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There is a bunch of junk orbiting right outside the atmosphere of the Earth, an issue that gets addressed more and more as space travel develops. How do they monitor the movement of these to avoid so many possible risks of collisions before launches, and how does it not interfere with the very precise satellite projects like Starlink, or even worse, the ISS?

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How do they monitor the movement of these[...]

Sensors a.k.a. radar (for LEO): the US Air - now Space - Force dedicated old Ballistic Missiles Defence Systems for Space Survaillance. This radars are tracking as much objects passing above as possible.

[...] to avoid so many possible risks of collisions [...]

To make it a bit simple: this measurements are put into a big computer. This computer tries to match the measurements with knows objects and than improoves the objects orbit data. After that, the orbits are prpagated into the furture and cross checked with orbits of functional satellites.

before launches,

an estimated early phase trajectory is used to check vs other objects, but in the end you have to take some risk.

and how does it not interfere with the very precise satellite projects like Starlink, or even worse, the ISS?

It does actually,... the ISS is doing risk mitigation maneuvers every couple of months. And even Star Link has engines and a risk mitigation system. (not evaluating if electrical engines are good for CA-purposes)

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