The minimum mass needed for a planet to have surface gravity depends on several factors, including the planet's radius and its composition.
To understand this, we can look at the concept of escape velocity, which is the minimum speed an object needs to reach in order to escape the gravitational pull of a celestial body. The escape velocity depends on the mass and radius of the object.
For a planet to have surface gravity, it must have enough mass to generate a gravitational force that keeps objects on its surface. This gravitational force is directly related to the planet's mass. The greater the mass, the stronger the gravitational force.
However, it's important to note that the mass alone is not the sole determinant of surface gravity. The planet's radius also plays a crucial role. For example, a small, dense planet with a relatively high mass may have a higher surface gravity than a larger, less dense planet with the same mass.
To give a rough estimate, a celestial body generally needs to have a mass of at least about 0.0001 times the mass of Earth (or approximately 0.06 times the mass of the Moon) to maintain surface gravity. Below this threshold, the gravitational force would likely be too weak to retain an atmosphere or hold objects on its surface.
It's worth mentioning that the specific properties of a planet, such as its composition, density, and distribution of mass, can further influence the surface gravity. So, while there is a minimum mass requirement, it's not the sole determining factor, and other factors must be considered when assessing the surface gravity of a planet.