# How to calculate the force of gravitational attraction between a person (mass=75 kg) & Earth (mass 5.98x10^24 kg and mean radius 6.37x10^6m) ?

Apr 20, 2016

$740 N$

#### Explanation:

The gravitational force can be calculated with the formula:

$\textcolor{b l u e}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} {F}_{g} = \frac{G M m}{R} ^ 2 \textcolor{w h i t e}{\frac{a}{a}} |}}}$

where:
${F}_{g} =$gravitational force
$G =$gravitational constant
$M =$mass of Earth
$m =$mass of object
$R =$distance from earth's centre to object's centre

Substitute your known values into the formula to determine the gravitational force. Assuming that the person is standing on the surface of the Earth, the value of $R$ would be the radius of the Earth.

${F}_{g} = \frac{G M m}{R} ^ 2$

${F}_{g} = \frac{\left(6.67 \times {10}^{-} 11 \frac{N \cdot {m}^{2}}{k {g}^{2}}\right) \left(5.98 \times {10}^{24} k g\right) \left(75 k g\right)}{6.37 \times {10}^{6} m} ^ 2$

${F}_{g} = 737.24 N$

${F}_{g} \approx \textcolor{g r e e n}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} 740 N \textcolor{w h i t e}{\frac{a}{a}} |}}}$