Detected by the radial velocity method, measuring the parent star being pulled toward and away from us by a variation of at little as 2-3 meters per second! It always blows my mind that we can measure that.
Something else I read about, that doesn't sound like it involves far out voodoo tech to me, that I wish I'd live long enough to see, is putting a probe out far enough and in the right position, to use the Sun's gravity as a telescope lens.
...and (maybe) actually get pictures of extrasolar planets.
I don't know if those pictures would be like Hubble's view of Pluto, or in principle could be much better.
If I could have one wish for something extraterrestrial, that is more achievable, it would be close up pictures of Haumea. Eris and others too, but Haumea most of all.
I care nothing at all for Mars colonies, but the most exciting thing about Starship for me is the hope that maybe combining it with in-orbit refueling could enable quicker travel to the outer solar system and loitering/orbiting instead of flying by at top speed.
One figure that stands out, the probe would need to be about 550 AU from the sun.
Voyager 1 is about 150 AU away from the sun right now, for comparison.
https://en.wikipedia.org/wiki/Interstellar_travel#Wait_calcu...