the famous SpaceX/Starlink satellites have downlinks in the Ku-Band as shown in this band allocation below.
This is indeed the same band used for Direct-TV geostationary satellites and also QO-100 (there are also downlinks in the Ka-Band for the Gateway-Links, but this is not the scope here).
OH MY GOD - ITS FULL OF STARS
here you can find some Starlink Coverage Tracker:
Same minds, same thoughts...
So, why not using a simple LNB as we use for QO-100 and try to receive Starlink satellites instead. Just point the LNB in the Sky and use an SDR to check if you can see something in the waterfall spectrum with your favorite SDR software. Indeed you may see only part of the signal as it is high bandwidth, but there are also some telemetry beacons like on 11.325 GHz.
Starlink Downlinks are usually circular polarized (RHCP/LHCP), so your LNB's linear polarization (H/V) does not matter!
Here is a pretty nice article from Derek OK9SGC with full explanation and further links:
73s Peter DB2OS