Acceleration due to gravity: what's the derivation? Modelling the Earth as a symmetric, spherical b

Cesar Mcguire

Cesar Mcguire

Answered question

2022-04-12

Acceleration due to gravity: what's the derivation?
Modelling the Earth as a symmetric, spherical body (and by using the law of gravitation), we come up with the equation
w = F g = G m E m R E 2
How do we arrive to the equation to get the acceleration due to gravity at the earth's surface?
g = G M E R E 2
Where:
G = gravitational constant = 6.67 × 10 11   N
M E = mass of Earth = 5.98 × 10 24   k g
R E = Earth's radius = 6380   k m
One thing I know of is the fact that we use Newton's second law, but how?

Answer & Explanation

Braxton Gallagher

Braxton Gallagher

Beginner2022-04-13Added 21 answers

So, it turns out that I am out of coffee.
Anyway, since we already know that:
w = m × g (Newton's Second Law)
We know that w = G m E m R E 2
Dividing the entire equation by m, we get:
w m = m g m
Which is equal to:
G m E m R E 2 m = g (Substituting the values)
And finally:
G m E R E 2 = g

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