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*Compute the flux of neutrinos arriving at Earth, i.e. the number of neutrions that land on each square meter of Earth's surface each second*.The question is referring to neutrinos created in the photon-photon chain in the Sun.

I already computed that the Sun releases [tex]1.78*10^{38}[/tex] neutrinos per second in the photon-photon chain.

So 1 square meter, if face-on to the Sun at Earth's distance should intercept[tex]\frac{1}{4 \pi r^2}*1.78*10^{38} [/tex] neutrinos per second, where r is 149598000000 the radius of Earth's orbit in meters.

So, 1 square meter, if face-on to the Sun at Earth's distance should intercept [tex]6.33*10^{14} neutrinos/s[/tex]

I have a feeling that this is the answer the teacher will consider correct. However, not all square meters on Earth's surface are face-on to the Sun. Only square meters where the Sun is directly overhead will receive a full dosing of [tex]6.33*10^{14} neutrinos/s[/tex]. Square meters of Earth's surface where the Sun is setting or rising should receive 0 neutrinos (consider the Sun a point or a whole new can of worms is opened!)

All points inbetween will receive anywhere between 0 and [tex]6.33*10^{14} neutrinos/s[/tex].

But the change from minimum to maximum not a linear function, so I can't just average it. What would I use to compute the average flux? Can I avoid integrating? This class is supposed to avoid Calculus, but I have a feeling the integration in this case is easy since it is related only to SIN.

Any thoughts?...