Hi, didn’t expect to see you here.

Let’s look at static differences first.
Absolute gravitational potential itself is impossible to measure, since all frames of reference act the same. But we can easily measure differences of potential using accurate clocks. This works well on the surface of earth in reference to outer space for example.
When measuring underground, we can also measure the accceleration along the path when walking there, since the acceleration is caused by the gradient in gravitational potential.
In practice though we would still use the clock method since we can measure time so much more accurately than acceleration.

Going into orbit though, we get another problem, namely we are no longer “still”. The idea of gravity itself is a neat model, but it’s still general relativity underneath which means effects of our movement and of “gravity” are always mixed. So you can put a clock in orbit, but have to very accurately know the exact orbit to make an absolute measurement.
In effect the gps satellites have done this, and we can see their rate of time and attribute it to their orbit vs. their location, often written special vs general relativistic effects.
This value is not very useful, since not only do we average over the entire orbit, we also don’t know the orbit precisely enough.

We can do better though, good enough to measure changes over time.
By building an even better optimized “clock”.
Regular clocks act kinda like gears. We have a mechanism that oscillates at a very stable high frequency, and then “gear” a mechanism to match it, but at a lower frequency, until we get to something we can measure with regular electronics. At that point, we get averages of many oscillations. We then have to send them on to a different clock, since we have nothing to measure our ticks against, for us they are evenly spaced. That receiver has to catch the very high bandwidth signal of billions of clock ticks, and compare it to a second clock.
Any anomaly of the signal path will look like a shift in time, a change in gravitational potential difference of the two clocks. Worse, atomic clocks are designed mainly for long-term accuracy, so they tend to have shifts in rates over shorter timeframes. Thus, instead we strip stuff to the bare minimum, and do our own clock with blackjack and hookers and without the whole clock part where it measured time.

Einstein had a few Gedankenexperiments that still show up in lessons on relativity because they are good. One common object is a laser clock. You bounce a laser between plates, and the rate of bouncing changes according to the local rate of time. This turns out to make a pretty shitty clock, but lets you do optics on the output making for a really good comparison between two different clocks, via interferometry.

Since you need to measure two locations anyway to get the time difference, you can send out two beams of the same source, thus matching exactly, and align them on the return, making their path lengths precisely equal. On average.
If you do this well enough, you can see temporary changes to this, as fast as you can measure the beam interferences, since those beams are in effect comparing at extremely high frequency.

You can now dump this instrument in orbit, and measure the changes along the orbital path, forming a high detail map of earths gravitational differences from the ideal. Or you can put it on earths surface or in outer space and wait for abrupt changes of gravity bumping into you.

Because ofc moving masses “update” the gravitational potential field, and if those updates happen quickly enough we can measure the change with our very precise change detector differential clocks, while the absolute difference might be too small to see on regular clocks, or affect all clocks equally due to great distance of the source, or the subsequent waves may cancel the change, averaging to 0.

Or would it not be possible because the sensor itself would interfere with the readings?

For one all the setups we have so far want to be extremely still, a single piece at rest. Not to prevent gravitational waves or even permanent changes in potential, but to prevent mechanical vibrations.
The equipemnt is extremely light as gravitational masses go though. When you go up in scale, mass changds with volume, with the cube, but strength of gravity, of the gradient, with the square of distance. So when comparing a small interferometer sitting on a 1m satellite, its effects are a million times weaker than earth, with a diameter on the order of millions of meters. Actually far less, since the satellite isn’t a solid ball of dense material.

If you wanted to you could probably spin up a large barbell shape in space right next to a gravitational wave detector and not annoy the scientists from vibrations but from the waves. Probably. Take care it’s in shadow, otherwise the changes in light reflection onto the satellite would probably overshaddow your waves.

I’d do it the same way as the GRACE satellites do, though maybe there is a better way. https://en.m.wikipedia.org/wiki/GRACE_and_GRACE-FO

LIGO… in space?

https://youtu.be/degD69wnZcY?

LISA…Laser Interferometer Space Antenna.