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?

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Acceleration due to gravity: what&#039;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&#039;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&#039;s radius  =  6380         k    m  One thing I know of is the fact that we use Newton&#039;s second law, but how?

Braxton Gallagher · Accepted Answer

So, it turns out that I am out of coffee.Anyway, since we already know that:  w  =  m  ×  g (Newton&#039;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

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

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