Question

Derive the equation for acceleration due to gravity?

Answer 1

Gravitational force (F) between an object of mass “m” and planet of mass “M” separated by distance “d” (where d ≥ Radius of planet) is given by
F = GMm / d²

Now, from Newton’s Law
a = F / m
g = (GMm / d²) / m
g = GM / d²

If object is at surface of planet then, d = R
g = GM / R²

Where, G = Universal Gravitational constant = 6.67 × 10⁻¹¹ N m² / kg²

Answer 2

$\textbf{Answer is in Attachment !}$