I've only read this doc quickly [1]. I would have guessed a lead case of a particular thickness would do the trick. But I don't know the thickness needed, maybe too much?
In theory you could just cover everything in lead and call it a day, IF, lead wouldn't also be one of the heaviest metals in the world, which kinda goes against the mantra of space travel.
Actually it doesn’t work that way (solely based on mass). Radiation doesn’t just get stopped by lead, it generates secondary particles. Lead happens to be effective against x-rays, which is why we tend to think of “lead shielding” but it’s not effective against all types of radiation. So it would help but you couldn’t just call it a day, and other materials are more mass efficient.
seriously, that's something I haven't thought much about. when designing rovers, do they calculate solely on the weight of what it will be on the destination, or limit it to weight limits of escaping earth's gravity well?
Rover designer here. The weight at the destination is important to characterize performance but it’s not a big driver of design. For example, once you consider losses due to friction inside gearboxes, there’s no big difference to size a motor. You want to be able to test on Earth easily anyway, so you wouldn’t design without a margin to allow that. I suppose if you designed a rover for Uranus you might take a different approach.
Launch mass is important as a constraint, but the launch environment is the main design driver for mass. The rover must be much stiffer than the rocket to not “couple” it’s response. The first vibration mode (think tuning fork) of a rocket is about 20Hz so the spacecraft inside needs a first vibration mode higher than 40Hz. Something inside the spacecraft similarly needs a first vibration mode higher than 60Hz or 80Hz, although you can make exceptions based on analysis.
But that’s not all, the sustained load on components during launch can easily be 10 to 30 times gravity (30G) and the instantaneous load can be 100G. You can’t just add material for these kinds of loads, it would be an endless feedback loop because adding mass decreases stiffness. Look closely and you’ll see that every deployable or movable part of the rover is locked down by a mechanism until it has landed.
It's not just the mechanical weight at the destination and the work required to escape earth's gravity (which is enormous). Mass of the rover also means more fuel to speed up and slow down if there is any delta-V changes en-route, the heat energy that needs to be dissipated during re-entry, the forces on parachute and lander as well. So really, that mass penalty gets paid over and over... and not often linearly.
[1] https://nepp.nasa.gov/files/25295/MRS04_LaBel.pdf