Answer :
Answer:
G = 6.6675 x [tex]10^{-11}[/tex] N[tex]m^{2}[/tex]/[tex]kg^{2}[/tex]
Explanation:
From Newton's law of universal gravitation,
F = [tex]\frac{GMm} {r^{2} }[/tex] .................. 1
Where F is the force of attraction, G is the universal gravitation constant, M is the mass of a massive object e.g earth, m is the mass of the smaller object e.g moon, r is the radius of the massive object.
Newton's second law states;
F = mg ................... 2
F is the force, m is the mass of the object and g is the gravitational force on the object.
Equating equations 1 and 2 gives;
mg = [tex]\frac{GMm} {r^{2} }[/tex]
So that;
g = [tex]\frac{GM}{r^{2} }[/tex]
⇒ G = [tex]\frac{gr^{2} }{M}[/tex]
where: g = 9.81 m/[tex]s^{2}[/tex], r = 6371 km, M = 5.972 x [tex]10^{24}[/tex] kg.
G = [tex]\frac{9.81*(6371000)^{2} }{5.972*10^{24} }[/tex]
= [tex]\frac{3.98184*10^{14} }{5.972*10^{24} }[/tex]
= 6.6675 x [tex]10^{-11}[/tex] N[tex]m^{2}[/tex]/[tex]kg^{2}[/tex]
The Universal Gravitational Constant (G) is 6.6675 x [tex]10^{-11}[/tex] N[tex]m^{2}[/tex]/[tex]kg^{2}[/tex].