Lunar Features, Essay Example

Introduction

The Earth’s moon, Luna, has physical characteristics such as craters, mountains and mares. Each of these features is approximately 3.8 x 10⁵ km away from each other. Since the features are visible through observations using a telescope from Earth, we are able to determine the diameter and height of each lunar feature using a digital image taken from a telescope of the moon. The objective of this project is to determine the lunar crater radius and diameter of the craters on the moon using the known radius of the moon, which is 1738 km, and comparing the physical and digital image distances. In addition, the project investigates the height of moon craters using shadows observed on the digital image features from the telescope of the moon.

Method

A scaling method was used in order to determine both the diameter and radius of a lunar crater. The ratio of the crater diameter (image D) and the radius of the moon (image moon R) on the digital image are equal to the ratio of the actual physical crater diameter (physical D) to the actual physical lunar radius (physical moon R; 1738 km).  In addition, a scaling method was used to determine the height of the lunar craters by using the shadow of the crater feature on the moon from the observation through the telescope. In looking at the image, the shadow is visible along the rim. Using the radius of the image, two right triangles were constructed and the sides and angles were calculated to obtain the height of the crater.

Data

Moon Crater Diameter and Radius

The measured diameter of the crater on the image (Figure 1), image crater D equals 3.81cm. 3.81 centimeters was converted to kilometers (3.81 cm divided by 1000 cm divided by 1000 meters) to equal 3.8 x 10^-6 km. The measured radius of the crater on the image (Figure 1), image moon R equals 12.7 cm or 9.4×10^-6 km. The physical diameter of the crater was calculated as follows: image crater D divided by image crater R multiplied by the physical moon R (D physical crater= image crater D/image crater R x radius moon or 3.8×10^-6 km/9.4×10^-6 km x 1738 km= 7.03×10^-9 km).

Height of Lunar Craters or Mountains

The distance between the feature and the terminator on the image is T equals 7.36×10^-6 km.  The radius of the moon on the image is R equals 9.4×10^-6 km. The length of shadow of the feature is S equals 2.54 x10^-6 km. (Figure 1). The height of feature on the image is calculated as H=T/RxS. (H=7.36×10^-6 km/9.4×10^-6 km x 2.54 x10^-6 km = 1.99×10^-18 km.  The physical height of the crater was calculated from the height of the feature divided by the radius of the feature multiplied by the radius of the physical moon (H/R x R physical moon or 1.99×10^-18 km/9.4×10^-6 km x 7.03×10^-9 km= 1.48×10^-21km.

Results and Uncertainty

The results of this exercise indicated that the diameter of the physical crater is 7.03×10-9 km long and the height of the physical crater is 1.48×10-21km. This indicates that the crater is much longer in distance than its height. The exact measurements of these results are not certain due to human error in measurements, as well as the formation of the triangle. The shadows were difficult to pick out along the rim of the moon. In order to improve these measurements, a better digital image, such as a high resolution image or perhaps more three-dimensional looking may work. In addition, perhaps knowing the field of view of the telescope could lead to a more accurate measurement in which the scale from two points on the image can be calculated from the field of view calculation. Furthermore, the use of a protractor could result in a more accurate measurement for the height of the crater.

Conclusions

In conclusion, the exercise illustrated the size and number of craters on the moon. It allowed the user to visualize the actual size of the moon. From Earth, the moon looks so small; however, in conducting the distance and height calculations on a crater that is observable in a telescope, gives an idea of the scope and size of the moon’s physical diameter. In addition, the overall exercise showed how ratios and scaling methods can be used in order to calculate the size of objects. This is a useful tool for calculating the diameters and heights of large objects, especially in space, or perhaps the ocean.