document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=277976>Question 277976</A>: <I><SPAN STYLE=\"word-break: break-all;\"> PLEASE HELP!!<BR>\n" );
document.write( "What is the ratio in brightness of Sirius, with apparent magnitude -1.44, to Polaris, with apparent magnitude 1.97?<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #202321 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=202321\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I got your answer from the following link:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<a  rel=nofollow HREF= \"http://en.wikipedia.org/wiki/Apparent_magnitude\" target = \"_blank\">http://en.wikipedia.org/wiki/Apparent_magnitude</a>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The apparent magnitude of Sirius is -1.44, and the apparent magnitude of Polaris is 1.97. Polaris is the fainter of the two stars, while Sirius is the brighter.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Difference in magnitude:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x = 1.97 - (-1.44) = 3.41\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Variation in brightness:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "vb = 2.512^{3.41} = 23.124\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "This means that sirius is 23.124 * the brigtness of Polaris.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The lower the magnitude number, the brighter the star.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "This stems from the greeks where they said the brightest star has a magnitude of 1 and the dimmest star seen with the naked eye has a magnitude of 6.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The modern system is slightly different but the concept is the same.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The brighter star has a magnitude less than the magnitude of the dimmer star.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "I won't pretend to really understand what they are saying, but this is how it works.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The difference in magnitude is the higher magnitude minus the lower magnitude.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Since Polaris magnitude is 1.97 and Sirius magnitude is -1.44, this becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1.97 - (-1.44) = 3.41.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The ratio between Polaris and Sirius becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "2.512 ^ 3.41 = 23.37630387 which means that:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Sirius is 23.37630387 times as bright as Polaris.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The second reference below describes how the base of 2.512 in the equation for the ratio was developed.   This was also mentioned in the first reference but I somehow clicked with the answer after using the second reference.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<a  rel=nofollow HREF= \"http://www.astronomynotes.com/starprop/s4.htm\" target = \"_blank\">http://www.astronomynotes.com/starprop/s4.htm</a>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The basis for that is that a star with a magnitude of 1 appears to be 100 times as bright as a star with a magnitude of 6.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "If you take a star with a brightness of 20 and you take a star with a brightness of 100 * 20 = 2000, then the star with the brightness of 2000 will have a magnitude of 1 and the star with the brightness of 20 will have a magnitude of 6.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The difference in magnitude will be 6 - 1 = 4\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The variation in magnitude will be 2.511886432^5 = 100\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Once again, my numbers might be off by a little, but the concept is the same.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "In either case, the formulas as stated are how you would find the difference in the mnagnitude and the ratio in brightness between Sirius and Polaris.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Hopefully this is what you were looking for.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );