Physics acceleration

Question

How do you find the vertical component of the acceleration of a projectile not on earth?

Answer 1

Start with two basic equations:

Equation 1) F = (Gm₁m₂)/r² (Newton's Universal Law of Gravitation)

In this equation, let's let m₁ be the mass of an object at the surface of the planet you are on and let's let m₂ equal the mass of the planet.

Equation 2) F = ma (Newton's second law) but let's apply it to the object that is on the surface of the planet you are on so m = m1 and since the acceleration it has is associated with gravity, then a = g. So that makes Newton's second law become F = m₁g

In these two equations, F (the force) is the same so the equations can be set equal to each other:

(Gm₁m₂)/r² = m₁g

Divide both sides by m₁ to get:

g = (Gm₂)/r² where G is the Universal Gravitation Constant (6.674 x 10⁻¹¹ m³/(kg•s²), again m₂ is the mass of the planet you are on, and "r" is the distance you are from the center or the radius of the planet