How close to the sun would a spacecraft have to go to reach the distance at which the flux of solar energy is 20 times as large as the solar energy flux at the earth?

1 Answer
Jan 17, 2016

.22 AU

Explanation:

The total amount of energy that that a star gives off is called the luminosity of the star. Luminosity cannot be measured directly for a star, however astronomers can measure how much energy is received from a star over a given area. That quantity is flux. Flux and luminosity are related by the formula;

L=4πR2f

Where L is luminosity, f is flux, and R is the distance to the star. We can rearrange this expression to solve the flux.

f=L4πR2

We can find the distance by setting the ratio of fluxes equal to 20.

f1f2=L4πR21L4πR22=R22R21=20

Rearranging the terms we get;

R21=R2220

R1=R220=(.22)R2

The distance between the Earth and the sun is defined to be 1 astronomical unit, so we can use this distance as R2, so when the spacecraft is as .22 AU, the flux will be 20 times the flux at Earth.