Level 8: Orbits for mission design

Gravity and orbits · level 8 of 8 · rough age 17 and beyond (a guide; anyone can start anywhere)

The last level is the orbital mechanics that real Mars missions are planned with. You add up a delta-v budget from the ground on Earth to the ground on Mars, bend a path with a planet's gravity, find the points where gravity and orbit balance, see how the bulge of Mars makes orbits drift (and how that drift is put to use), work out the slow death of Phobos, and meet the corrections from Einstein's relativity that navigators cannot leave out.

Lesson	You will be able to
Delta-v budgets	Build the delta-v budget for a trip from Earth's surface to Mars's and back, and explain the Oberth effect
Gravity assists	Find the turn and the speed change from a flyby, and why Mars is a useful stepping stone
Lagrange points	Locate the Sun–Mars Lagrange points, explain their stability, and the Hill sphere of Mars
Orbits that drift	Use the \(J_2\) term to find nodal drift, and design a sun-synchronous orbit round Mars
The fate of Phobos	Explain tidal decay inside the synchronous orbit and estimate how long Phobos has
Relativity and orbits	Find the relativistic perihelion shift of Mars, the Shapiro delay, and how Mars clocks run against Earth's

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