Moving body approaching Neutron Star

MOVING BODY APPROACHING NEUTRON STAR 

INTRODUCTION

The Neutron Star is a highly compact star primarily composed of neutrons. It has density the same as that of an atom. A Neutron star is born from a supernova explosion. Consider a body of mass m moving with an initial speed of 10 km/s approaching the star at a distance of 4R from its surface. As the body enters Neutron Star’s gravitational field, it begins accelerating. This type of acceleration is continuous acceleration as it's continuously being accelerated due to Neutron Star’s gravity.

CALCULATION

The final velocity of the moving body when it touches Neutron Star’s surface is,

v² = u² + 2GM [(1/R) – (1/R+h)] 

Where, G = 6.67*10^-11 Nm²/kg² [Universal Gravitation Constant]

R – Radius of Neutron Star [R = 11000m]

M - Mass of Neutron Star, M = 2*2*10³⁰ kg

h - Height above the surface of Neutron Star, h = 4R

u - Initial velocity of the mass, u = 10km/s

v - Final velocity of the mass

v² = u² + 2GM [(1/R) – (1/R+4R)]

v² = u² + 2GM [(1/R) – (1/5R)]

v² = u² + 2GM [4R/5R²]

v² = u² + GM [8/5R]

Substituting all values we get,

v² = 10⁸ + [3.88*10¹⁶] 

v² = 3.88*10¹⁶

v    = 196,977,156 m/s

CONCLUSION

Thus the final velocity of the body on the surface of Neutron Star is 196,977,156 m/s or if it's moving with an initial velocity of 10km/s. It depends on the initial velocity of the body, mass and radius of planet but independent of mass of object.