The Collaborative International Dictionary of English v.0.48:

Aerostat \A"["e]r*o*stat\, n. [F. a['e]rostat, fr. Gr. ? air + ?
   placed. See Statics.]
   1. (A["e]ronautics) A balloon, especially a passive balloon;
      a balloon without motive power. Contrasted with
      aerodyne.
      [1913 Webster +Webster 1913 Suppl.]

   2. A balloonist; an a["e]ronaut.
      [1913 Webster] Aerostatic