Jim asked:
I Need help from some of you math wiz-bangs. I looked up on a chart of surface brightness that M1 has a surface brightness of 35 * 10 to the minus 6; or .000035.
The answer is 20.6 mpsas. The following url links to my javascript calculator that includes an option "Convert extended object size (arcmins) and apparent brightness (V) to MPSAS". The back matter to the computation is in the bibliography: Formula: objB_mpas = objMagnitude + (2.5 * (Log10((PI() / 4) * objMajorAxis_arcsec * objMinorAxis_arcsec))) Sources: Clark, R.N., 1990. Appendix E in Visual Astronomy of the Deep Sky, Cambridge University Press and Sky Publishing.http://www.clarkvision.com/visastro/appendix-e.html Covington, M. (1998, 2d). Appendix A, Astrophotography for Amateurs. pp. 259-261 http://www.covingtoninnovations.com/ Clark's Appendix E contains pre-computed surface brightnesses in mpsas for about 620 commonly observed DSOs. Also note the related contrast index method for determining the contrast index between a given object and the current sky brightness. In general, I find the mpsas method of computing an object's surface brightness to be a good predictor for compact PNs and galaxies. It is a poor predictor for dispersed open clusters like M41. The difference between the predicted result and your first try is in the conversion of an elliptical object into magnitudes per square arcsec. That's the PI() / 4) * objMajorAxis_arcsec * objMinorAxis_arcsec part of the above equation. Note the obejct dimensions used in the formula are in arcsecs while the size of most DSO is given in arc minutes. Other variations between surface brightness estimates by Berry in the Handbook and Clark's Appendix E can be attributed to their differing estimates of the size of an object. Clear Skies - Kurt P.S. - Here's my vba code. The javascript code for the same can be found in the web page calculator above. Public Function PhotogObjectArea2MPAS(ByVal objMagnitude_tmp, ByVal objType_tmp As String, ByVal objMajorAxis_arcmin_tmp, ByVal objMinorAxis_arcmin_tmp, ByVal B_mpas_tmp As Double) As String ' Accepts Magnitude and dimensions and background B_mpas. ' Returns object brightness in MPAS and contrast index. ' Valid object types are " Extended | Stellar | Stellar-CI " ' Where object type is stellar, objMajorAxis_arcmin_tmp and objMinorAxis_arcmin_tmp are ignored. ' Source: Covington, M. Astrophotography for Amateurs, Appendix A ' Clark's Visual Astronomy of the Night Sky, Appendix E ' http://clarkvision.com/visastro/appendix-e.html ' Departs from Covington extended object model for stellar sources. ' For a stellar source, the V-mag is the MPSAS without adjustment for area. ' Tests and usage ' Test against objects in Clark's Appendix E catalogue ' Clark assumes dark sky background of 24.25 MPAS ' NGC7814 ' ? PhotogObjectArea2MPAS(12, 1, 5, 24.25) ' 22.3759059661737 0.749637613530523 ' Checks against Clark's results ' NGC40 ' ? PhotogObjectArea2MPAS(10.5, 1, 0.7, 24.25) ' 18.7412260553693 2.20350957785228 ' Checks against Clark's results ' NGC45 ' ? PhotogObjectArea2MPAS(7.8, 25, 40, 24.25) ' 23.9284809553336 0.128607617866541 ' Checks against Clark's results ' Define variables Dim objMagnitude, objMajorAxis_arcmin, objMinorAxis_arcmin, B_mpas As Double Dim objMajorAxis_arcsec, objMinorAxis_arcsec Dim objB_mpas, ContrastIndex As Double Dim strOut As String Dim objType As String ' Object type - Extended or Stellar Dim ContrastIndexStrOut ' Temporary working variable for output Dim strSpacer ' Temporary working variable for output ' Get input objMagnitude = objMagnitude_tmp objType = Trim(objType_tmp) objMajorAxis_arcmin = objMajorAxis_arcmin_tmp objMinorAxis_arcmin = objMinorAxis_arcmin_tmp B_mpas = B_mpas_tmp ' Convert object dimensions to arcsecs objMajorAxis_arcsec = 60# * objMajorAxis_arcmin objMinorAxis_arcsec = 60# * objMinorAxis_arcmin ' A) Convert objective size and v-mag to B_mpsas ' Departs from Covington extended object model for stellar sources. ' For a stellar source, the V-mag is the MPSAS without adjustment for area. Select Case objType Case "Extended" ' Compute results objB_mpas = objMagnitude + (2.5 * (Log10((PI() / 4) * objMajorAxis_arcsec * objMinorAxis_arcsec))) ' Contrast index formula is from http://clarkvision.com/visastro/appendix-e.html ContrastIndex = -0.4 * (objB_mpas - B_mpas) ContrastIndexStrOut = CStr(ContrastIndex) strSpacer = " " Case "Stellar" objB_mpas = objMagnitude ContrastIndex = -0.4 * (objB_mpas - B_mpas) ContrastIndexStrOut = CStr(ContrastIndex) strSpacer = " " Case "Stellar-CI" objB_mpas = objMagnitude ContrastIndex = -0.4 * (objB_mpas - B_mpas) ContrastIndexStrOut = CStr(ContrastIndex) strSpacer = " " Case "Not applicable" ' Should not be submitted to function, gracefully return zero objB_mpas = "" ContrastIndexStrOut = "" strSpacer = "" Case "Incomplete" ' Should not be submitted to function, gracefully return zero objB_mpas = "" ContrastIndexStrOut = "" strSpacer = "" Case Else ' Handle general error with graceful return of zero objB_mpas = "" ContrastIndexStrOut = "" strSpacer = "" End Select PhotogObjectArea2MPAS = Trim(CStr(objB_mpas)) & strSpacer & Trim(ContrastIndexStrOut) End Function