## What is a Solar Day vs. a Sidereal Day?

Earth rotates on its axis once every day. In this case however the day is not the standard 24 hour solar day, but the approximately 4-minutes-shorter sidereal day.

What’s a sidereal day? It’s best explained in relation to the normal, or ‘solar’ day that we usually use when talking about a day.

- A solar day is Earth’s rotational period with respect to the Sun, and is defined as the time interval from when the Sun is highest in the sky (noon for local standard time) until the next time the Sun is highest in the sky. The solar day is 24 hours long.
- The sidereal day is Earth’s rotational period with respect to the stars. A sidereal day is defined as the time interval from when a star is highest in the sky until the next time the same star is highest in the sky.
- Sidereal days are about 4 minutes shorter than solar days, because while Earth is rotating on its axis, it is also traveling about 1/365th of its orbital distance around the Sun. Because it is referenced to the stars and not affected by Earth’s orbital motion, the sidereal day is the appropriate time interval for one rotation on earth’s axis. A sidereal day is 23 hours 56 minutes and 9 seconds or 86,164 seconds long.

## Earth’s Rotational Speed and Acceleration

According to NASA, Earth’s equatorial radius is 6378 kilometers or 6.378X10^{6} meters (6378000 meters). As Earth makes one complete rotation on its axis, a point on the equator travels a distance of 2 (π) (radius). Recall that the geometrical formula for the circumference of a circle is 2πr.

The speed of a point on Earth’s equator is therefore shown by the following formula:

Speed = distance/time.

We add the figures that we know into the equation to arrive at the following calculation:

Speed = 2 (π) (6.378X10^{6})meters/86164seconds.

Finally, a few moments on a calculator later, we end up with some actual numbers:

Speed = 465.1 meters per second = 1041 miles per hour.

Neglecting the fact that Earth is not quite a perfect sphere, the speed of Earth’s rotation at some latitude not at the equator is given by the following formula:

Speed at latitude = (speed at equator) cosine (latitude).

The centripetal acceleration of a point on Earth’s equator would then be found through this formula:

Centripetal acceleration = speed squared/radius.

We plug in the information we’ve already found, and reach this calculation:

Centripetal acceleration = ((465.1 meters per second)^2)/(6.378X10^{6} meters).

Finally, we can break it down, with the handy helping hand of a little math, to an answer:

Centripetal acceleration = 0.03392 meters per second squared.

The acceleration of gravity on Earth’s surface is about 9.8 meters per second squared, so the acceleration due to Earth’s rotation on its axis, as found above, is by comparison quite small.

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