thought I'd give you a little bit of a help with the homework problems that are on homework chapter 17 for Astro 120 the first of the mathematical questions is number 14 it's the question that relates how much flux would Jupiter receive from our Sun versus how much flux we receive at the earth and it kind of shows you you know that it's a matter of setting up doesn't show you but it implies that we set up a ratio to figure this out what's our master equation for luminosity and flux well the flux of any star received at a certain location is given by this formula the power of the source the velocity divided by four PI d squared where D at the distance between the source giving off that amount of power and where the flux is actually received so since our source of luminosity is our Sun and of course both the Earth and Jupiter are experiencing the same source of power from this object it's only a matter of their differences in distances that determines the flux that we receive at these two locations so what's your hypothesis do we achieve more or less flux in Jupiter's distance from the Sun yeah of course red is further away and how much further away is it well if Earth is one astronomical unit away from the Sun it tells you that Jupiter is five times that distance are five au s-- away from the Sun so all right the implication we're going to set up a ratio and I'm going to set up like this I'm going to say the flux received at Jupiter I'll call that the versus the flux received at Earth and then substitute in know what the equation is for that for F in both instances Jupiter's case you're gonna have L divided by 4 pi de in this case it'll be the Jupiter son distance say J - s for Jupiter son distance and don't forget to square it / same equation for Earth's flux recedes so it's all divided by 4 PI D but in this case it's for some distance of es and don't forget to square it and it looks like a real mess but here's the good part a lot of this stuff is going to cancel out from the from the ratio R isn't it the luminosity estimate for that the Sun and again luminosity does not differ as you get further and further away from it its total power output is the same so the elves cancel and what else cancels the constants right for pi in both instances so 4pi goes away here and 4pi goes away here well you're left with in the DS aren't you so this reduces to 1 over the distance that Jupiter from our Sun squared divided by 1 over the distance of Earth from our Sun squared and that's that's a very strange-looking fraction well that one was - but what do you recall about taking a fractions of fractions when you're dividing a fraction by a fraction what's the rule take the denominator inverted flip it and multiply through the numerator so if I do that correctly flip this and multiply through by the top I'll get 1 over well let's take it away sorry well get the distance of Earth to the Sun make sure to show it huh so I'm going to take this D a piece of s squared all over 1 I'm flipping it multiplying through by what's in the numerator better what's that equal its business of hearth design the square divided by distance from Jupiter to the Sun square now would it be nice if these are both in the same units like meters or inches or astronomical units so they would both cancel out their their units and answer of course is yes the problem did give it to you that way didn't it so all right get out here taking this distance of Earth the Sun is just one a you and I got a square it and dividing it by it's the Jupiter some distance in astronomical units that's equal to five isn't it five eight squared I'm gonna get you know one squared is one and it will be an au squared moment and in five squared is 25 that'll also be au squared let's again the units are going to cancel and what do you have ultimately it's just 1 over 25 isn't it now that relates to this fraction so you know Jupiter gets the numerator one and earth gets the denominator the 25 so the amount of flux that Jupiter receives is only one compared to 25 times what the earth gets or it's only 125th as much flux as earth receives so algebraically you can just write in the end do over here that the Flex received in Jupiter's just equal to multiply it through and give me get 1 over 25 times the flux species yeah there's a nice way to write a that's sort of a final answer so the hardest part of these questions when it says compare as always oh it's implying to take a fraction or to take a ratio in the south or the equation and many times things cancel out nicely and it really just comes down to a number that relates one value to the other just number 14