# How is the mass of the earth calculated?

Apr 17, 2016

See below.

#### Explanation:

We can approximate the mass using the formula for density which relates mass and volume of the object.

Density = mass/Volume

If the Earth's diameter is known and we assume the earth is spherical we can calculate the volume from

$V = \frac{4}{3} \pi {r}_{3}$

Using an average density we could then approximate the mass of the Earth.

With todays modern technology and the use of satellites we can get a more accurate figure for the volume.

Apr 18, 2016

$5.97 X {10}^{24}$ kg, nearly.

#### Explanation:

A formula for approximating mass of the Earth:

$m = {r}^{2} \frac{g}{G}$,
r = Earth radius =6378 km,
g = acceleration due to Earth's gravity =0.0098 km/${s}^{2}$ and
G - gravitational constant = 6.67 E-20${\left(k g\right)}^{- 1} {\left(k m\right)}^{- 3} \left(s\right) \left(- 2\right)$

Units are compatible, in both dimensions and units,.

#So, m =(6378^2)(0.0098)/(6.67 E-20) kg = 5.97 E+24 kg.