Line of sight on surface of Neutron Star

LINE OF SIGHT ON SURFACE OF NEUTRON STAR

INTRODUCTION

Neutron Star or a Pulsar is an extremely compact mass with an average radius of 10 Km. A Neutron Star is born after a supernova explosion provided the remnant mass after explosion is between 3 and 5 solar masses. Neutron Stars are extremely dense and also rotate extremely fast since they complete 1 complete rotation in 1 second or less. Although the equatorial radius is not equal to its polar radius, we can approximate the Neutron Star 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 Neutron Star assuming that he will not be crushed to death due to extreme tidal forces.

ASSUMPTIONS

1.      The surface of Neutron Star is smooth

2.      Neutron Star 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 Neutron Star is not curved but flat

6.      The observer is at ground level

CALCULATION

Figure .1

From fig. 1,

R–Radius of Neutron Star [m]                                                                                                                              

R = 10 Km = 10000 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*10000*1.5+1.5²)

d = 173.2115 m

d = 0.1732 Km = [0.1075 miles]

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

INSIGHTS

1. The observer will be able to conclude that Neutron Star is curved because of extremely small linear field of view while assuming the space time near the star is flat.

2. There is a huge error in this calculation which arises since gravity was neglected. In reality the field of view on the surface of Neutron star expands to such an extent that an observer can see the diametrically opposite side of the star.

3. This happens because light follows a curved path along the circumference of the star since the space time is heavily curved around the star.

CONCLUSION

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