Peel orange and remove white membrane. Remove membranes from sections. Squeeze 2 tablespoons juice from membranes into a bowl.
To the bowl, add 1/4 cup vinegar, sugar to taste depending on sweetness of oranges, and tarragon. Mix and pour into a pitcher.
In a frying pan boil about 1 inch of water and remaining 1/4 cup vinegar. Add spears to boiling water. Cook, uncovered, until asparagus is just tender when pierced, about 4 minutes. Drain and immerse in ice cold water. Drain.
Crisp onion slices: Thinly slice onion. Put in a bowl with water to cover. Squeeze onions to bruise slightly; drain. Add 4 cups ice cubes, 2 cups water, and 1/4 cup vinegar. Let stand until crisp, 20 - 30 minutes. Drain and discard ice.
Divide onion slices among 4 plates. Arrange spears and orange segments on plates. Add dressing. Salt and pepper to taste.