# Equation of the speed of rotation of a planet

## v = 2πr/T

Updated March 17, 2023

The mathematical formula that determines the speed (in km/h) at which a planet rotates on itself is a simple equation. It corresponds to the calculation of the circumference C of a sphere of radius r (C = 2πr in km) divided by the time (T in hours) necessary for the planet to perform a complete rotation called rotation period.
The basic equation used to calculate the rotational speed of a planet is:
v = 2πr/T where v is the speed of rotation at the equator, r is the radius of the planet, and T is the period of rotation. The constant π (pi) is a mathematical number which represents the relationship between the diameter d and the circumference C of a circle that is to say C/d, it is generally rounded off to 3.14.
Using this formula, it is possible to calculate the rotation speed at the equator of all the planets of the solar system. For example, the Earth has a radius of about 6371 km and a rotation period of about 24 hours, which gives a rotation speed of about 1670 km/h.
Mars has a radius of about 3,389 km and a rotation period of about 24 hours and 36 minutes, giving a rotational speed of about 868 km/h.
Warning: this rotational movement around the axis of rotation of the planet takes place at a constant speed when you are located on the equator.
As the lines parallel to the equator decrease as one approaches the poles, the speed of rotation also decreases. Indeed for an increasingly small distance the period of rotation does not change, it is always 24 hours for the Earth.

Thus, at the North and South poles, the rotational speed is actually zero, because this is the point where the Earth's axis of rotation meets its surface. This means that the poles do not rotate, but are stationary relative to the Earth's axis of rotation.
About 600 million years ago, the length of a day on Earth was about 22 hours, which means that the Earth rotated faster than today.
Also, the equation does not necessarily apply to all celestial bodies.
Stars, for example, do not spin in the same way as telluric planets.
The stars are gaseous and their period of rotation is differential, it depends on the latitude, the equatorial regions rotate faster than the polar regions.
For example for the Sun, the period of rotation near the equator is about 34 days while near the poles it is about 25 days. Its rotation speed at the equator is 1997 km/s.

What is v = 2πr/T for?
Knowing the rotational speed of a planet is essential to understanding the physical characteristics and dynamic processes that occur on that planet.
The rotation speed of a planet is directly related to its rotation time, or day. This information can help astronomers better understand the history and evolution of the planet.
The speed of rotation can affect the geology and climate of a planet such as on Jupiter where rapid rotation creates huge storms.

### Image: the speed of rotation of the Earth at the equator is 1670 km/h. At the North and South poles, the speed of rotation is zero.

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