Engineering Proof of the Consistent Low Orbit Period of Rocky PlanetsEngineering Proof of the Consistent Low Orbit Period of Rocky Planets

The two-hour rule of thumb turns out to be supported by the math, proves aerospace engineer Max Fagin.

Dan Carney, Senior Editor

July 9, 2024

This image depicts the approximately 12,000 objects in Earth orbit.European Space Agency/AFP via Getty Images

At a Glance

• Orbital period depends on the planet's density, not its radius or mass
• Earth is the densest planet in our solar system
• This rule is for objects made of rock. Other materials' periods depend on their density.

Simple axioms can seem too simple. That was the case for aerospace engineer Max Fagin, when he encountered the rule of thumb that orbit at the surface level of rocky planets takes two hours.

Dubious, Fagin broke out his whiteboard to calculate a proof one way or the other. Surprised by his results, Fagin shared his findings with the world through a Twitter thread. Look at this: his calculations determined that the orbital period of a body with the density of rock is 2.01 hours!

He also found that this orbital period has an effect on the spin rate of asteroids because asteroids that spin faster than once every two hours fling material off into orbit until they shrink and slow down.

The mass and radius of objects don’t matter, he found, only the density determines orbital periods.

Once he had the basics set up, Fagin ran the numbers for materials with different densities. He found that a metal body would have a period of 1.2 hours, gas giant planets are 2.8 hours, and water is 3.3 hours.

Scroll through Fagin's thread below to discover what his calculations showed.

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Thanks to Max for walking us through those calculations!