1. Combine 1/2 cup grapefruit juice and sugar in a small saucepan over medium heat. Cook until sugar dissolves, stirring frequently.
2. Combine the sugar mixture and the remaining 2 1/2 cups grapefruit juice in a medium bowl; cover and refrigerate until chilled.
3. Pour mixture into the freezer can of an ice-cream freezer, and freeze the mixture according to manufacturer's instructions. Spoon the sorbet into a freezer-safe container; cover and freeze for 1 hour or until the sorbet is firm.