The distance between earth and mars varies between 150 and 2000 light seconds.
> throw tons of datacenter and compute that's anywhere more than a few light-seconds from the nearest existing datacenter
I think I'm misinterpreting the comment.
We wouldn't need to blanket the solar system in data centers to be able to communicate with other planets. We would only need enough connections so that no matter where in their respective orbits they are, there is a line of radio "sight" that is clear enough for high bandwidth communications to work.
I don't have access to the specifics, but I imagine something between 5 and 10 satellite data centers orbiting the sun in between earth and mars would be enough to maintain communications with minimum delay regardless of when in the solar year the comms take place.
Once you take into consideration the sun, plus the fact that the you'd need to cover the full disk to keep all data centers within a few minutes of another one in an unbroken chain back to both planets, I just don't get the math involved here.
But, I'm also terrible at both math and visualization, so I readily concede I may be missing something obvious.
The inner circle has Earth's orbit in it. The outer circle is Mar's orbit.
The middle circle would be a ring of relatively stationary satellites in between them.
And in the center of all 3 circles is the Sun, which will not allow radio signals to pass through.
I drew a crappy illustration to demonstrate: https://ibb.co/tP2rkzS0
When Mars and the Earth are on opposite sides of the sun, a satellite ring can transmit around the sun and keep the communication lines open.
Having a ring of relay satellites gives you a set distance to transmit from Mars. The satellites can then transmit their received data from the one that is closest to Mars to the one that is closest to Earth, which would then send the data to Earth.
This is helpful for a variety of reasons, but the most important one is that with this setup, even when the Sun is in between Earth and Mars, you could still send data around the sun.
Constant communication, no communications breakdowns. Even if 1 satellite failed for some reason, a bit of maneuvering would allow the others to backfill the gap until it could be repaired or replaced.
Even when Earth and Mars are close together, it would still be smart to use the relay so that the power levels are easily calculated and maintained.
There will be some lag as each satellite would need to cache the data before retransmitting, and it would need to store that data for a short period as well in case of failure, so assume that it would double the time for each stop under ideal locations, so to get information 4 light seconds away would take approx 8 seconds, and a minimum of 16 seconds for a response assuming they started replying the instant they received.