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Physics Final Year Topic: Energy Conservation in Numerical Integrations of a Two-Body Gravitational Orbit

This Physics final year project compares long-run numerical behaviour of integration schemes on a known mechanical model.

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Why choose this project topic?

A focused study of orbit integrators gives you a specific question in computational mechanics. It compares long-run numerical behaviour of integration schemes on a known mechanical model. The bounded comparison creates room to explain how your evidence supports an interpretation and where the method has limits.

How do time step and integration method affect energy drift and orbital phase error in a two-body simulation?

Agree the apparatus or dataset, comparison range and feasible measurement schedule for orbit integrators with your supervisor.

Proposed project objectives

  1. 01Define the materials, variables and comparison conditions for orbit integrators.
  2. 02Specify units and initial conditions with a known reference orbit.
  3. 03Evaluate the measurements or model outputs in relation to this question: How do time step and integration method affect energy drift and orbital phase error in a two-body simulation?

A suggested research approach

Specify units and initial conditions with a known reference orbit. Compare at least two justified integrators at several time steps, report convergence and distinguish bounded energy oscillation from secular drift. Agree the available resources and record uncertainty, deviations from the protocol and any observations that challenge the initial interpretation.

What you will need

  • A documented two-body model and reference orbit
  • Numerical computing environment
  • A convergence plan and conserved-quantity diagnostics

Keep your project scope clear

A two-body numerical result does not include additional bodies, relativistic corrections or a spacecraft's operational constraints.

Physics project chapter outline

Use this outline as a starting point. You can edit the chapter titles to match your department’s format during setup.

  1. Chapter 1Introduction
  2. Chapter 2Literature Review
  3. Chapter 3Theory and Methodology
  4. Chapter 4Results and Applications
  5. Chapter 5Summary, Conclusion and Recommendations

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