The minimum rotation speed required for a planet or star to break free from its own gravitational field is known as the escape velocity. The escape velocity depends on the mass and radius of the celestial body.
For a spherically symmetric object like a planet or star, the escape velocity can be calculated using the following formula:
v = √(2GM/R)
Where:
- v is the escape velocity
- G is the gravitational constant (approximately 6.67430 × 10^(-11) m^3 kg^(-1) s^(-2))
- M is the mass of the celestial body
- R is the radius of the celestial body
If the rotational speed of the celestial body exceeds the escape velocity at its surface, then objects or particles on its surface would be able to overcome the gravitational pull and escape into space.
It's important to note that the concept of a planet or star breaking free from its own gravitational field due to rotation alone is not commonly observed in nature. The escape velocity is generally achieved through the collective gravitational pull of the celestial body, rather than rotation alone.