Explain how the mass and average density of the earth can be estimated from the knowledge of G?

Mass of the Earth:

The mass of the Earth can be calculated using the relationship between gravitational acceleration g, the gravitational constant G , and the Earth’s radius R . By substituting the known values of g, G, and R, the Earth’s mass is determined to be approximately 6 \times 10²⁴ kg.

This calculation was made possible when the value of G was first experimentally determined by Cavendish, earning him the distinction of being the first person to weigh the Earth.

Average Density of the Earth:

The average density of the Earth can also be estimated using its mass and volume. Although the density of the Earth’s upper layers is around 2700 kg/m³, the inner layers have much higher densities, leading to an overall average density of about 5500 kg/m³.