For this project, you'll do most of your research in The Astrophysics Data System.
Description from their page:
The ADS maintains three bibliographic collections containing more than 15 million records covering publications in astronomy and astrophysics, physics, and general science, including all arXiv e-prints. Abstracts and full-text of major astronomy and physics publications are indexed and searchable through the new ADS modern search form as well as a classic search form. A browsable paper form is also available.
The best research method is the one that works for you, as long as you abide by good information literacy practices. Here is one potential research method for this project: