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Author: CharlesBell

CometActiveFraction.py

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+# -*- coding: utf-8 -*-
+"""
+Created on Fri Mar 20 10:40:41 2020
+
+@author: charb
+
+Example 
+for comet 9P/Tempel
+r = 1.53
+albedo = 0.04
+Q = 6.8E+27  
+A = 1.7E+08
+f = 0.0056
+f = activeFraction = getActiveFraction(r, Q, A, albedo)
+print('f', f)
+
+"""
+# CometActiveFraction
+
+import math
+
+"""
+The Correlation Between Visual Magnitudes and Water Production Rates
+Jorda, L.; Crovisier, J.; Green, D. W. E.
+Asteroids, Comets, Meteors 2008
+LPI Contribution No. 1405, paper id. 8046
+Pub Date: 2008 
+Bibcode: 2008LPICo1405.8046J 
+link: https://www.lpi.usra.edu/meetings/acm2008/pdf/8046.pdf
+log Q[H2O] = 30.675 (0.007) – 0.2453 (0.0013) mH
+"""
+def getQH2OFromMagnitudeCorrelation(mH):
+    return math.pow(10, 30.675 - 0.2453 * mH)
+
+"""
+P. R. Weisman mass-brightness relationship for new comets (1991)
+log Mc = 20.0 - 0.4 log H10  -possible error
+log Mc = 20.0 - 0.4 * H10  mass in grams
+from a distribution of 256 long period comets compiled by Everhart 1967.
+Page 313 Introduction to Comets by John C. Brandt and Robert D. Chapman 2nd Edition
+Cambridge University Press, 2004
+http://adsabs.harvard.edu/abs/2004inco.book.....B
+
+Dynamical history of the Oort cloud
+Authors:	 Weissman, Paul R.
+Affiliation: AA(JPL, Pasadena, CA)
+Publication: In: Comets in the post-Halley era. Vol. 1 (A93-13551 02-90), p. 463-486.  1991
+Bibliographic Code:	1991ASSL..167..463W
+http://adsabs.harvard.edu/abs/1991ASSL..167..463W
+
+Title:	Intrinsic distributions of cometary perihelia and magnitudes
+Authors:	Everhart, Edgar
+Publication:	Astronomical Journal, Vol. 72, p. 1002 (1967) (AJ Homepage)
+Publication Date:	10/1967
+Origin:	ADS
+DOI:	10.1086/110376
+Bibliographic Code:	1967AJ.....72.1002E
+http://adsabs.harvard.edu/abs/1967AJ.....72.1002E
+"""
+def getNewCometMass(h10):
+    massGrams = math.pow(10, 20.0 - 0.4 * h10)
+    return massGrams 
+
+
+"""
+        r^2 Q m L
+f = ---------------------
+      1368 A (1 - a)
+	
+r = heliocentric distance in AU
+solar conststant S = 1368 watts/m^2
+Q = water production rate in mol/sec
+m = mW or mass of water molecule 3.0 x 10^-26 kg
+L = 2.62 x 10^6 Joule/kg
+A = area in m^2
+a =  albedo
+Comet 9P/Tempel 1: before and after impact
+David W. Hughes
+Monthly Notices of the Royal Astronomical Society, Volume 365, Issue 2, 11 January 2006, 
+Pages 673–676, https://doi.org/10.1111/j.1365-2966.2005.09742.x
+Published: 11 January 2006
+for r = 1.53 AU, albedo = 0.04, Q = 6.8 x 10^27  A = 1.7 x 10^8, f = 0.0056
+"""
+def getActiveFraction(r, Q, A, albedo):
+    m  = 3E-026
+    S = 1368
+    L = 2.62E+006 
+    return (r * r * Q * m * L)/(S * A * (1 - albedo))
+
+
+rn = 2000
+area = 4*math.pi*rn*rn
+
+# JPL Horizons ephemeris for 2020-Mar-20 
+r = 1.686892344370
+delta = 1.09209154734205
+
+# Approximate total mag from recent COBS data by observers Maik Meyer and Carl Hergenrother
+vmag = 8
+
+mH = vmag - 5 * math.log10(delta)
+print('heliocentric distance r ', r)
+print('observer distance delta ', delta)
+print('V magnitude', vmag)
+print('heliocentric magnitude mH ', mH)
+QH2O = getQH2OFromMagnitudeCorrelation(mH)
+
+print('QH2O mol/s ', QH2O)
+
+# JPL Horizons 
+#    M1=  7.9      M2=  13.3     k1=  21.    k2=  5.      PHCOF=  .030           
+h10 = 7.9
+cometMassGrams = getNewCometMass(h10)
+cometMassKG = cometMassGrams* 0.001
+
+"""
+The Rosetta blog (Emily Baldwin Senior Science Editor) 
+preliminary science data on comet 67P/Churyumov-Gerasimenko October 3, 2014
+Density	0.4 g/cm^3 = 400 kg/m^3
+"""
+density  = 400
+volume = cometMassKG/density
+
+albedo = 0.04
+radius = math.pow((3 * volume / (4 * math.pi)),0.33333333)
+area = 4 * math.pi * radius * radius
+activeFraction = getActiveFraction(r, QH2O, area, albedo)
+print('mass Kg', cometMassKG)
+print('volume m^3', volume)
+print('radius  m^2', radius)
+print('activeFraction ', activeFraction)
+