LINE OF SIGHT ON SURFACE OF SIRIUS

LINE OF SIGHT ON SURFACE OF SIRIUS

INTRODUCTION

Sirius is a star which is approximately 8 light years away from Earth. It is the brightest star in the night sky. It has a mean radius of 1.191 million km. Although the equatorial radius is not equal to its polar radius, we can approximate the Sirius 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 Sirius assuming that he can withstand the extreme conditions of temperature and gravity.

ASSUMPTIONS

1.      The surface of Sirius is smooth

2.      Sirius is a homogeneous sphere

3.      The atmosphere is clear and vision is not obscured

4.      Light does not undergo diffraction and refraction

5.      Space time around Sirius is not curved but flat

6.      The observer is at ground level

CALCULATION

Figure .1

From Fig .1,

R – Radius of Sirius [m]                                                                                                                            

R = 1.191*10⁹ 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*1.191*10⁹*1.5+1.5²)

d = 59,774.5765 m

d = 59.7745 Km = [37.1199 miles]

This is the distance that can be viewed by an observer on the surface of Sirius provided there aren't plasma storms.

CONCLUSION

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