Question

Determine the Universal Gravitational Constant (G).

Answer 1

Answer:

G = 6.6675 x $10^{-11}$ N$m^{2}$/$kg^{2}$

Explanation:

From Newton's law of universal gravitation,

F = $\frac{GMm} {r^{2} }$  .................. 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 = $\frac{GMm} {r^{2} }$

So that;

g = $\frac{GM}{r^{2} }$

⇒ G = $\frac{gr^{2} }{M}$

where: g = 9.81 m/$s^{2}$, r = 6371 km, M = 5.972 x $10^{24}$ kg.

G = $\frac{9.81*(6371000)^{2} }{5.972*10^{24} }$

  = $\frac{3.98184*10^{14} }{5.972*10^{24} }$

  = 6.6675 x $10^{-11}$ N$m^{2}$/$kg^{2}$

The Universal Gravitational Constant (G) is 6.6675 x $10^{-11}$ N$m^{2}$/$kg^{2}$.