for number 15 on homework chapter 17 the question is asking about the main sequence star regulus alpha Leonys the brightest star in the constellation of Leo has a mass of about 5 times that of the Sun and it says use the mass the velocity relationship to eliminate our estimate excuse me estimate the luminosity of Regulus well you know what's the importance of the fact that it's a main sequence star it's the fact that the mass the velocity relationship only works for main sequence stars so that was key and now we know that our Sun is also the main sequence star so all right bully we can actually do this the mask luminosity relationship states that the luminosity of the star compared to the luminosity of the Sun is almost equal to the mass of that star compared to the mass of the Sun all raised to the 3.5 power you know that's the more technical way that I write it your author uses you know to the parrot or to the fourth but I'm going to use to the 3.52 bit more accurate so what does this equation when they state eye with the luminosity of the star compared to the luminosity of the Sun a ratio if I just know how much more massive that star is compared to the Sun and you know that's what the problem is telling me isn't it so all right if I substitute in the values it's a little bit off see the star compared to the luminosity of the Sun is equal to how much more massive is the star compared to the Sun it's five times already in parentheses years is just five solar masses divided by one solar mass so it's just five and then don't forget to raise it to the three and a half power so on your calculator you know how do you do this right will you punch in five and then there's a button on your calculator probably looks like this you know like to the X or maybe still we're at X to the Y that's just telling you that whatever you input you know the five you can raise it to whatever other value you'd like to raise it to so it's five and then hit the button and then type in 3.5 and you'll be able to raise it to this kind of keep our three and a half after doing so what do you get tri yeah I got two hundred seventy nine point five it's a ratio so what's it telling us it says the luminosity of our star is how much more than the sun's or how much more power doesn't put out to the Sun versus almost you know three hundred times as much power even though it only has five times as much fuel five times it's a much mass so what again is that implying sure you got five times the amount of fuel but if you're burning it at three hundred times the rate what's gonna happen they gonna flame it out much faster aren't you yeah you have a much quicker lifespan as a result so it's always true of our billion and massive stars as they have intense and very short durations to their lifetimes because of just how brightly they burn if you will or how much power they put out every single second