The topic of Newtonian gravity offers a unique vantage point from which to investigate and encourage conceptual change because it is something with which everyone has daily experience, and because it is taught in two courses that reach a wide variety of students - introductory-level college astronomy ("Astro 101") and physics ("Phys 101"). Informed by the constructivist theory of learning, this study characterizes and measures Astro 101 and Phys 101 students' understanding of Newtonian gravity within four conceptual domains - Directionality, Force Law, Independence of Other Forces, and Threshold. A phenomenographic analysis of Astro 101 student-supplied responses to open-ended questions about gravity results in the characterization of students' alternative mental models and misapplications of the scientific model. Student difficulties inform the development of a multiple-choice assessment instrument, the Newtonian Gravity Concept Inventory (NGCI). Classical Test Theory statistics, student interviews, and expert review show that the NGCI is a reliable and valid tool for assessing both Astro 101 and Phys 101 students' understanding of gravity. Comparing and contrasting the Astro 101 and Phys 101 CTT values and student response patterns shows qualitative differences in each of the four conceptual domains. Additionally, performing an Item Response Theory (IRT) analysis of NGCI student response data calibrates item parameters for all Astro 101 and Phys 101 courses and provides Newtonian gravity ability estimates for each student. Physics students show significantly higher pre-instruction and post-instruction IRT abilities than astronomy students, but they show approximately equal gains. Linear regression models were used to investigate the differential effect of Astro 101 compared to Phys 101 curricula. Results show that differences in post-instruction abilities are most influenced by students' pre-instruction abilities and the level of interactivity in the classroom.