09 Dec 2020

Bad launch leads to real world relativistic math

A Galileo launch went awry and the satellite entered an elliptic orbit rather than a circular one. Which led to everyone encountering some real world relativistic math:

Time runs slower in a gravitational field. If an orbit is ever so slightly eccentric, the satellite spends half of the orbit in a slightly stronger gravitational field than in the other half of the orbit. Or put another way, during a full orbit, the clock will first run slightly ‘ahead’ of where it needs to be and in the second half it will drop behind by the exact same amount. Averaged out over a whole orbit, the clock speed is not impacted by the eccentricity. But during the orbit, it is.

I can't pretend to understand a 10th of the math described here, but this is an excellent write up.

Incidentally, the launch of multiple very precise atomic clocks in these eccentric orbits did enable some very good science. Using the data from E14 and E18 it was possible to determine the accuracy of one prediction of Einstein’s theory of General Relativity by a factor of four beyond what has been achieved previously.