# Gravity Formula

Gravity is the Force of attraction between two objects times the gravitational constant, and inversely related to the square of the distance between the objects.

Force = [gravitational constant x masses (m_{1} x m_{2})] / (radius)^{2}

F = [Gm_{1}m_{2}] / r^{2}

F = force of gravity, N/kg

G = gravitational constant, 6.67 x 10^{-11} N-m^{2}/kg^{2}

m_{1} = 1st mass, kg

m_{2} = 2nd mass, kg

r = distance between the two masses, m

Gravity Formula Questions:

1) What is the gravitational force acting upon two objects of masses 15 g and 15 kg, that are 11 m apart?

Answer: the gravitational constant, G, is defined as 6.67 x 10 ^{-11} N-m^{2}/kg^{2} ; m_{1} = 15 g = 0.015 kg; m_{2} = 15 kg; r = 11m.

F = [Gm_{1}m_{2}] / r^{2}

F = [6.67 x 10^{-11} N-m^{2}/kg^{2} (0.015 x 15)kg] / (11 m)^{2}

F = 1.24 x 10^{-13} N / kg

2) If the gravitational force between two objects is equal to 1.1 x10^{-11}N/kg, and the masses are 6 kg each, what is the distance between them?

Answer: The force, F = 1.1 x 10^{-11} N/kg, and both m_{1} and m_{2} have masses = 6 kg.

G is defined.

F = [Gm_{1}m_{2}] / r^{2}

r^{2} = [Gm_{1}m_{2}] / F

r^{2} = [ 6.67 x 10^{-11} N-m^{2}M/kg^{2} (6 kg)(6kg)] / 1.1 x 10^{-11} N/kg

r^{2} = 2.18 x 10 ^{-20} m^{2}

r = √(2.18 x 10 ^{-20} m^{2})

r = 1.48 x 10^{-10} m

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