The Physics of Reddit’s Spinning Solar System Icon

This data looks nice and linear. That means that the inner and outer planets orbit at a constant rotational rate (which is expected). The angular velocity is defined as the change in angular position divided by a change in time—that means the slope of angle vs. time would actually be the angular velocity (we use the symbol ω for this), and I can find that from the plot. From this, the inner planets orbits at 3.203 radians/second (based on the slope of the line), and the outer ones moves at 2.084 radians/second. Of course, this assumes that the loading graphic is in “real time,” but who knows.

But should a planet that’s farther from the center have a longer orbital period? Well, that’s what happens with the planets in our actual and real solar system. Why is that? There are really two big physics ideas to consider.

The first physics concept is the universal gravitational force. This is an interaction between any two objects with mass. So, let’s consider the inner planet (or maybe it’s a moon) and the big thing in the middle, the “sun.” Since both objects have a mass, there is an attractive force between them. This force depends on the value of the two masses (m₁ and m₂) as well as the distance between their centers (r).

In this expression, G is the universal gravitational constant with a value of 6.67 x 10^-11 N*m²kg²—at least that’s its value here in the real world. But notice that the gravitational force decreases with distance. That’s important.

The second big idea is Newton’s second law and acceleration. This says that the magnitude of the acceleration of an object is related to the magnitude of the total force on an object with the following expression.