodium alloy- which have coinciding centers of mass (as shown on the figure to the right). As a matter of fact, the Microscope mission has two devices (see on the left): one with two cylinders of the same material, and one with cylinders of different materials. This allows to make sure that any effect observed with the two different cylinders is not observed with the two identical cylinders!

Actually, the cylinders are not in strictly free fall. Remember that an object in orbit keeps falling, with horizontal velocity. The satellite, and the two coaxial cylinders, are in orbit but they have slightly different motions: the satellite is submitted to non-gravitational perturbations (inducing friction or drag) which are compensated by micro-thrusters. And, in case the equivalence principle is violated, the two cylindrical masses should have tiny differences of motion. In the Microscope experiment, they are forced to follow the same motion at the center of the satellite by applying on them electrostatic forces, or if you prefer external acceleration on them. If the applied accelerations need to be different on the two masses, this means their natural motion is different: there is a violation of the equivalence principle. In other words, different accelerations on the two cylindrical masses mean different gravitational motions. Another beautiful illustration of the equivalence between acceleration and gravitational field!

It is very important to make sure that the effect observed must be attributed to a violation of the equivalence principle, and not to the set up malfunctioning. In order to do so, the physicists have a clever way of modulating the signal, that is of making the potential violation signal vary with time at a given frequency. Here is the trick. The satellite is following a quasi-circular orbit at an altitude of 710 km. The axis of the cylinders is pointing in a direction fixed with respect to the distant stars, and the acceleration measurement is made along this axis. As you can see in the figure above, there are positions along the orbit where the gravitational attraction is perpendicular to this axis, and thus not active along this axis. There are other positions where it is parallel or antiparallel, and thus the effect is maximal. In this way, one modulates the effect at a known frequency which is directly related to the frequency of rotation along the orbit. Any effect of violation of the principle of equivalence must have such a modulation. In order to further check the results, the physicists of Microscope have decided also to spin the satellite around the axis perpendicular to the orbital plane with a period of 1000 seconds. In this way, they introduce a further modulation of the signal.

If you want to watch the launch of the Microscope mission from Kourou, see here.

### 4 Comments

• Alan H Douglas VMD

Elegant experiment! Thanks for bringing us along on another exciting science voyage.

• Dan To

I second Alan’s comment. These “more to explore” additions to the classes are fun and enlightening.

• Alan H Douglas VMD

Thanks, Dan, the Prof offered us the.MOOC that keeps on giving. So glad that I joined!

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