The correct answers are By next Tuesday, I will have been orbiting Earth for exactly one year. and By next Tuesday, I'll have been living on this space station for exactly one year.

The Future Perfect Continuous tense (will have been + verb-ing) is used to show that an action will continue up until a specific point in the future.

"Will have been orbited" is grammatically incorrect (it mixes continuous and passive forms incorrectly).

"Will be orbiting" is the Future Continuous tense; while it describes an action happening at a future time, it cannot be used with the duration phrase "for exactly one year" to sum up the time spent.