Sprinkle 1/4 cup sugar over grapefruit.
Add lime juice to sherbet; as sherbet melts, stir occasionally to blend.
Combine remaining sugar and gelatin in a saucepan.
Add enough water to pineapple syrup to make 2 cups liquid.
Mix 1 cup of the liquid into the gelatin mixture.
Stir over low heat until gelatin is dissolved.
Remove from heat; add remaining liquid and the sherbet.
If necessary, beat with hand rotary or electric beater until well mixed.
Chill until mixture is the consistency of thick, unbeaten egg white, stirring occasionally.
Fold in grapefruit (including syrup), pineapple, and cherries.
Turn into a 5-cup star-shaped mold.
Chill until firm.
Unmold onto serving plate.