Explanation

To calculate the moment of inertia of the Earth about its diameter, we can use the formula for the moment of inertia of a sphere:

I = (2/5)MR^2

where:

I = moment of inertia

M = mass of the Earth (10^25 kg)

R = radius of the Earth (diameter/2 = 12800 km / 2 = 6400 km = 6.4 × 10^6 m)

Plugging in the values, we get:

I = (2/5) × 10^25 kg × (6.4 × 10^6 m)^2

= (2/5) × 10^25 kg × 4.096 × 10^13 m^2

= 1.6384 × 10^38 kg m^2

≈ 1.64 × 10^38 kg m^2