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What long range forces? Almost all probes that go a long way away can (and are) used to test general relativity.

The energy levels needed to brute force more interesting physics is quite possibly beyond being achievable by humanity.

I don't know enough Quantum Field Theory to calculate it on the spot but I have read that to detect any gravitons at all we would need a planet sized detector orbiting closely around a black hole

> obscenely high power experiments

Like the energy released when 2 black holes collide? We're going to need a bigger capacitor.

What would you want studied with that satellite? Which forces?

afaik gravity is pretty well studied by predicting the planets

Gravity is poorly tested at the smallest scales: https://arxiv.org/pdf/1408.3588.pdf . Perhaps space based experiments could help. I also think astronomy would greatly improve.