LIne of sight on surface of Betelgeuse

LINE OF SIGHT ON SURFACE OF BETELGEUSE

INTRODUCTION

Betelgeuse also known as Alpha Orionus is one of the largest stars in the observable Universe. It is approximately 1000 times bigger than our Sun. It is so large that light would itself take 1 day to travel from one end to the other. To put into perspective, light would take 0.04 second to travel from one end of Earth to the other. Although the equatorial radius is not equal to its polar radius, we can approximate the Betelgeuse 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 Betelgeuse assuming he could withstand the extreme conditions of temperature and tidal forces.

ASSUMPTIONS

1.      The surface of Betelgeuse is smooth

2.      Betelgeuse 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 Betelgeuse is not curved but flat

6.      The observer is at ground level

CALCULATION

Fig .1

From figure 1,

R – Radius of Betelgeuse [m]                                                                                                                                                                                                                                                

R = 1180*R_SUN

R = 1180*695,700*1000 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*6371000*1.5+1.5²)

d = 1,569,324.058 m

d = 1,569.324 Km [973.3082 miles]

This is the distance that can be viewed by an observer on the surface of Betelgeuse provided the weather is clear.

INSIGHTS

1. The observer will not be able to conclude that Betelgeuse is curved because of the extreme linear field of view.

2. The observer’s obvious conclusion would be that Betelgeuse is a vast flatland.

3. Theoretically one will be able to look this long but in reality a human eye cannot register objects beyond a certain distance. However we can use a binocular to gaze those thousands of Kilometers.

CONCLUSION

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