Line of sight on surface of Moon

LINE OF SIGHT ON SURFACE OF MOON

INTRODUCTION

The Moon is a natural satellite of our planet earth which has a mean radius of 1737 km. Although the equatorial radius is not equal to its polar radius, we can approximate the Moon as a sphere. Any object on the surface of sphere has a finite view due to the curvature of the sphere. Thus any one can view only up to a finite distance before the horizon. The horizon is itself defined on the height of the object, the greater the height the more the view. In this article, we intend to determine the line of sight for an average human being on the surface of Moon.

ASSUMPTIONS

1.      The surface of Moon is smooth

2.      Moon is a homogeneous sphere

3.      Space time around Moon is not curved but flat

4.      The observer is at ground level

CALCULATION

 Fig .1

From figure 1,

R – Radius of Moon [m]                                                                                                                           

R = 1737 Km = 1737000 m (Eq. 1)

h – Height of the observer [m]

h = 5 feet

   = 1.5 m (Eq. 2)

                                                                                                                               {⸪ 1 feet = 0.3 m}

d – Observable distance by observer [m]                                                                                         

We can apply Pythagorean Theorem, 

d² = (R+h)² – R² (Eq. 3)

d² = 2Rh + h²

d = √ (2Rh+h²) (Eq. 4)

Now substitute equations (1), (2) in equation (4)

d = √ (2*1737000*1.5+1.5²)

d = 2282.7619 m

d = 2.2827 Km = [1.4175 miles]

This is the distance that can be viewed by an observer on the surface of Moon provided there is no dust storm.

CONCLUSION

We thus determined the line of sight or field of view for an observer on the surface of Moon.