Monday, February 6, 2023

The physics of the rotating solar system icon from Reddit

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This data looks beautiful and linear. This means that the inner and outer planets orbit at a constant rotational speed (which is expected). Angular velocity is defined as the change in angular position divided by a change in time – this means that the slope of the angle as a function of time would actually be angular velocity (we use the symbol ω for this), and I can find this from the field. From there, the inner planets are spinning at 3,203 radians / second (based on the slope of the line), and the outer planets are moving at 2,084 radians / second. Of course, this assumes that the loading graph is in “real time”, but who knows.

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

The first physical concept is the universal gravitational force. It is an interaction between two objects with a mass. So, consider the inner planet (or maybe it’s a moon) and the big thing in the middle, the “sun”. Since both objects have mass, there is a force of attraction between them. This force depends on the value of the two masses (m1 and M2) as well as the distance between their centers (r).

Illustration: Rhett Allain

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 note that the gravitational force decreases with distance. It is important.

The second big idea is Newton’s second law and acceleration. Having said 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.

Illustration: Rhett Allain

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