Source : Webster's Revised Unabridged Dictionary (1913)

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.

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

         Politicians who naturally gravitate towards the
         stronger party.                          --Macaulay.

Source : WordNet®

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"