This is one of the little ball-shaped remote controls that activate the viewing screen of the spaceship Heart of Gold. This is used by Trillian (Zooey Deschanel) early in the film, and then by Zaphod when he's showing the crew the Magrathea tapes. Pressing one of the three buttons on top will activate the light.

 

Here's some screen shots showing Trillian and Zaphod using this.
It sits over the hole that Zaphod places the storage cube into to play back the video.