The acceleration due to gravity ‘g’ for objects on or near the surface of earth is related to the universal gravitational constant 4G’ as (‘M’ is the mass of the earth and ‘R’ is its radius):

The acceleration due to gravity 'g' is derived from Newton's Law of Universal Gravitation and Newton's Second Law of Motion. According to the law of gravitation, the force (F) between the Earth (mass M) and an object (mass m) at a distance r is F = GmM/r² [1]. For an object on or near the Earth's surface, the distance r is approximately equal to the Earth's radius R. Newton's Second Law states that F = mg, where g is the acceleration due to gravity. By equating these two expressions (mg = GmM/R²), the mass of the object (m) cancels out, resulting in the formula g = GM/R². This relationship shows that 'g' depends on the Earth's mass and radius but is independent of the falling object's mass [1].

Sources

1. [1] https://imagine.gsfc.nasa.gov/observatories/learning/swift/classroom/law_grav_guide.html