As well as the Airport Tycoon quests where you unlock conventional planes there are also Space Trek quests which feature spaceships from well known sci-fi movies such as Star Wars, Star Trek, and Battlestar Galactica.
The Star Trek event is a limited time event that is initiated by the developers at random intervals. Although the quests for the Star Trek event will appear in the 'Quest' menu it does not necessarily mean they are available. If you find the Star Trek event has not comenced you just need to be patient and wait awhile for it to be added to the game.
Once you have access to the Star Trek event you will be able to complete the Star Trek quests. These quests are more or less the same as the standard Airport quests except you have to fill your board with a certain number of Star Trek planes in order to complete them. Gems are earned when you complete the Star Trek quests, there are 15 spaceships to unlock and unlocking them is accomplished the same way as you would do the standard Airport quests.
Instead of propeller coins the secondary currency in the Star Trek event resembles a circuit board and as with the standard Airport quests you trade coins for these circuit boards which you can then go to the boost tab in the store and use to buy boosts. These include overall multipliers to your income and plane discounts.