The minimum rotation speed required for a planet or star to break free from its own gravitational field depends on its mass and radius. This critical rotational speed is known as the escape velocity.
The formula to calculate the escape velocity (v) is given by:
v = sqrt((2 * G * M) / R)
Where:
- G is the gravitational constant
- M is the mass of the planet or star
- R is the radius of the planet or star
To break free from the gravitational field, the rotational speed at the equator must be equal to or greater than the escape velocity.
It's important to note that planets and stars typically rotate differentially, meaning their equatorial regions rotate faster than their polar regions. As a result, the equatorial rotational speed needs to be higher to compensate for the slower rotational speed at the poles.
For example, Earth's escape velocity is about 11.2 km/s. However, Earth's equatorial rotational speed is only about 0.465 km/s. So, Earth is rotating far below the escape velocity, and its gravitational field easily holds onto its atmosphere and objects on its surface.
In summary, the minimum rotation speed required for a planet or star to break free from its own gravitational field is equal to or greater than its escape velocity, which depends on its mass and radius.