Zaphod, Trillian, Arthur, Ford, and Marvin "the paranoid android" (3) prepare to explore the surface of the planet. Note: Marvin isn't really an android, he's a robot. Also, he's not paranoid, but just depressed. But tell that to these guys, who made a song with that title anyway.
Trillian is upset (not Marvin-level upset, but just regular upset) that her white mice have escaped. However, no one else is upset, which is probably because people don't know that humans weren't the second-most intelligent life on Earth, but the third-most.
Eddie's super friendly personality has been switched (by Zaphod) to a smothering mother personality, who warns them about catching colds and playing with the wrong type of alien. Eddie finally lets them out when Zaphod threatens it with an ax.
So the group leaves for Magrathea.
And then, surprising Eddie, another group leaves the ship to see Magrathea. If you can't guess, the narrator will pretty much tell us in twelve chapters' time—in Chapter 31—who that other group was.