Using Newton's universal law of gravitation and second law of motion, find the mathematical expression for acceleration due to gravity on the surface of any planet.

Explanation

Newton.s universal law of gravitation states that everybody in this universe attracts every other body with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
If the mass of the planet is `M_p` and its radius `R_p.` then gravitational force acting on the object of mass m at a distance `r (rgt R_p)` from its centre is,
`F=G (M_pm)/r^2 .........(1)`
As per the Newton.s second law of motion, the force acting on the object is equal to the product of the mass of the object and its acceleration.
`F=ma ...........(2)`
From equations (1) and (2)
`ma=G (M_p m)/r^2`
As per the defination of gravitional acceleration.
a=g
`mg=G (M_pm)/r^2`
`g=G ""M_p/r^2`
Taking `r=R_p`
`g=G""M_p/R_p^2`