The Gallileo GNSS satellites numbers 5 and 6 have been used to make a record-breaking precision measurement of gravitational time dilation as a bi-product of them being in the wrong orbit. See (just for example) Space.com's Einstein's 'Time Dilation' Gets Pinpoint Measure Thanks to Wayward Satellites or [this synopsis](https://physics.aps.org/synopsis-for/10.1103/PhysRevLett.121.231102] or these two back-to-back Phys Rev Letters:
- Test of the Gravitational Redshift with Galileo Satellites in an Eccentric Orbi
- Gravitational Redshift Test Using Eccentric Galileo Satellites
What's discussed here is not the special relativity effect of going fast so "clocks slow down", it's the much smaller effect of being in a deeper gravitational well, so "clocks slow down".
You can see where I've worked out the magnitude of the two effects to first order for Parker Solar Probe in this answer.
But my question is not about this result. Instead it's about the statements in the Space.com article:
The Soyuz delivered the satellites to incorrect orbits, which were too elliptical for Galileo 5 and 6 to do sat-nav work. (During the close-approach phase of these orbits, the spacecraft were unable to keep the entire Earth in view, which they needed to do to "center" their signal beams.)
The satellites' handlers managed to raise and circularize the pair's orbits over time. But the paths of Galileo 5 and 6 are still elliptical; both satellites climb and fall about 5,280 miles (8,500 km) twice per day, European Space Agency (ESA) officials said.
This characteristic isn't great for navigation work; Galileo team members are still evaluating whether the two satellites can join the proper constellation. But the situation is tailor-made for a time-dilation measurement, especially since Galileo 5 and 6 both have precise atomic clocks of their own, which remain stable to within 1 second every 3 million years.
While the rest of the Galileo satellites have a revs-per-day of 17/10 sidereal days (or ~1.705 24-hour days), satellites number 5 and 6 (
B have a higher revs per day (lower orbit) in addition to the remaining eccentricity and inclination status.
Right now with a different period than the rest of the constellation, they are not much practical good for GNSS. But if the orbit could be raised a bit, they could take their place in the Galileo constellation, albeit in a sort-of wobbly way.
If the orbits could be raised, could they still contribute to Galileo, or would the eccentricity need to be reduced further and/or the inclination adjusted? Roughly how much delta-v would be needed for each of these three corrections?