Ap physics algebra based intensity of 3d spherical waves

Question

the sun radiates energy at a rate of about 4 *10^26 W. Estimate how much of the suns energy is about 150*10^6 km from the sun. What assumptions did you make?

Answer 1

The answer to this question requires that you think in terms of the amount of energy that is emitted by the sun in one second..The power of the sun's emission is P=4*10²⁶.W. energy emitted in that 1 second is

E = P*t W*s = 4* 10²⁶ Joules. We assume that there is no absorption of energy as the emitted.energy travels to 150 *10^6 kilometers. This is reasonable because the planets and other space dust between the sun and the distance is extremely small so no radiation is absorbed.

The formal way to prove this would be to integrate the energy with spherical coordinates from the distance 0.5 s before the light is at R = 150 * 10 ⁶ km to the time period 0.5s after the radiation reaches 150* 10⁶ km.

See the diagram in the short Video I hope this solidifies your understanding Do'nt worry about the math in the diagram.