Fair Compensation Act of 2009 - Confers upon the U.S. Court of Federal Claims jurisdiction to hear, determine, and render final judgment on any legal or equitable claim against the United States to receive just compensation for the taking of certain lands in the state of Missouri by reason of the decision and notice of interim trail use or abandonment authorized by the National Trails System Act and decided by the Interstate Commerce Commission (ICC) on March 25, 1992.