NASA lands missions such as the Perseverance Mars Rover land at specific spots. I understand they can de-orbit to those spots to explore them, but the aerodynamic drag from the atmospheric re-entry would slow the craft and change its trajectory. So how do they calculate where the rover would land after entry?
So how do they calculate where the rover would land after entry?
By simulations, multiple simulations of various levels of fidelity. A very simple simulation can be built in a spreadsheet. While simple, spreadsheets do offer some nice search capabilities. This very simple simulation would use a very simple model of the atmosphere, a very simple model of the interaction (e.g. drag) between the spacecraft and the atmosphere, and a very simple model of Mars gravity. While very simple, this will give a fairly good idea of where to hit the atmosphere so as to arrive at the desired landing site.
This simplicity can and is changed to increasing complexity via a range of simulations. A three degree of freedom simulation (position only) might add better models of the atmosphere, the parachutes, and final descent. A six degree of freedom simulation (position and orientation) adds even more complexity and higher fidelity models, but is slower. A decent six DOF sim will certainly add randomness so that the landing ellipsoid can be estimated via Monte Carlo techniques.
The next step up is a flight software in the loop simulation. This kind of simulation uses the flight software (or a close replica thereof) to control the simulated vehicle. At this point, even more randomness can be added, and also simulated failures of various kinds.
One final step is a flight hardware in the loop simulation. This kind of simulation uses a flight computer (are a close replica thereof) running the as-coded flight software. Unfortunately, this final step results in a rather slow simulation because it has to be run at realtime, as opposed to several times faster than realtime. However, this final step is a very essential step.
