Question

Estimate how much energy Earth receives from the Sun every year.

The solar constant is about 1000 Watts per square meter.

An area scales as a distance squared.

1. Estimate the surface area of the Earth facing the Sun (in meters²)

2. Estimate how much power reaches the Earth's surface (in Watt).

3. Estimate how much solar energy reaches the earth per year (in Joule).

4. Estimate the current annual world consumption of energy per year (in Joule).

5. Estimate the ratio of the energy delivered by the Sun to the energy consumed by humans.

Answer 1

(1)

The surface area of the Earth facing the sun is equal to the area of a disc of radius same as that of the Earth.

where R_E is the radius of the Earth.

The radius of the earth is

(2)

Solar constant is the rate at which the energy from the sun reaches Earth. Given S=1000W/m². Total power received by the Earth is

(3)

1 Watt = 1 Joule per second.

The Earth constantly receive the energy from the sun at rate .

1 year has 365 days, each day has 24 hours, each hour has 60 minutes, and each minute has 60 seconds. So,

Total energy received by the Earth from the Sun in 1 year is

(4)

The current annual world consumption of energy is estimated to be

(5)