>>12871021MarsNet would be wholly independent of EarthNet. LunaNet would eventually become its own thing too.
For the next 50-100 years or so, I imagine we'll get by with light lag from Earth to Mars or Moon to Mars. But eventually, once production in space becomes cheap, I can totally see space telecoms yeeting comm bouys every light minute between planetary bodies with major infrastructures.
As far as internet on Mars goes, the Red Planet would likely get 3rd or 4th Gen Starlink satellites. Elon in a tweet has mentioned in the past, I think, that Gen2 Starlink Satellites will be capable of 300Gbps per satellite up/down (combined). Gen1 is 60Gbps. So Gen3 or Gen4 could theoretically mean ~1Tbps per satellite. Mars is roughly 53% the size of the Earth. Also, most settlements on Mars will likely take place along the equator or N/S meridian lines. This is to maximize sunlight capture until NASA's KiloPower or better power systems are brought online to supplant existing energy generation infrastructure (besides solar and maybe wind). I think it takes roughly 240 Starlink satellites to wrap around the Earth once. So, at 53%, you'd need probably 120-150, I'd bank on 150 for redundancy.
A single Cargo ship would be able to deposit 400 Starlink satellites into Mars orbit. I assume that SpaceX will go with a middle Mars orbit rather than low Mars orbit in order to extend satellite lifespan from 5 years to 7 years and then when they're EOL, they'll use most of their fuel to yeet the satellites out into deep space rather than burning them up in Martian atmosphere (since there's barely enough to matter) and you don't want to litter the Martian surface with dead satellites. Higher orbit will likely mean slightly greater latency; rather than say 15-30ms, Martians may experience 30-40ms instead. Any human presence on Martian surface will likely get dedicated 1Gbps up/down links be it rover, drone, truck, car, or base. Science potential will be staggering.