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If you are in radio/laser communication with a base at a known location, it is pretty easy to work out the distance to that point by the round-trip time of signals, and your velocity by the Doppler shift of the signals.If you are approaching a planet fairly closely, it is possible to work out your distance and velocity using radar.Within the Solar system, it is possible to triangulate from the (known) positions of the planets.When traveling to Proxima Centauri, it is possible to triangulate from the (known) positions of nearby stars.There is always "dead reckoning" - record how fast you accelerated, in which direction, and for how long; from this you can calculate your position and velocity. But it's wise to cross-check with some of the other methods, because any errors that creep into dead reckoning tend to build up over time.
Time dilation might invalidate your dead reckoning.
Flying in deep space is even easier! All you need do is calculate where your target is going to be by the time you get there, allow for or avoid any significant gravitational fields en route (you can see them - they have bloody great stars in the middle!) and just point yourself in the calculated direction. No wind, no competing traffic, etc.
I strongly disagree. You're dismissing the very important fact that various things can affect the course of an objects trajectory. Such discrepancies are referred to as perturbations. For example; the presence of the planet Neptune was deduced from the perturbations caused by Uranus.
Radiation pressure can have a considerable effect on large area/mass satellites. One such example was the satellite Echo.
If you'd like I can look more deeply into this and get back to you. Don't forget that one way to navigate in deep space is by the stars!