Question

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?

Answer 1

.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 = 4pi R^2 f`

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 = L/(4pi R^2)`

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

`(f_1) / (f_2) = (L/(4pi R_1^2))/(L/(4pi R_2^2)) = R_2^2/R_1^2 =20`

Rearranging the terms we get;

`R_1^2 =R_2^2/20`

`R_1 = R_2/sqrt(20) = (.22) R_2`

The distance between the Earth and the sun is defined to be 1 astronomical unit, so we can use this distance as `R_2`, so when the spacecraft is as .22 AU, the flux will be 20 times the flux at Earth.