| DIAMETER & DEPTH OF LUNAR CRATERS
A paper by
Andre James Clayden
of the
Springbrook Research Observatory
Introduction
This project
(measuring the diameter & depth of craters on the lunar surface) will show a method to
calculate the sizes and height of features on the lunar surface using a photographic
technique and how to acquire, process, measure, and calculate these features.
Aim
To measure the size and depth of features
on the lunar surface and. devise a measuring technique based on timing the passage of the
features past the datum. The method will utilise digital photographic technique, and will
show how to calculate the size and depth of the object from a digital image.
Materials used
 |
 |
 |
| C14 working @F11 |
ST7E CCD Camera |
Ruler |
| |
|
|
| Lunar map |
Scientific calculator |
Stopwatch |
Good astronomical
data base program that has been synchronized with the computer and the
atomic clock.
Method used
A)
A number of targets were chosen from a lunar map. These objects
show good surface structure, Theophilus, Cyrillus fabricius Piccolomini, Steinheil, Vlacaq
Latitude and longitude of the objects had
to been noted. This helped determine the correction factor (moon being round) Camera had
to be focused and a number of imagestaken to be sure the sharpest possible images had been
acquired
B)
At the precise time of the image being taken, the time had to
been noted. This enabled determination of the distance and the angle of the sun on the
lunar surface. A print out from the astronomical database program (Sky version 5) was
taken, the distance of the moon from earth at the precise time of the image being taken.
Example below
Moon
Earth-Moon distance: 397250.1 km (246840.4 miles)
True Equatorial RA: 19h 30m 27.2s Dec: -23°42'58"
Topocentric coordinates: RA: 19h 30m 42.5s Dec:
-23°38'09"
Rise: 10:01 Transit: 17:10 Set:
------
Angular diameter: 00°30'34"
Azm: 37°00'15” Alt:
+83°40'29" (with refraction:
83°40'35”)
Physical ephemeris
Phase: 42.03 %, Phase angle: 99.17°
Position angle of the
bright limb: 261.5°
True ecliptical
coordinates: Lambda: 290°37'25” Beta:
01°52'53"
Parallax: 00°55'11.
875"
Geocentric angular
diameter: 00°30'05"
Optical libration: l':
5.458 °, b': 2.423
Physical libration:
l": 0.025, b": 0.055
Total libration: l:
5.483, b: 2.477
Position angle: -10.24°
Rates ra: 0.3299 Dec:
0.0339 (arc-secs/sec)
C)
From the web http://www.xylem.demon.co.uk/kepler/jsmoon.html
a print out of the "Sun's selenographic colongitude" was
also taken which was used to find the length of was the shadow.
D)
The crater size and the
latitude, longitude was obtained from http://www.fourmilab.ch/earthview/lunarform/cratnear.html
E)
The image size 765*510 pixels from the st7eto process the
image using Photoshop
F)
Unsharp mask
was high light the feature in the image and saved as a jpg image.
G)
To measure the size of the crater, the image was printed out
maintaining the pixel size and the pixels then converted into km. This was done by using
the method below. Using the Crater Theophilus
as an example - lat 11.4s long 26.4e and referenced size110km
H)
1 pixel =0.35 arcsec 0.35 =000098
3600
Distance
of the Moon from Earth = 397 251.3
1
pixel =D (397251.3) *tan (0.000098= 1.710422)
1
pixel =0.67946728 km
Image
size = 765 * 0.67946728 km =519.792
Pixels 510
* 067946728 km =346.528
Image
size in mm 141mm *90mm
141mm/519.7927354
km = 3.850 km to 1mm
90mm/346.5284903
km = 3.686
km to 1mm
· Average
the two figures = 3.768 km to 1 mm
·
I)
Now we have the image, the latitude,
longitude, time of the image when it was taken, the distance from Earth to the moon and
the sun selenographic colongitude, size of the image in pixels and the diameter of the
crater and the length of the shadow
a)
Close up of Theophilus and Cyrillus showing the dark
area around bottom of the rim of the crater this is the shadow that we need to measure the
length by obtaining the sun’s selenogrphic colongitude this will give use angle
theta.
J)
Measure the size of the crater by using a ruler. The
size per mm is = 3.768 km to 1 mm, and
in this instance it will change with every image so the same method used above will need
to be repeated. To calculate size use the method below
Correction
factor for moon surface
1
_______________________
Cos
(latitude) *Cos (longitude) =CF
1
_____________
11.4 *
26.4
(0.980271174) *(
0.89571176) = CF 1.138899735 this allows for curviture of the moon
Size
of the crater in mm =25.5mm diameter
· 25.5mm
* 3.7683949 km *CF (1.138899735)
·
· Diameter of Crater Theophilus = 109.429 km
The method used to determine the height
of craters or mountains
Measuring the length of the shadow in
mm multiply that by 3.76839493 then
By the CF (1.12342645) as shown below
Shadow
= L
Theta = 10.79deg
L=
shadow length in mm3.768 * km to 1 mm) *CF (1.123)
Theta
= tan (angle of the sun) 10.24deg (0.190)
H
______________________________________
Height =Theta (angle) 10.79Tan (0.190579324)
L
___________________________________________________
H= L (6.5mm)* 3.76839493 km *CF (1.12342645) *Theta (0.190)
The Height of Theophilus is = 5244.3m
Time 19.39.02 Date 10/23/2001 Earth Moon
Distance 397729.5.3km Angle –10.79deg
Image size 765pixels*510 pixels telescope
C14 camera st7e f11
“Crater Fabricus lat 40.3s
long 43.3e Ref size 78km”
1 pixel =0.35 arcsec 0.35 =000098
3600
Distance of the Moon from Earth =
397729.5.3km
1 pixel =D (397729.5km) *tan (0.000098)
tan = 1.710422669
1 pixel = 0.680285552km
Image size = 765 *0.680 km = 520.418 km
Pixels
510 *0.680 km = 346.945 km
image size in mm 141mm *90mm
141mm/520.4184474 km = 3.690km to 1mm
90mm/346.9456315 km = 3.854km to 1mm
Averaged the two figures = 3.772 km to
1 mm
Correction factor for moon surface
1
Cos (latitude) *Cos (longitude) =CF
42.9 * 42.0
(0.732) *(0.743) = CF
1.836
Size of the crater in mm = 11.5mm diameter
11.5mm * 3.772 km *CF (1.836)
Diameter of Crater Fabricus = 79.7
km
http://www.fourmilab.ch/earthview/lunarform/cratnear.html
|
