Another great question about about one of the incredible acheivments engineers, astronomers, and physicists have managed – while our politicians have been shoving their heads deeper up their asses.

Your answer is here:
https://timeandnavigation.si.edu/navigating-space/deep-space

And here:
https://m.youtube.com/watch?v=61ZV6IsqnwQ

Basically, as @zenvelo points out below, it involves triangulation similar to that used for 4 centuries by earth explorers at sea. But for missions far into deep space and beyond earth based telemetry NASA scientists are already developing technology that will allow future spacecraft to find theur way independently.

How does a ship out in the middle of the Pacific navigate? By triangulating its location relative to known locations.

The same is true for space travel, just a bit more complicated equation. But a spaceship would know where it is relative to known objects, and wouldcalculate based on those objects.

And how does the spacecraft brake, when it reached its destination?

^^^^^ @rebbel Retro Rockets

The JWT will be slowed down by the pull of gravity from the sun and the earth. Once it reaches the Lagrangian point it will stop. The analogy is reaching the top of a hill by pedalling a bicycle vigorously only at the very beginning of the climb, generating enough energy and speed to spend most of the way coasting up the hill so as to slow to a stop and barely arrive at the top.

Thanks, guys!

@flutherother If gravity slows the craft, what is to stop it from falling back into the sun?
At some point it will have to turn into it’s orbit around the sun, at the same orbit speed as to match that of Earth so it can maintain it’s distance from Earth of one million miles.

Thanks a lot guys…. I think I get the basic idea of how it all works… Btw, a bit early but Happy New Year anyway.

@kritiper The Lagrangian points aren’t fixed in space. L2 where the JWT will be placed orbits the sun in step with the Earth. It is a place where the gravitational forces and the orbital motion of the telescope are balanced. It is like earth orbit only two large masses are involved, the sun and the Earth.

@flutherother I thought I said that.
Also, I don’t know what a Lagrangian point is, and I don’t think anyone else here knows what it is either. It’s not in my 2012 ed. of Merriam-Webster’s Collegiate Dictionary, so please define for us, if you will.

Lagrange point, after the guy who discovered them (after someone else found them first, I should add).
Look up James Webb and you’ll find articles and videos that also explain Lagrange points.
Although, in big lines, @flutherother did that too in his last post.
Simply put, there seems to be no gravity (due to two big bodies being at such a distance separated from each other that both their gravitational pull balance each other out), or something to that effect.

Well, I have watched too many videos on jwst… I know what Lagrange points are sort of but just didn’t know how a spacecraft would reach there without some sort or map. For me, It’s like driving down the long road in a desert, and you don’t know where to stop since there nothing there that identifies as a stop point.

One of the answers tells that the spacecraft would slow down and eventually stop when it has reached the L2 point since there’s no gravitation pull there. And the other answer says using triangulation. I’m guessing it calculates it’s location by using nearby stars ..

@Sam4One I was referring to @kritiper, about the Lagrange points.

I will search a bit more on how they finally park it at L2.