Answer:
The surface gravity of the neutron star is [tex]g = 6.63x10^{12}m/s^{2}[/tex]
Explanation:
To determine the value surface gravity is necessary to combine the equation of the weight and the equation for the Universal law of gravity:
[tex]W = m.g[/tex] (1)
Where m is the mass and g is the value of the gravity
[tex]F = G \frac{M.m}{R^{2}}[/tex] (2)
Equation (1) and equation (2) will be equal since the weight is a force acting on the object as a consequence of gravity:
[tex]m.g = G \frac{M.m}{R^{2}}[/tex] (3)
Then g will be isolated from equation 3:
[tex]g = G \frac{M.m}{m.R^{2}}[/tex]
[tex]g = \frac{G.M}{R^{2}}[/tex] (4)
The mass of the Sun has a value of [tex]1.989x10^{30} kg[/tex]
Therefore, the mass of the neutron star will be:
[tex]m_{nstar} = 5(1.989x10^{30} kg)[/tex]
[tex]m_{nstar} = 9.945x10^{30} kg[/tex]
Finally, equation 4 can be used:
[tex]g = \frac{(6.67x10^{-11} N.m^{2}/kg^{2})(9.945x10^{30}kg)}{(10000m)^{2}}[/tex]
[tex]g = 6.63x10^{12}m/s^{2}[/tex]
Hence, the surface gravity of the neutron star is [tex]g = 6.63x10^{12}m/s^{2}[/tex].
