The authors imagine that the dream of the astronauts will be partly fulfilled after landing on the moon’s surface. This success of course will lead them to search further and photograph interesting objects which will be found on this unknown soil. These astronauts will be charmed to see and record spots of land, mineral bound rocks, craters etc. Probably, their most important task after landing would be to find out the source of water. Recently astronomers are convinced that water-ice can be found at the moon’s poles inside the shadowed craters [1]. Bjorn Davidson, a scientist at NASA confirmed by Stratospheric Observatory detected the possible presence of water on the day side surface of the moon [1]. We know water will be essential for the survival of the astronauts and also to continue lunar exploration. Hosseini said “if water is available in the form of frost in sunlit regions of the moon, future explorers may use it as a resource for fuel and drinking water” [1]. So far, we have the impression that the water will be available in certain locations of the moon. Now the question arises how the water sources are stored on the moon’s surface. The mappers of moon mineralogy will be interested to draw also the maps of water recourses while they will continue investigations on Geology and Geography.

In this paper the authors propose to present a new rapid technique for the measurements of abnormally bended flat surfaces bearing water-ice on the moon. At present we do not know any other technique to apply for such measurements. So, the authors suggests an alternative method which also include a simple formula I=W10² to apply for measurements of all types of complicated flat areas on the moon’s surface [2,5,6].

The authors suggest to prepare slide-photographs of some selected areas of the moon’s surface. These should be taken vertically from the areas to be photographed. These photographs should be sent to a previously assigned laboratory on the earth for further manipulations. These slides will be projected vertically on to a large piece (40cm * 60 cm) of polyethylene sheet (PES). This piece of PES should be previously tested to confirm its special property of uniform density [2]. This piece of PES should be placed on a table. The images should be focused accurately. Bended curve lines of the images will be seen clearly. Now the edges of these images should be cut off and separated by the help of an eclectically heated needle. These separated portions of PES should be weighed in an electric balance one by one and recorded. These measurements should be done by five experts of the earth and the average data should be recorded in the form of a table.

The above illustrated procedure was followed by one of the authors and four other experts using simulated models of water resource of the moon. The data were recorded as mentioned before and the detailed results and discussion were written by the authors on the basis of the findings.

Figure 1: A Recent Photograph of the Full Mineral Moon.

Source Of This Image: Internet (Google link):-https://www.lightstalking.com/mineral-moon-photography/

The Moon’s surface material, known as regolith, has subtle color differences dictated by the mineral composition in any particular area. The blue color is caused by the higher amount of Titanium on the lunar soil, the orange red color due to iron, and the other colors are caused by other minerals and where titanium is found in a lesser percentage.

We dream that one day all these colored spots on the moon will be identified and measured by the same formula I=W10²– Authors.

Figure 2: Simulated Diagram of a Frosted Area on the Moon’s Surface.

Calculations
The area of the rectangle in the photo-image (Figure-2) 18 cm PES* 14cm PES = 252² cm PES and its GW is 1638 mg (measured by balance, w2).
The gravitational weight (GW) 10 cm PES * 10 cm PES = 100² cm PES = 650 mg GW of the PES measured in an electric balance. 1² cm PES = 6.5 mg or
1 mg of PES = 1/6.5² cm PES
The GW of unknown area = 525 mg (measured in a balance), marked as w₁
According to the theorem I=W10^{2 =  * 100}, I=525/1638=0.3205 mg
0.3205*100=32.05% of the known area 252² cm.

According to the theorem I=W10² =   ^*, I=525/1638=0.3205 mg
0.3205*100=32.05% of the known area 252² cm.
Direct measurements of unknown bended area
1² cm PES = 6.5 mg
1 mg PES = 1/6.5² cm
525 mg PES = 525*1/6.5 = 80.76² cm that is the area of the unknown.
Determination of the actual land area
The length of the photo-image is 18 cm and the breadth is 14 cm but
in actual measurement the length is 9 meter and breadth is 7 meter so the actual area will be 9*7=63² meter or 900 cm * 700 cm = 630000² cm is the area of the rectangular land.
63000² cm is divided by 252² cm = 2500 times larger than the image area.

Application of the theorem I=W10² or 
Determination of the unknown area
w1  = Weight of the unknown frosted area = 525 mg .
w2 = Weight of the known rectangle = 1638 mg.
 
0.3205 * 100 = 32% of the known rectangular area.

Direct Measureent of the unknown bended area:-
1² cm PES = 6.5 mg or 1 mg = 1/6.5² cm
 525 mg = 525*1/6.5 = 80.76² cm area.

Figure 3: Measurements of different portions of bended areas: On Moon’s Surface Simulated Areas of Water.

ABCD=Moist Rock. W=Water-Traps. EFGH=Frost Pockets
According to the methods mentioned before GW of the areas marked ABCD, EFGH, and We were converted to areas in Square Centimeters. Such as: AB*BC=204² cm (total area) the GW of the areas marked EFGH and W were converted to areas,
Such as: E+F+G+H = 64² cm frosted portion.
W = 95.5² cm Ice-water portion.
MR = 44.5²cm moist rock portion.
Total area = 64+95.5+44.5= 204² cm.

Table 1: ABCD=Moist Rock. W=Water-Traps. EFGH=Frost Pockets.

Vide-Figure 3.  AB*BC = 204 ± 0.0 total area.

In this study the authors assume that lunar water may be found in certain spots of moon’s surface. It has been reported that shadows created by the roughness on the lunar surface provide shelter for water-ice [1]. It is also expected that water will be available in the form of frost in sunlit region of the moon [1]. Some believe that water molecules may be trapped inside the rocks or impact glasses which are formed due to high temperature and pressure developed by the collision of meteorites on the moon’s surface [1]. In a recent report we come to know that enough water in different forms are available in the south pole of the moon [1]. It is also reported that water may exists in the form of patches. Because of the harsh climate the details of these patches have not been explored. The depths of the water patches need to be known. The measurements of these water field locations are considered to be important. In order to meet these requirements the authors present a dependable rapid method which can be used in all types of abnormal areas that will be identified by the explorers on the moon’s surface. The authors are also interested to mention that now-a-days radar is used for the measurements of areas. We believe the use of radar has limitation in the measurement of different area types as well as the sizes. Such as in case of very big size of areas or microscopically size of areas the use of radar is never been reported. In our case of experiment I=W10² is considered to be the best method [5].

The theorem I=W10² can be applied for the rapid measurements of abnormal areas located on the earth or the moon or any heavenly body revolving about the sun.

Acknowledgement

The authors are indebted to the technical experts for their help in photography and other assistance in various aspects of this study.

Statements and Declarations

The authors declare that no funds, grants, or other support were received during the preparation of this manuscript.

Competing Interests

The authors have no relevant financial or non-financial interests to disclose.

Author Contributions

The authors are the persons who have contributed to this study.

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