Measuring Mt. Biot

While imaging some Lunar 100 features in Nov 2005 I found by chance an interesting mountain range close to Petavius/Wrottesley. This mountain was not named in Rukl or the Virtual Moon Atlas but I eventually found it on the very detailed 1960's LAC charts (chart 98). See also Lunar Orbiter photo

This reference named the feature as Mount Biot (named afet Jean-Babtiste Biot) and shows the highest point as 1330m. Reading the text on the LAC chart it says that the elevations on the chart were determined by shadow measuring techniques. Since my image shows a nice profile of the Biot ridge shadow I decided to try and reproduce the results of the 1960s measurements.

Biot_LAC98map.jpg (257273 bytes) Extract of the LAC98 chart showing the Biot/Wrottesley area (click thumbnail for full size image)

Biot_051118.jpg (64949 bytes) My source image: 19th Nov 2005 00:10 UTC.  LX-200 10", f20, ToUCam approx 1000 frame stack.

Here are some closeup selections of Mt. Biot  (my image rotated and enlarged x3 to match the chart):

 

Next I took the Biot ridge shadow and rotated/cropped the image to just give the ridge profile:

Then I performed a quick check to see how my profile compared with the LAC one. The LAC chart shows 6 heights on the chart, these are shown below 

Ref LAC marked height Relative to 1330m
1 1050 0.79
2 960 0.72
3 1330 1
4 1020 0.77
5 800 0.60
6 820 0.62
 

Using the bottom of the frame as a baseline I measured the pixel heights to the main ridge features

Feature Pixels Relative to highest
1 114 0.95
2 68 0.57
3 119 1
4 93 0.78
5 86 0.72
6 63 0.53

This only shows a very general agreement with the chart profile. 

Next I did a Google search on "height of lunar mountains" - this gave several references and it seems that several universities use this exercise as part of student coursework.

Rochester Institute of Technology have a good description of the calculations at http://stupendous.rit.edu/classes/phys236/moon_mount/moon_mount.html

From Virtual Moon atlas I obtained the following data for the time of my image :-

Co-longitude of the sun, Co 121.14

Sub-solar point Latitude, Bo -1.1

Earth-Moon distance 388,028 km

I carried out image frame calibration by reference to recent images of Mars with identical optical setup. These gave a disk of 96 pixels for the planet at 18.8 arc sec size (value from Carte Du Ciel). Hence image is 0.1958 arcsec/pixel.

Knowing the Earth-Moon distance thus gives 0.368 km/pixel, but this must be corrected for the tilt of the Moons surface at the Lat/Long being imaged. Therefore the effective resolution around Mt Biot is 0.676 km/pixel

The maths described in the above link was used to determine the sun illumination angle which worked out to 4.09. I then rotated the image -23 so that all the shadows were running directly across the image - this made the shadow pixel lengths easier to determine.

Putting all the data into the maths gave the following results...

 
Feature My estimated height Chart height % error
1 1111 1050 +6%
2 773 960 -19%
3 1449 1330 +9%
4 1256 1020 +23%
5 483 800 -39%
6 676 820 -17%

These results seemed to vary considerably with the chart data. As another check I used similar maths to measure the diameters of crater Biot and Wrottesley, comparison with Virtual Moon Atlas values.

 
Crater My estimate
km
Atlas size
km
Error
Biot 17.1 14 +22%
Wrottesley 65 60 +8%
 


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