all right for number 18 on chapter 17 homework it's a question that relates apparent and absolute magnitudes to each other remember what these quantities actually you know tell us apparent magnitude you know how bright a star appears to be which is a function of both its true power to the manasa T as well as its distance and the further way any star gets from he of course the the dimmer it becomes and the apparent magnitude goes up doesn't larger members mean dimmer absolute magnitude is a hypothetical value if you had all the stars at the exact same distance away from you 10 parsecs is the is the hypothetical for a absolute magnitude then how bright would they appear to be well no longer is it a function of distance they're all the same distance away from you and therefore whoever would appear to be the brightest would truly be the most powerful wouldn't they they would have the greatest luminosity so absolute magnitude or a capital M in this equation is a is really a measurement of true power luminosity and apparent magnitude not so much that's more about your location the galaxies and where these other stars are located as well okay so I got this fairly complicated and mathematical equation and it says you know hypothetically if you had a star with a parent magnitude of 5 the name was the star from number 11 in the homework set which was a and now we know a thousand it's not even the right number it's number 17 the one before it but it's a thousand parsecs away then how would we go about calculating its absolute magnitude well over here on the Left I'm going to write down that log base 10 logs at least are not that complicated the log of 10 is equal to 1 because it has one zero the log of 100 is equal to two and the log of a thousand if she figured it out is 3 so you know how do you write these numbers otherwise 10 and 100 and 1000 you write them is you know 10 is just 10 to the 1st power isn't it right 100 is 10 to the 2nd power a thousand is 10 to the 3rd power so this value appear in the exponent is merely what the log this number is equivalent to the log of 10 to the second is to the log of 10 to the third is 3 okay so it's not quite as complicated maybe as you thought it was a second ago now back to my problem for number 18 it would like me to get the value for the absolute magnitude capital M so let's solve the capital M I'm gonna leave capital m on the left side of the equation and get rid of the smaller so I got to subtract that from both sides don't act so negative Big M is equal to 5 times the log of D minus 5 and then minus algebra now finally make both if I were to make the capital M a positive value not a negative value but have to multiply through the entire equation by negative 1 don't I so that flips the sign and everything so that becomes the capital M is equal to negative 5 times the log of D plus 5 plus M yep all the signs change okay my master working with this I think so again the misprinted never talked about this in question 18 is talking about the star number 11 it's the star number 17 the one right before it which we just calculated heading distance up a thousand parsecs so the log of a thousand is three and therefore we got Capital m is equal to negative five times the log of D which I now know the log of a thousand it's gonna be three and they don't forget to add five and what was the apparent magnitude given to you in the problem it was awesome equal to five so I'm just substituting in numbers here aren't I I know what D is now and I know what M is that was given to me so the final step is well this is 1/2 negative 5 times log of a thousand three plus five plus five well hit the pause button now you're back I forgot to say what to do when you hit the pause button but try to solve this in your head what do you get negative 5 times 3 is negative 15 right negative 15 plus 5 or it would be negative 10 plus 5 more would be negative 5 so what would the absolute magnitude of that start be I'd be negative 5 and it's a negative value so you know that tells you what about this object tells you would be incredibly brilliant right so the star was you know a thousand part our thousand parsecs away then my goodness you know what would in if it was still showing up as a parent magnitude five you can actually see with your naked eye ball it would have to be incredibly brilliant which is exactly what it's true let's start with an O with an absolute magnitude to make it applied 18