According to newton's law of gravitation, the gravitational force(F) is directly proportional to the product mass of the moon(Mm) and the mass of the planet (Mp) and it is inversely proportional to the square of the separation between them.
Fg ∝ (Mp)(Mm) →(1)
Fg ∝ 1/d²→(2)
Combining equation (1) and (2),
Fg ∝ (Mp)(Mm)/d²
Fg = G(Mp)(Mm)/d²
This is an equation that describes the relation between mass of moon (Mm) and mass of planet (Mp) and separation(d) between them.
To support the claim in favuor of this equation we use this equation to obtain the value of acceleration due to gravity on earth.
Let m be the mass of an object on earth then Fg between earth (Mp) and mass of an object is obtained by:
Fg = G(Mp)(m)/R², where R= Radius of earth
This force is equal to the weight of an object i.e.,
g= G(Mp)/R²
Putting the values of G, Mp and R , we get, g=9.81 m/s²
which is the value we obtained on earth for acceleration due to gravity.
To know more about gravitational constant, visit:
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