Question

If two planets orbit a star, but planet B is twice as far from the star as planet A, planet A will receive ____ times the flux that planet B receives.

Answer 1

The nearest plant (A) receives 4 times more radiation from the farthest plant

Step-by-step explanation:

The energy emitted by the star is distributed on the surface of a sphere, whereby intensity received is the power emitted between the area of ​​the sphere

I = P / A

P = I A

The area of ​​the sphere is

A = 4π r²

Since the amount of radiation emitted by the star is constant, we can write this expression for the position of the two planets

P = I₁ A₁ = I₂ A₂

I₁ / I₂ = A₂ / A₁

Suppose index 1 corresponds to the nearest planet,

r2 = 2 r₁

I₁ / I₂ = r₁² / r₂²

I₁ / I₂ = r₁² / (2r₁)²

I₁ / I₂ = ¼

4 I₁ = I₂

The nearest plant (A) receives 4 times more radiation from the farthest plant