Average Moon Temperature

Answer = 200.2 K

The Diviner Lunar Radiometer Experiment onboard the Lunar Reconnaissance Orbiter (LRO) has been acquiring moon data since July 2009. A very detailed paper [Williams 2017] was written, yet nowhere does it answer the simple question: what is the average temperature of the moon?

[Nikolov & Zeller 2014] intelligently guessed that the mean moon temperature is 197.3 K, based on techniques and data from [Vasavada 2012].

Today I will be using derived diviner data to calculate the average temperature on the moon. My data has two sources: UCLA and WUSTL. The first has hourly data, and the other has 15 minute data (although many fields are missing). The final result of the two should not differ highly.

I will be using a moon flattening parameter of 1/581.9 from [Araki 2009].

Paste the following into a new file called moontemp.sh:

# source moontemp.sh
# Zoe Phin, 2020/02/12

download1() {
    for l in {000..345..15}; do                   
        echo http://luna1.diviner.ucla.edu/~jpierre/diviner/level4_raster_data/diviner_tbol_snapshot_${l}E.xyz        
    done | wget -ci -
}

download2() {
    base="https://pds-geosciences.wustl.edu/lro/lro-l-dlre-4-rdr-v1/lrodlr_1001/data/gcp"
    for l in {0..8}; do let m=l+1; wget -c $base/global_cumul_avg_cyl_${l}0n${m}0n_002.tab; done    
    for l in {9..1}; do let m=l-1; wget -c $base/global_cumul_avg_cyl_${l}0s${m}0s_002.tab; done 
}

avg() { 
    awk '{ f=1/581.9; e=2*f-f^2; r=atan2(0,-1)/180
        T[$1]+=$3; N[$1]+=1; A[$1]+=r/2876.71*(1-e)*cos(r*$1)/(1-e*sin(r*$1)^2)^2
    } END { for (L in T) print L" "T[L]/N[L]" "A[L]}' | sort -n | awk '{
        printf "%6.2f %7.3f %.9f\n", $1, $2, $3; T+=$2*$3
    } END {printf "\nMoonT: %7.3f\n", T}'
}

calc_ucla() {
    awk '{T[$2" "$1]+=$3;N[$2" "$1]+=1} END {for (L in T) print L" "T[L]/N[L]}' *.xyz | avg 
}

calc_wustl() {
    awk -F, '$11>0{T[$2" "$1]+=$11;N[$2" "$1]+=1} END {for (L in T) print L" "T[L]/N[L]}' *.tab | avg          
}

Source the file and download all:

> source moontemp.sh
> download1
> download2

Run UCLA data:

> calc_ucla

-89.75 110.538 0.000019126
-89.25 111.747 0.000057376
-88.75 100.500 0.000095622
-88.25  86.845 0.000133861
-87.75  95.390 0.000172088
-87.25  93.020 0.000210302
-86.75 102.408 0.000248500
-86.25 111.180 0.000286677
-85.75 115.274 0.000324832
-85.25 116.388 0.000362962
-84.75 108.500 0.000401062
-84.25 114.433 0.000439131
-83.75 121.392 0.000477164
-83.25 127.846 0.000515160
-82.75 131.893 0.000553116
-82.25 128.598 0.000591027
-81.75 129.399 0.000628891
-81.25 128.545 0.000666706
-80.75 133.838 0.000704468
-80.25 136.010 0.000742174
-79.75 138.313 0.000779822
-79.25 137.705 0.000817407
-78.75 138.701 0.000854928
-78.25 139.370 0.000892381
-77.75 144.802 0.000929764
-77.25 146.782 0.000967073
-76.75 144.926 0.001004310
-76.25 148.518 0.001041460
-75.75 149.069 0.001078530
-75.25 152.516 0.001115520
-74.75 152.217 0.001152410
-74.25 152.631 0.001189220
-73.75 152.798 0.001225930
-73.25 155.469 0.001262550
-72.75 156.950 0.001299060
-72.25 159.616 0.001335480
-71.75 160.702 0.001371780
-71.25 161.436 0.001407980
-70.75 161.486 0.001444070
-70.25 161.645 0.001480050
-69.75 163.806 0.001515910
-69.25 164.137 0.001551640
-68.75 165.462 0.001587260
-68.25 167.220 0.001622750
-67.75 168.373 0.001658120
-67.25 168.937 0.001693350
-66.75 170.094 0.001728450
-66.25 169.680 0.001763410
-65.75 170.751 0.001798240
-65.25 173.129 0.001832920
-64.75 173.381 0.001867460
-64.25 173.632 0.001901860
-63.75 173.722 0.001936100
-63.25 174.360 0.001970190
-62.75 175.614 0.002004130
-62.25 177.573 0.002037910
-61.75 179.016 0.002071530
-61.25 178.989 0.002104990
-60.75 179.494 0.002138290
-60.25 179.960 0.002171410
-59.75 181.011 0.002204370
-59.25 182.461 0.002237150
-58.75 182.690 0.002269760
-58.25 183.011 0.002302190
-57.75 183.615 0.002334440
-57.25 184.528 0.002366510
-56.75 185.143 0.002398400
-56.25 186.270 0.002430100
-55.75 186.498 0.002461600
-55.25 187.116 0.002492920
-54.75 187.195 0.002524040
-54.25 188.222 0.002554970
-53.75 188.844 0.002585690
-53.25 189.003 0.002616220
-52.75 189.486 0.002646540
-52.25 190.722 0.002676650
-51.75 191.521 0.002706560
-51.25 192.018 0.002736260
-50.75 192.537 0.002765740
-50.25 192.778 0.002795010
-49.75 193.104 0.002824070
-49.25 193.643 0.002852900
-48.75 193.701 0.002881510
-48.25 194.512 0.002909900
-47.75 194.982 0.002938070
-47.25 195.687 0.002966010
-46.75 196.402 0.002993710
-46.25 196.603 0.003021190
-45.75 197.278 0.003048430
-45.25 197.688 0.003075440
-44.75 197.725 0.003102210
-44.25 198.564 0.003128740
-43.75 199.242 0.003155030
-43.25 199.568 0.003181080
-42.75 199.526 0.003206880
-42.25 199.664 0.003232430
-41.75 200.097 0.003257730
-41.25 200.912 0.003282790
-40.75 201.339 0.003307590
-40.25 202.002 0.003332140
-39.75 202.196 0.003356430
-39.25 202.276 0.003380460
-38.75 202.741 0.003404230
-38.25 203.329 0.003427750
-37.75 203.479 0.003451000
-37.25 203.857 0.003473980
-36.75 204.337 0.003496700
-36.25 204.448 0.003519150
-35.75 204.869 0.003541330
-35.25 205.275 0.003563240
-34.75 205.667 0.003584880
-34.25 205.934 0.003606240
-33.75 206.271 0.003627330
-33.25 206.483 0.003648140
-32.75 206.833 0.003668680
-32.25 207.007 0.003688930
-31.75 207.205 0.003708900
-31.25 207.485 0.003728590
-30.75 207.829 0.003747990
-30.25 208.459 0.003767110
-29.75 208.617 0.003785940
-29.25 208.895 0.003804480
-28.75 209.002 0.003822740
-28.25 208.976 0.003840700
-27.75 209.538 0.003858370
-27.25 209.768 0.003875750
-26.75 210.352 0.003892830
-26.25 210.413 0.003909620
-25.75 210.867 0.003926110
-25.25 211.035 0.003942300
-24.75 211.327 0.003958190
-24.25 211.227 0.003973790
-23.75 211.620 0.003989080
-23.25 212.096 0.004004070
-22.75 212.105 0.004018760
-22.25 212.073 0.004033140
-21.75 212.344 0.004047210
-21.25 212.649 0.004060980
-20.75 212.928 0.004074450
-20.25 213.122 0.004087600
-19.75 213.306 0.004100450
-19.25 213.395 0.004112980
-18.75 213.606 0.004125210
-18.25 213.724 0.004137120
-17.75 213.809 0.004148720
-17.25 214.029 0.004160010
-16.75 214.091 0.004170990
-16.25 214.020 0.004181650
-15.75 214.188 0.004191990
-15.25 214.468 0.004202020
-14.75 214.733 0.004211730
-14.25 214.766 0.004221120
-13.75 214.743 0.004230200
-13.25 215.075 0.004238950
-12.75 215.175 0.004247390
-12.25 215.205 0.004255510
-11.75 215.291 0.004263300
-11.25 215.631 0.004270780
-10.75 215.731 0.004277940
-10.25 215.824 0.004284770
 -9.75 215.847 0.004291280
 -9.25 216.019 0.004297470
 -8.75 216.254 0.004303330
 -8.25 216.301 0.004308870
 -7.75 216.361 0.004314090
 -7.25 216.454 0.004318980
 -6.75 216.384 0.004323550
 -6.25 216.570 0.004327790
 -5.75 216.539 0.004331710
 -5.25 216.662 0.004335300
 -4.75 216.713 0.004338570
 -4.25 216.684 0.004341510
 -3.75 216.822 0.004344120
 -3.25 217.028 0.004346410
 -2.75 217.014 0.004348370
 -2.25 217.030 0.004350000
 -1.75 217.149 0.004351310
 -1.25 217.148 0.004352290
 -0.75 217.118 0.004352940
 -0.25 217.131 0.004353270
  0.25 217.131 0.004353270
  0.75 217.240 0.004352940
  1.25 217.215 0.004352290
  1.75 217.240 0.004351310
  2.25 217.256 0.004350000
  2.75 217.107 0.004348370
  3.25 217.113 0.004346410
  3.75 217.040 0.004344120
  4.25 216.983 0.004341510
  4.75 216.931 0.004338570
  5.25 216.871 0.004335300
  5.75 216.831 0.004331710
  6.25 216.701 0.004327790
  6.75 216.656 0.004323550
  7.25 216.717 0.004318980
  7.75 216.789 0.004314090
  8.25 216.628 0.004308870
  8.75 216.441 0.004303330
  9.25 216.380 0.004297470
  9.75 216.352 0.004291280
 10.25 216.287 0.004284770
 10.75 216.194 0.004277940
 11.25 216.113 0.004270780
 11.75 215.904 0.004263300
 12.25 215.766 0.004255510
 12.75 215.754 0.004247390
 13.25 215.668 0.004238950
 13.75 215.504 0.004230200
 14.25 215.449 0.004221120
 14.75 215.361 0.004211730
 15.25 215.048 0.004202020
 15.75 214.742 0.004191990
 16.25 214.674 0.004181650
 16.75 214.590 0.004170990
 17.25 214.502 0.004160010
 17.75 214.531 0.004148720
 18.25 214.349 0.004137120
 18.75 214.273 0.004125210
 19.25 214.167 0.004112980
 19.75 213.801 0.004100450
 20.25 213.556 0.004087600
 20.75 213.123 0.004074450
 21.25 213.120 0.004060980
 21.75 212.942 0.004047210
 22.25 212.636 0.004033140
 22.75 212.513 0.004018760
 23.25 212.112 0.004004070
 23.75 211.977 0.003989080
 24.25 211.909 0.003973790
 24.75 211.629 0.003958190
 25.25 211.476 0.003942300
 25.75 211.027 0.003926110
 26.25 210.862 0.003909620
 26.75 210.510 0.003892830
 27.25 210.405 0.003875750
 27.75 210.150 0.003858370
 28.25 209.810 0.003840700
 28.75 209.589 0.003822740
 29.25 209.128 0.003804480
 29.75 209.121 0.003785940
 30.25 208.887 0.003767110
 30.75 208.520 0.003747990
 31.25 208.118 0.003728590
 31.75 207.895 0.003708900
 32.25 207.487 0.003688930
 32.75 207.224 0.003668680
 33.25 206.852 0.003648140
 33.75 206.578 0.003627330
 34.25 206.238 0.003606240
 34.75 205.897 0.003584880
 35.25 205.553 0.003563240
 35.75 205.236 0.003541330
 36.25 204.862 0.003519150
 36.75 204.382 0.003496700
 37.25 204.062 0.003473980
 37.75 203.723 0.003451000
 38.25 203.273 0.003427750
 38.75 202.940 0.003404230
 39.25 202.578 0.003380460
 39.75 201.890 0.003356430
 40.25 201.613 0.003332140
 40.75 201.259 0.003307590
 41.25 200.688 0.003282790
 41.75 200.437 0.003257730
 42.25 200.291 0.003232430
 42.75 199.786 0.003206880
 43.25 199.203 0.003181080
 43.75 198.752 0.003155030
 44.25 198.529 0.003128740
 44.75 198.064 0.003102210
 45.25 197.678 0.003075440
 45.75 196.640 0.003048430
 46.25 196.054 0.003021190
 46.75 195.885 0.002993710
 47.25 195.866 0.002966010
 47.75 195.388 0.002938070
 48.25 194.087 0.002909900
 48.75 193.621 0.002881510
 49.25 193.414 0.002852900
 49.75 193.144 0.002824070
 50.25 192.485 0.002795010
 50.75 191.851 0.002765740
 51.25 191.477 0.002736260
 51.75 190.991 0.002706560
 52.25 190.311 0.002676650
 52.75 189.843 0.002646540
 53.25 189.517 0.002616220
 53.75 188.474 0.002585690
 54.25 187.944 0.002554970
 54.75 187.390 0.002524040
 55.25 187.308 0.002492920
 55.75 186.351 0.002461600
 56.25 185.324 0.002430100
 56.75 185.153 0.002398400
 57.25 184.717 0.002366510
 57.75 184.195 0.002334440
 58.25 183.457 0.002302190
 58.75 182.550 0.002269760
 59.25 181.897 0.002237150
 59.75 180.882 0.002204370
 60.25 180.425 0.002171410
 60.75 179.733 0.002138290
 61.25 178.569 0.002104990
 61.75 177.431 0.002071530
 62.25 177.406 0.002037910
 62.75 176.133 0.002004130
 63.25 174.992 0.001970190
 63.75 174.263 0.001936100
 64.25 174.045 0.001901860
 64.75 173.420 0.001867460
 65.25 172.958 0.001832920
 65.75 171.647 0.001798240
 66.25 170.659 0.001763410
 66.75 168.890 0.001728450
 67.25 168.258 0.001693350
 67.75 167.299 0.001658120
 68.25 166.353 0.001622750
 68.75 165.771 0.001587260
 69.25 164.839 0.001551640
 69.75 164.604 0.001515910
 70.25 163.729 0.001480050
 70.75 162.392 0.001444070
 71.25 160.312 0.001407980
 71.75 159.079 0.001371780
 72.25 158.767 0.001335480
 72.75 158.000 0.001299060
 73.25 155.641 0.001262550
 73.75 154.728 0.001225930
 74.25 152.357 0.001189220
 74.75 152.286 0.001152410
 75.25 152.446 0.001115520
 75.75 151.423 0.001078530
 76.25 149.418 0.001041460
 76.75 147.758 0.001004310
 77.25 145.345 0.000967073
 77.75 145.334 0.000929764
 78.25 143.694 0.000892381
 78.75 143.395 0.000854928
 79.25 141.426 0.000817407
 79.75 139.245 0.000779822
 80.25 134.396 0.000742174
 80.75 134.638 0.000704468
 81.25 132.923 0.000666706
 81.75 131.281 0.000628891
 82.25 128.608 0.000591027
 82.75 125.593 0.000553116
 83.25 124.031 0.000515160
 83.75 122.858 0.000477164
 84.25 117.375 0.000439131
 84.75 110.464 0.000401062
 85.25 111.891 0.000362962
 85.75 113.233 0.000324832
 86.25 109.398 0.000286677
 86.75 113.166 0.000248500
 87.25 109.039 0.000210302
 87.75  98.730 0.000172088
 88.25  95.876 0.000133861
 88.75  86.159 0.000095622
 89.25  89.165 0.000057376
 89.75 109.777 0.000019126

MoonT: 201.082

First column is latitude, 2nd is average temperature for that latitude +/- 0.5 degrees, and 3rd is the surface area proportion of that latitude +/- 0.5 degrees. 3rd column adds up to 1. MoonT is the area-weighted mean of all latitudes.

Now we do the same for WUSTL data:

> calc_wustl

-89.75 111.192 0.000019126
-89.25 111.660 0.000057376
-88.75 100.290 0.000095622
-88.25  86.871 0.000133861
-87.75  95.084 0.000172088
-87.25  92.831 0.000210302
-86.75 102.601 0.000248500
-86.25 111.243 0.000286677
-85.75 115.981 0.000324832
-85.25 116.198 0.000362962
-84.75 108.497 0.000401062
-84.25 115.692 0.000439131
-83.75 123.413 0.000477164
-83.25 130.003 0.000515160
-82.75 133.344 0.000553116
-82.25 129.484 0.000591027
-81.75 129.702 0.000628891
-81.25 128.091 0.000666706
-80.75 133.846 0.000704468
-80.25 136.168 0.000742174
-79.75 138.256 0.000779822
-79.25 137.502 0.000817407
-78.75 138.429 0.000854928
-78.25 138.730 0.000892381
-77.75 143.939 0.000929764
-77.25 145.831 0.000967073
-76.75 144.331 0.001004310
-76.25 147.966 0.001041460
-75.75 148.465 0.001078530
-75.25 152.140 0.001115520
-74.75 151.776 0.001152410
-74.25 152.297 0.001189220
-73.75 152.585 0.001225930
-73.25 155.127 0.001262550
-72.75 156.952 0.001299060
-72.25 159.367 0.001335480
-71.75 160.486 0.001371780
-71.25 161.450 0.001407980
-70.75 161.246 0.001444070
-70.25 161.774 0.001480050
-69.75 163.612 0.001515910
-69.25 163.996 0.001551640
-68.75 165.422 0.001587260
-68.25 167.346 0.001622750
-67.75 168.544 0.001658120
-67.25 169.355 0.001693350
-66.75 170.667 0.001728450
-66.25 170.258 0.001763410
-65.75 171.491 0.001798240
-65.25 174.150 0.001832920
-64.75 174.220 0.001867460
-64.25 174.762 0.001901860
-63.75 174.905 0.001936100
-63.25 175.696 0.001970190
-62.75 177.189 0.002004130
-62.25 179.499 0.002037910
-61.75 180.929 0.002071530
-61.25 181.092 0.002104990
-60.75 181.633 0.002138290
-60.25 182.008 0.002171410
-59.75 183.258 0.002204370
-59.25 184.545 0.002237150
-58.75 184.681 0.002269760
-58.25 184.960 0.002302190
-57.75 185.818 0.002334440
-57.25 187.257 0.002366510
-56.75 187.572 0.002398400
-56.25 188.767 0.002430100
-55.75 188.732 0.002461600
-55.25 189.269 0.002492920
-54.75 189.528 0.002524040
-54.25 190.825 0.002554970
-53.75 191.269 0.002585690
-53.25 191.363 0.002616220
-52.75 191.864 0.002646540
-52.25 193.107 0.002676650
-51.75 194.078 0.002706560
-51.25 194.501 0.002736260
-50.75 194.990 0.002765740
-50.25 195.240 0.002795010
-49.75 195.366 0.002824070
-49.25 196.196 0.002852900
-48.75 196.037 0.002881510
-48.25 196.876 0.002909900
-47.75 197.586 0.002938070
-47.25 198.416 0.002966010
-46.75 199.182 0.002993710
-46.25 199.469 0.003021190
-45.75 199.996 0.003048430
-45.25 200.541 0.003075440
-44.75 200.536 0.003102210
-44.25 201.071 0.003128740
-43.75 201.588 0.003155030
-43.25 201.680 0.003181080
-42.75 201.665 0.003206880
-42.25 201.937 0.003232430
-41.75 202.546 0.003257730
-41.25 203.719 0.003282790
-40.75 204.205 0.003307590
-40.25 204.736 0.003332140
-39.75 204.970 0.003356430
-39.25 204.972 0.003380460
-38.75 205.850 0.003404230
-38.25 206.663 0.003427750
-37.75 206.584 0.003451000
-37.25 207.040 0.003473980
-36.75 207.439 0.003496700
-36.25 207.656 0.003519150
-35.75 208.246 0.003541330
-35.25 208.680 0.003563240
-34.75 209.273 0.003584880
-34.25 209.473 0.003606240
-33.75 209.612 0.003627330
-33.25 209.509 0.003648140
-32.75 209.973 0.003668680
-32.25 209.766 0.003688930
-31.75 210.415 0.003708900
-31.25 211.005 0.003728590
-30.75 211.611 0.003747990
-30.25 212.332 0.003767110
-29.75 212.587 0.003785940
-29.25 212.645 0.003804480
-28.75 212.918 0.003822740
-28.25 213.020 0.003840700
-27.75 213.443 0.003858370
-27.25 213.599 0.003875750
-26.75 214.268 0.003892830
-26.25 214.016 0.003909620
-25.75 214.252 0.003926110
-25.25 214.595 0.003942300
-24.75 215.184 0.003958190
-24.25 214.881 0.003973790
-23.75 215.254 0.003989080
-23.25 215.482 0.004004070
-22.75 214.994 0.004018760
-22.25 215.303 0.004033140
-21.75 215.699 0.004047210
-21.25 215.885 0.004060980
-20.75 216.148 0.004074450
-20.25 216.335 0.004087600
-19.75 215.992 0.004100450
-19.25 216.290 0.004112980
-18.75 216.212 0.004125210
-18.25 216.517 0.004137120
-17.75 216.406 0.004148720
-17.25 216.614 0.004160010
-16.75 216.567 0.004170990
-16.25 216.449 0.004181650
-15.75 216.859 0.004191990
-15.25 217.096 0.004202020
-14.75 217.008 0.004211730
-14.25 216.947 0.004221120
-13.75 216.897 0.004230200
-13.25 216.589 0.004238950
-12.75 216.806 0.004247390
-12.25 216.571 0.004255510
-11.75 216.447 0.004263300
-11.25 216.478 0.004270780
-10.75 216.249 0.004277940
-10.25 216.115 0.004284770
 -9.75 216.419 0.004291280
 -9.25 216.589 0.004297470
 -8.75 216.901 0.004303330
 -8.25 216.549 0.004308870
 -7.75 216.389 0.004314090
 -7.25 216.261 0.004318980
 -6.75 216.297 0.004323550
 -6.25 216.072 0.004327790
 -5.75 216.128 0.004331710
 -5.25 215.923 0.004335300
 -4.75 215.805 0.004338570
 -4.25 215.933 0.004341510
 -3.75 216.061 0.004344120
 -3.25 216.258 0.004346410
 -2.75 216.291 0.004348370
 -2.25 215.959 0.004350000
 -1.75 215.765 0.004351310
 -1.25 215.792 0.004352290
 -0.75 215.759 0.004352940
 -0.25 215.570 0.004353270
  0.25 215.419 0.004353270
  0.75 215.150 0.004352940
  1.25 215.066 0.004352290
  1.75 214.871 0.004351310
  2.25 214.831 0.004350000
  2.75 214.809 0.004348370
  3.25 214.578 0.004346410
  3.75 214.599 0.004344120
  4.25 214.262 0.004341510
  4.75 213.976 0.004338570
  5.25 213.812 0.004335300
  5.75 213.690 0.004331710
  6.25 213.126 0.004327790
  6.75 212.800 0.004323550
  7.25 212.827 0.004318980
  7.75 212.963 0.004314090
  8.25 212.537 0.004308870
  8.75 212.270 0.004303330
  9.25 211.869 0.004297470
  9.75 211.598 0.004291280
 10.25 211.233 0.004284770
 10.75 211.009 0.004277940
 11.25 210.931 0.004270780
 11.75 210.785 0.004263300
 12.25 210.905 0.004255510
 12.75 210.935 0.004247390
 13.25 210.643 0.004238950
 13.75 210.358 0.004230200
 14.25 210.152 0.004221120
 14.75 209.363 0.004211730
 15.25 208.773 0.004202020
 15.75 208.371 0.004191990
 16.25 208.195 0.004181650
 16.75 208.633 0.004170990
 17.25 208.545 0.004160010
 17.75 208.499 0.004148720
 18.25 208.173 0.004137120
 18.75 208.080 0.004125210
 19.25 207.456 0.004112980
 19.75 207.185 0.004100450
 20.25 206.943 0.004087600
 20.75 206.466 0.004074450
 21.25 206.488 0.004060980
 21.75 206.295 0.004047210
 22.25 205.953 0.004033140
 22.75 205.895 0.004018760
 23.25 205.286 0.004004070
 23.75 205.249 0.003989080
 24.25 204.794 0.003973790
 24.75 204.654 0.003958190
 25.25 204.500 0.003942300
 25.75 203.869 0.003926110
 26.25 203.385 0.003909620
 26.75 203.094 0.003892830
 27.25 203.295 0.003875750
 27.75 203.300 0.003858370
 28.25 203.156 0.003840700
 28.75 202.549 0.003822740
 29.25 202.184 0.003804480
 29.75 201.900 0.003785940
 30.25 201.414 0.003767110
 30.75 201.026 0.003747990
 31.25 200.339 0.003728590
 31.75 200.075 0.003708900
 32.25 199.678 0.003688930
 32.75 199.134 0.003668680
 33.25 199.242 0.003648140
 33.75 198.870 0.003627330
 34.25 198.542 0.003606240
 34.75 197.986 0.003584880
 35.25 197.710 0.003563240
 35.75 197.292 0.003541330
 36.25 196.695 0.003519150
 36.75 196.182 0.003496700
 37.25 195.985 0.003473980
 37.75 195.376 0.003451000
 38.25 195.215 0.003427750
 38.75 194.945 0.003404230
 39.25 194.702 0.003380460
 39.75 194.408 0.003356430
 40.25 194.084 0.003332140
 40.75 193.454 0.003307590
 41.25 192.829 0.003282790
 41.75 192.537 0.003257730
 42.25 192.213 0.003232430
 42.75 191.841 0.003206880
 43.25 191.122 0.003181080
 43.75 190.537 0.003155030
 44.25 190.296 0.003128740
 44.75 190.286 0.003102210
 45.25 189.988 0.003075440
 45.75 189.450 0.003048430
 46.25 188.734 0.003021190
 46.75 188.502 0.002993710
 47.25 188.434 0.002966010
 47.75 187.969 0.002938070
 48.25 186.444 0.002909900
 48.75 186.200 0.002881510
 49.25 186.058 0.002852900
 49.75 185.592 0.002824070
 50.25 185.071 0.002795010
 50.75 184.626 0.002765740
 51.25 184.254 0.002736260
 51.75 184.047 0.002706560
 52.25 183.452 0.002676650
 52.75 182.817 0.002646540
 53.25 182.411 0.002616220
 53.75 181.747 0.002585690
 54.25 181.146 0.002554970
 54.75 180.724 0.002524040
 55.25 180.913 0.002492920
 55.75 180.215 0.002461600
 56.25 179.626 0.002430100
 56.75 179.553 0.002398400
 57.25 178.901 0.002366510
 57.75 178.362 0.002334440
 58.25 177.475 0.002302190
 58.75 176.981 0.002269760
 59.25 176.461 0.002237150
 59.75 176.088 0.002204370
 60.25 175.993 0.002171410
 60.75 175.367 0.002138290
 61.25 174.353 0.002104990
 61.75 173.586 0.002071530
 62.25 173.660 0.002037910
 62.75 172.696 0.002004130
 63.25 171.946 0.001970190
 63.75 171.428 0.001936100
 64.25 171.687 0.001901860
 64.75 171.416 0.001867460
 65.25 171.483 0.001832920
 65.75 170.581 0.001798240
 66.25 169.589 0.001763410
 66.75 168.143 0.001728450
 67.25 167.852 0.001693350
 67.75 167.419 0.001658120
 68.25 166.735 0.001622750
 68.75 166.388 0.001587260
 69.25 165.532 0.001551640
 69.75 165.550 0.001515910
 70.25 164.822 0.001480050
 70.75 163.915 0.001444070
 71.25 162.093 0.001407980
 71.75 161.380 0.001371780
 72.25 161.240 0.001335480
 72.75 160.716 0.001299060
 73.25 158.450 0.001262550
 73.75 157.668 0.001225930
 74.25 155.624 0.001189220
 74.75 155.580 0.001152410
 75.25 156.122 0.001115520
 75.75 155.565 0.001078530
 76.25 154.319 0.001041460
 76.75 153.155 0.001004310
 77.25 150.936 0.000967073
 77.75 151.168 0.000929764
 78.25 149.753 0.000892381
 78.75 148.941 0.000854928
 79.25 146.770 0.000817407
 79.75 143.766 0.000779822
 80.25 138.198 0.000742174
 80.75 137.521 0.000704468
 81.25 134.825 0.000666706
 81.75 132.612 0.000628891
 82.25 129.110 0.000591027
 82.75 124.871 0.000553116
 83.25 122.797 0.000515160
 83.75 121.661 0.000477164
 84.25 116.752 0.000439131
 84.75 110.306 0.000401062
 85.25 111.987 0.000362962
 85.75 113.071 0.000324832
 86.25 109.478 0.000286677
 86.75 113.206 0.000248500
 87.25 108.943 0.000210302
 87.75  98.809 0.000172088
 88.25  96.164 0.000133861
 88.75  86.252 0.000095622
 89.25  89.380 0.000057376
 89.75 110.643 0.000019126

MoonT: 199.386

It’s hard to choose which data is better. The first is complete hourly data, while the latter is 15 minute data but with many missing pieces.

The results are 201.086 K and 199.386 K.

The average of the two results is 200.2 K, and I will leave it at that.

Answer = 200.2 K

Enjoy 🙂 -Zoe

Update

I was curious about Equations 12 and 13 of [Nikolov & Zeller 2014], so I wrote a little bit more code into moontemp.sh above:

eq12_13() {
    seq 0.05 0.1 89.95 | awk '{ R=atan2(0,-1)/180; L=R*$1
        T=216.313+9.919*L-119.814*L^2+307.116*L^3-466.244*L^4+321.317*L^5-84.973*L^6
        AVG+=T*cos(L)*0.1*R
    } END { printf "MoonT: %7.3f\n", AVG }'
}

I used 216.313 K as my average equatorial temperature, which I got by averaging UCLA & WUSTL data between -0.25 and 0.25 latitude.

> . moontemp.sh; eq12_13

MoonT: 200.777

The result is only off by half a degree from our answer. This formula is pretty good.