Question

With a bit of algebraic reasoning find your gravitational acceleration toward any planet of mass M a distance d from its center.

Answer 1

The acceleration due to gravity is given as:

                             g = GM/r²

Derivation of gravitational acceleration:

According to Newton's second law of motion,

F = ma

where,

F = force

m = mass

a = acceleration

According to Newton's law of gravity,

Fg = GMm/(r + h)²

Fg = gravitational force

From Newton's second law of motion,

Fg = ma

a = Fg/m

We can refer to "a" as "g"

a = g = GMm/(m)(r + h)²

g = GM/(r + h)²

When the object is on or close to the surface, the value of g is constant and height has no considerable impact. Hence, it can be written as,

g = GM/r²

Learn more about gravitational acceleration here:

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