Apparent Brightness

[ASTRONOMYCLASS]

<p>The question is as follows -- The distance from Earth of the Red Supergiant Betelgeus is approximately 427 LY. If it were to explode as a supernova it would be one of the brightest stars in the sky. Right now the brightest star other than the Sun is Sirius, with a Luminosity of 26Lsun and a distance of 8.6 LY. How much Brighter than sirius would the Betelgeus supernova be in our sky if it reached a maximum luminosity of 10 ^10 Lsun? </p><p>&nbsp;</p><p>I know we need to use the calculation of Apparent Brightness = Luminosity / 4 pie R squared&nbsp; and find a ratio, but I am stuck at what the problem would look like. Any help would be greatly appreciated </p><p>&nbsp;</p><p>Thankyou</p>

 

[Mee_n_Mac]

Replying to:<BR/><DIV CLASS='Discussion_PostQuote'>The question is as follows -- The distance from Earth of the Red Supergiant Betelgeus is approximately 427 LY. If it were to explode as a supernova it would be one of the brightest stars in the sky. Right now the brightest star other than the Sun is Sirius, with a Luminosity of 26Lsun and a distance of 8.6 LY. How much Brighter than sirius would the Betelgeus supernova be in our sky if it reached a maximum luminosity of 10 ^10 Lsun? &nbsp;I know we need to use the calculation of Apparent Brightness = Luminosity / 4 pie R squared&nbsp; and find a ratio, but I am stuck at what the problem would look like. Any help would be greatly appreciated &nbsp;Thankyou <br />Posted by <strong>ASTRONOMYCLASS</strong></DIV><br /><br />Let me point the way with&nbsp;3 questions.&nbsp; How much brighter would Sirius appear to be to us here on Earth&nbsp;if, keeping it's distance @ 8.6 LY, it went from 26 to 10^10 Lsuns ?&nbsp; (I'm assuming Lsun is luminosity relative to the Sun, ie 26 times or 10^10 times as luminous as the Sun)&nbsp; If 2 things have the same luminosity but differ only in their distance from the Earth, what's their difference in&nbsp;apparent brightness (using your formula).&nbsp; If it helps lets say you have a star with 1Lsun at 8.6 LY and another star with 1Lsun @ 427 LY.&nbsp;&nbsp; What's the apparent brightness of each ? <div class="Discussion_UserSignature"> <p>-----------------------------------------------------</p><p><font color="#ff0000">Ask not what your Forum Software can do do on you,</font></p><p><font color="#ff0000">Ask it to, please for the love of all that's Holy, <strong>STOP</strong> !</font></p> </div>

 

[Saiph]

<p>Well, you've got everything you need right there in the problem &nbsp; I like stating the obvious.</p><p>I think you're trying to make it a bit harder on yourself than you have to.&nbsp; If you want an elegant approach, you can try to do some algebra beforehand and make a ratio by dividing the equation for sirius by the equation for betelguese, canceling like terms and then plugging numbers in for the rest.</p><p>&nbsp;</p><p>But you could do a straightforward plug and chug approach here if you'd like.&nbsp; You have the numbers for all the vairables accept the apparent brightness, which is what you're looking for anyway.&nbsp; Just plug the numbers in for each, then compare the answer for sirius to the answer for Betelguese (simple division).&nbsp; and Viola! </p><p>&nbsp;</p><p>another tip...running the numbers myself, it looks like you'll get a really big number, so don't panic if you <strong>don't</strong> get something "reasonable" like, oh 5 times brighter. </p> <div class="Discussion_UserSignature"> <p align="center"><font color="#c0c0c0"><br /></font></p><p align="center"><font color="#999999"><em><font size="1">--------</font></em></font><font color="#999999"><em><font size="1">--------</font></em></font><font color="#999999"><em><font size="1">----</font></em></font><font color="#666699">SaiphMOD@gmail.com </font><font color="#999999"><em><font size="1">-------------------</font></em></font></p><p><font color="#999999"><em><font size="1">"This is my Timey Wimey Detector.  Goes "bing" when there's stuff.  It also fries eggs at 30 paces, wether you want it to or not actually.  I've learned to stay away from hens: It's not pretty when they blow" -- </font></em></font><font size="1" color="#999999">The Tenth Doctor, "Blink"</font></p> </div>