Planet Vanishes - How does this affect the orbiting starships?

In the climactic final battle Faction A engages Faction B on Faction B's planetary base, both in orbital and ground combat. Realizing they can't win, Faction A activates a device that transports and traps the entire planet in what can be compared to a pocket dimension.

So basically the entire planet vanishes from existence in (almost) an instant. Now there are two fleets of ships around the space where a planet used to be.

What is the effect (if any) on said ships?

Half of me thinks that because it's in space there won't be any effect, but of course it would be cool if there was some sort of displacement effect.

EDIT: A few answers mention the planet returning at some point. I'll have the trapped people escape several decades later, but the planet itself remains lost.

Several answers have been extremely useful, but unfortunately I can only pick one, so I went with the one that gave me the best alternative. The rest get upvotes though. Thanks to everyone that took the time to answer.

posted over 7 years ago

Lu22‭

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