VERB (3)

1. move toward;
- Example: "The conversation gravitated towards politics"

2. be attracted to;
- Example: "Boys gravitate towards girls at that age"

3. move due to the pull of gravitation;
- Example: "The stars gravitate towards each other"

The Collaborative International Dictionary of English v.0.48:

Gravitate \Grav"i*tate\, v. i. [imp. & p. p. Gravitated; p.
   pr. & vb. n. Gravitating.] [Cf. F. graviter. See
   Gravity.]
   To obey the law of gravitation; to exert a force or pressure,
   or tend to move, under the influence of gravitation; to tend
   in any direction or toward any object.
   [1913 Webster]

         Why does this apple fall to the ground? Because all
         bodies gravitate toward each other.      --Sir W.
                                                  Hamilton.
   [1913 Webster]

         Politicians who naturally gravitate towards the
         stronger party.                          --Macaulay.
   [1913 Webster]

WordNet (r) 3.0 (2006):

gravitate
    v 1: move toward; "The conversation gravitated towards politics"
    2: be attracted to; "Boys gravitate towards girls at that age"
    3: move due to the pull of gravitation; "The stars gravitate
       towards each other"