alright I am having a big issue with getting this question started up properly.

Question

alright I am having a big issue with getting this question started up properly. I would love some help with setting this up and possibly more depending on what set up is required. I will write the question out word-for-word and ask that someone help me out pleaes.

Assuming that the distance between the Earth and the Sun is approximately 1.5E11m, the mass of the sun is 1E31g, and that the energy fluence imparted on the Earth from the sun is 1.4E3W m^(-2), how long do we have before the sun runs out of fuel?

Please help.

Explanation / Answer

Hi, so the flux of energy from the sun can be thought of as being even distributed throughout the whole surface are of the sun.

If we take F= Flux

Then the flux at a distance follows an inverse square law. The surface area of a sphere is 4*Pi*r^2

Thus if you take F / 4*Pi*r^2 you can calculate the flux received per unit area of a sphere. If you make the radius of this sphere be the distance from the earth to the sun you will then get 1.4 *10^3 W / m^2

F / 4*Pi*(1.5*10^11 m)^2 = 1.4 *10^3 W / m^2

From this you can get the flux of energy escaping the sun

1.4 *10^3 W / m^2 *4*Pi*(1.5*10^11 m)^2 =Flux in watts

Now a watt is a unit of energy equal to 1 J/s.

To get how long the sun has before running out of fuel you need to calculate how much energy total the sun has.

I am not sure how you are asked to calculate this. If you are just assuming the sun burns up all its mass according to E=mc^2

Then the time would just be E/ Flux in Watts

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