Question

Determine the Universal Gravitational Constant (G).

Answer 1

G = 6.6675 x
`10^(-11)` N
`m^(2)`/
`kg^(2)`

Step-by-step 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 =
`(GM)/(r^(2) )`

⇒ G =
`(gr^(2) )/(M)`

where: g = 9.81 m/
`s^(2)`, r = 6371 km, M = 5.972 x
`10^(24)` kg.

G =
`(9.81*(6371000)^(2) )/(5.972*10^(24) )`

=
`(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)`.