In physics, why does this happen in Newton's Law of Universal Gravitation?

Question

why is ag(the "g" is a subscript) usually substituted in place of g (just regular small "g") when using this law?

Answer 1

F=ma.

At the surface of the earth, F=ma(g), which is the acceleration due to gravity at the surface of the earth.

wherever we use this equation, the distance from the ground to us (if we are above the ground, of course) is mostly negligible compared to the distance b/w the ground and the centre of the earth.

It is the same even if you are underground.

therefore, the a(g) is converted to a constant and taken to be "g".

Answer 2

The acceleration due to gravity is 9.8m/s^2. Since it is a constant, the need for the a (acceleration) is not necessary. Just given g (gravity) one can conclude 9.8m/s^2.

Hope That Helps....