Problem — Science fiction: non-conserved angular momentum

Problem

Imagine a universe in which angular momentum is not conserved. Discuss the consequences for planetary orbits and satellite missions.

Solution

Conservation of angular momentum is the pillar of orbital stability (it is, among other things, Kepler’s second law). Without it:

• orbits would lose their Keplerian regularity; planets could spiral into the Sun or drift away unpredictably;
• stability over timescales of billions of years, which allowed life to develop, requires $L$ to be conserved;
• space missions would be impossible to design: manoeuvres such as gravitational slingshots rely on the controlled exchange of angular momentum between probe and planet.

$\ev{\text{unstable orbits, no Keplerian regularity, unpredictable missions}}$

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Topics: Rotational dynamics Concepts: Conservation of angular momentum Skills: Analysis of limiting cases and science fiction