Question

Derive the relation between the acceleration due to gravity and the universal gravitational constant

Answer 1

hey there

F = G x M x m/ r2
E = F x r = (G x M x m/ r2) x r
E = mgr = (G x M x m/ r2) x r
=> g = G x M/ r2

OR G = g{r2/M}

where,
F = Force of attraction between twoo bodies(N/m2)
E = energy in smaller body w.r.t the heaviour body(J)
M = mass of heaviour body/planet (kg or slug)
m = mass of smaller body(kg or slug)
g = acceleration due to gravity (m/s2 or ft/s2)
G = universal gravitational constant (m3/kg/s2 or 
ft3/slug/s2)
r = distance between the centres of the two bodies(m or ft) 
The value of G is known and has been estimated by 
scientists as: 
G = 6.673 x 10-11 m3/kg/s2 in the Metric system
G = 3.439 x 10-8 ft3/slug/s2 in the English system

hope this helps

Answer 2

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