# The radiation power of the Sun is L0 = 4 • 10 ^ 26 watts. How much energy will the sun emit in one year?

The radiation power of the Sun is L0 = 4 • 10 ^ 26 watts. How much energy will the sun emit in one year? According to the theory of relativity, energy is equivalent to mass, so estimate how much mass the Sun loses each year through radiation. The sun will “die” if it loses 0.001 of its mass. Estimate the lifetime of the sun.

In one year (3 • 10 ^ 7 s) the Sun will radiate energy E = L0 • t = 4 • 10 ^ 26 • 3 • 10 ^ 7 = 1.2 • 10 ^ 34J. According to A. Einstein E = mc2, therefore, the mass lost to radiation is m = E / c ^ 2 = 1.2 * 10 ^ 34 / (3 * 10 ^ 8) ^ 2 = 1.3 * 10 ^ 17 kg. Since the mass of the Sun is M = 2 • 10 ^ 30 kg, the Sun before death can only lose
ΔM = 2 • 10 ^ 27kg. Therefore, the Sun can live only t = ΔM / m = 1.5 • 10 ^ 10 years.

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