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Nandika Kohli,
- Student, Department of Mathematics, Miranda House, University of Delhi, Delhi, India
Abstract
Spacecraft trajectory design is fundamentally a mathematical problem involving the prediction, evaluation and optimisation of motion under complex physical constraints. This article explores how mathematical modelling and optimisation are used to determine feasible and efficient trajectories for spacecraft. Beginning with the simplified two-body model, the article introduces the differential equation governing gravitational motion and explains how initial position and velocity determine the subsequent trajectory. It then examines how trajectory design moves beyond prediction to optimisation, where objectives such as fuel consumption, travel time and mission requirements must be considered alongside practical constraints. Since realistic trajectories may not have convenient analytical solutions, numerical methods provide a way to approximate spacecraft motion and evaluate possible trajectories computationally. Gravity assists are discussed as an important application, with the Voyager missions providing a practical example of how planetary geometry and carefully selected trajectories can reduce the need for onboard propulsion. The article also considers the role of modern trajectory-design software such as NASA’s Copernicus and the importance of accounting for uncertainty in real missions. Finally, the work of mathematician Katherine Johnson illustrates how mathematical reasoning remained essential during the early era of electronic computing, when computer-generated trajectory calculations still required independent verification.
Keywords: Spacecraft trajectory; mathematical modelling; trajectory optimisation; numerical methods; gravity assists
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Journal of Aerospace Engineering & Technology
| Volume | 16 | |
| 03 | ||
| Received | 15/09/2026 | |
| Accepted | 05/10/2026 | |
| Published | 10/10/2026 | |
| Publication Time | 25 Days |