The National Science Foundation offers graduate fellowships to students at the beginning of the postgraduate careers. Students must be US citizens or permanent residents and must have completed no more than 20 semester hours in graduate study by the start of the semester that applications are due. This restriction limits eligibility to current students in their first or second year or to undergraduates in their senior year who are in the process of applying to graduate school. In past years the deadline has been early November. Each year NASA offers a number of graduate fellowships that can support students in the astronomy graduate program.
Fellowships are for three years, renewable annually.
The best time to apply for these fellowships is when you have a detailed plan for your dissertation research. Only US students are eligible. For more information see the Sigma Xi page. Applicants do not have to be members of Sigma Xi.