Gravitation

Gravitation

RELATION BETWEEN G AND  g
We want to measure g due to M at a point P as per the procedure.
Place a point mass m at P measure the force imparted by M on the test mass m.
this is equal to   Fg=GMm/r²

\( g_p = \frac{{F_g }} {m} = \frac{1} {m}\left( {\frac{{GMm}} {{r^2 }}} \right) \)
\( g_p = \frac{{GM}} {{r^2 }} \) and it is directed towards the mass M.
Hence, \( \vec g_p = \frac{{GM}} {{r^2 }}\hat a_r \) where \( \hat a_r = (\vec r/r) \)
Acceleration due to gravity on surface on earth
\( g = \frac{{GM}} {{r^2 }} \)
Where G = 6.67 × 10^–11         (universal gravitational constant)
    M = 5.983 × 10²⁴ Kg (mass of earth) 
    R = 6.378 × 10⁶ m (equation radius of earth)
    r = distance between the particle and centre of earth