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"

Moby Thesaurus II by Grady Ward, 1.0:

57 Moby Thesaurus words for "gravitate":
   bend to, bias, cascade, cataract, collapse, come down, conduce,
   contribute, crash, descend, dip down, dispose, down, drop,
   drop down, drop off, fall, fall down, fall off, go, go down,
   go downhill, have a tendency, head, incline, lead, lean, look to,
   lose altitude, parachute, pitch, plummet, plunge, point, point to,
   pounce, pour down, precipitate, rain, redound to, serve, set,
   set toward, settle, show a tendency, sink, stoop, subside, swoop,
   tend, tend to go, trend, trend downward, turn, verge, warp,
   work toward