Define acceleration due to gravity. What is the value?

Prove mathematically that the value of acceleration due to gravity has a constant value at a place.

How does value of acceleration due to gravity vary with altitude

If a planet existed whose mass and radius were both half of that of the eawrth. What would be the acceleration due to gravity at the surface of the planet in terms of that on the surface of the earth?

Assuming that mass M of the largest stone that can be moved by a flowing river , rho the density of water and 'g' the acceleration due to gravity, show that mass M varies as the sixth power of velocity.

How does value of acceleration due to gravity vary with depth