Question

derivation of G and derivation of g. with the calculation​

Answer 1

Answer:

These two laws lead to the most useful form of the formula for calculating acceleration due to gravity: g = G*M/R^2, where g is the acceleration due to gravity, G is the universal gravitational constant, M is mass, and R is distance...

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Answer 2

Modelling the Earth as a symmetric, spherical body (and by using the law of gravitation), we come up with the equation

$\sf \: W = F_g = G \frac{m_Em}{ {R_E}^{2} }$

we already know that:

w=m×g (Newton's Second Law)

We know,

$\sf \: W = G \frac{m_Em}{ {R_E}^{2} }$

Dividing the entire equation by m, we get:

$\sf \ \frac{w}{m} = \frac{mg}{m}$

which is equal to :

$\sf \: g = G \frac{m_Em}{ {R_E}^{2} m}$

And Finally :

$\sf \: g = G \frac{m_E}{ {R_E}^{2} }$