[fugyk]

What is the benefit of having time period larger than geosynchronous satellite? I see quite some satellite like that, e.g. OPS 6638 which has a time period of 6,701.8 minutes. I can think of no benefit of it, and on the downside it will require stronger rocket and provide low visibility.

[InclinedPlane]

There are some reasons for science spacecraft to be in high orbits but most of what you see is decommissioned comsats in graveyard orbits, which are supersynchronous. This is because such orbits have the least chance of decaying or of colliding with other satellites and creating a debris problem.