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.

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.

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.

Line of sight on surface of Sun

LINE OF SIGHT ON SURFACE OF SUN

INTRODUCTION

Sun is a star which is in the center of our solar system that has a mean radius of 695,700 km. Although the equatorial radius is not equal to its polar radius, we can approximate the Sun 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 Sun assuming that he can withstand extreme temperature and gravity conditions.

ASSUMPTIONS

1.      The surface of Sun is smooth

2.      Sun 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 Sun is not curved but flat

6.      The observer is at ground level

CALCULATION

Fig .1

From Figure .1,

R – Radius of Sun [m]                                                                                                                               

R = 695,700 Km = 695,700,000 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*695700000*1.5+1.5²)

d = 45,684.7896 m

d = 45.6847 Km = [28.3701 miles]

This is the distance that can be viewed by an observer on the surface of Sun provided there aren't any solar storms to obscure the vision.

CONCLUSION

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

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.