Question

How is the mass of the earth calculated?

Answer 1

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 = 4/3pi 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.

Answer 2

`5.97 X 10^24` kg, nearly.

Explanation:

A formula for approximating mass of the Earth:

`m = r^2g/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`(kg)^(-1)(km)^(-3)(s)(-2)`

Units are compatible, in both dimensions and units,.

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