Anything’s possible but the mass of the satellite won’t cease to be something they need to optimize, even with a heavier booster. Those little satellites use thrusters themselves when they’re in orbit.
Since Starship itself is made of steel, it seems possible that the satellites could be as well.
Assuming it's overall heavier, you have to carry more fuel, and then the rocket equation kicks in and you have to carry more fuel than that. That's all extra weight that makes your launch more expensive. But if your cost to launch is $30/lb instead of $1200/lb, you've got the budget for it.
But it's not just the cost of the launch, its also going to be the cost of the satellite itself.
More mass means you need larger reaction wheels (or CMGs) to control the attitude of the spacecraft, larger reaction wheels means you need more power to control those reaction wheels, more power means you need more solar arrays/batteries, more solar arrays means more mass and moment of inertia...which means you need larger reaction wheels and on and on and on.
Often people talk about the "tyranny of the rocket equation" but many other things on a satellite are the "tyranny of other non-linear systems"
You can end up seeing that in companies like K2 Space. Their goal is to take advantage of cheaper launch costs with large, cheap satellites. But if you read in the article [0] they had to do things like develop new reaction wheels in house because "there was not a suitable supply chain for spacecraft bus like Mega Class". Starting from scratch on mechanisms like that for space is not super cheap.
These are good points, but I still think it's technically feasible to make non-aluminum satellites, and reasonably economical even if it costs somewhat more. If the only alternatives are giving up on large satellite networks or destroying the ozone layer, then switching away from aluminum seems like the way to go.
I'm not claiming steel is the best option though. Other metals, or even non-metal materials as mentioned in other comments might be better.
I don't think needing new components is really a downside except in the very short term. With much cheaper launch at much higher volume, we're going to be doing a lot of that anyway. We're going to have all sorts of new applications that weren't economically feasible before.
True, it's definitely feasible to make non-aluminum satellites. I do tend to go get up on my systems engineering soap box when people just talk about launch cost as it's a conversation I have too frequently in my job as well.
The mass consideration has certainly changed things in general. One of the things we have seen is a shift from aluminum honeycomb panels to just machined aluminum plates which weigh more for the same stiffness but are easier and faster to manufacture.
Steel might also drive more spacecraft to have to do a controlled re-entry (something the Starlink satellites are not currently designed for) as with the higher melting point and more mass it is more likely to survive re-entry. Although it does have a lower specific heat capacity than aluminum so I'm not quite sure on that one but usually the things I have seen that we expect to survive re-entry are titanium tanks and large glass mirrors. They also have the benefit of being in the center so there is a bit of an ablative shield.
There's a lot of really smart people that understand chemistry at a much better level than the typical reader on an internet forum. Do we really need to "guess"? Seems like we could study this to actually determine what would happen with controlled experiments. One might go so far as to call that the scientific method.
There are some oddities here. The least interesting is that drag is not the only reason satellites station keep and I can't imagine why you'd say it is. The weirdest is that we're actually having an argument about whether satellite mass continues to matter once the satellite is in orbit.
More interestingly, the majority (perhaps not yet "vast majority" [0]) of active satellites right now are Starlink satellites. Those things actually maneuver all the time in the interest of collision avoidance, and the rate at which they maneuver is predicted to increases as the number of satellites increase for obvious reasons. [1]
