Modelling Orbital Dynamics

Produce a modelling brief for an orbital question that specifies the system boundary, intended outputs, Newtonian point-mass assumptions, omitted effects, and equation–simulation–validation workflow.

Choose an inertial reference frame and define the position–velocity state of a system of point masses.

Derive the vector gravitational acceleration produced by a point mass from Newton's inverse-square law.

Express Newtonian motion as an initial-value problem and convert its second-order equations into first-order state-space form.

Nondimensionalise a gravitational model using characteristic mass and length scales and derive its characteristic orbital timescale.

Formulate the coupled equations of motion for two mutually gravitating bodies.