Line of sight on surface of Jupiter

LINE OF SIGHT ON SURFACE OF JUPITER

INTRODUCTION

Jupiter is the fifth planet in our solar system which has a mean radius of 69,911 km. Although the equatorial radius is not equal to its polar radius, we can approximate Jupiter 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 Jupiter assuming that the human can withstand the immense gravity and climate.

ASSUMPTIONS

1.      Jupiter has a surface and it is smooth

2.      Jupiter is a homogeneous sphere

3.      The Jovian sky is clear and vision is not obscured

4.      Light does not undergo diffraction and refraction

5.      Space time around Jupiter is not curved but flat

6.      The observer is at ground level

CALCULATION

Fig .1

From Fig .1,

R – Radius of Jupiter [m]                                                                                                                          

R = 69,911 Km = 69,911,000 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*69911000*1.5+1.5²)

d = 14,482.1615 m

d = 14.4821 Km = [8.9933 miles]

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

CONCLUSION

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