The mass of a certain neutron star is 2.0 x 1030 kg and its radius is 6,000 m (6 km). What is the acceleration of gravity at the surface of this condensed, burned out star?
acceleration= GM/r^2
To find the acceleration of gravity at the surface of the neutron star, we can use Newton's law of universal gravitation, which states that the force of gravity between two objects is given by:
F = (G * m1 * m2) / r^2
Where F is the force of gravity, G is the gravitational constant (6.67430 x 10^-11 N m^2/kg^2), m1 and m2 are the masses of the two objects, and r is the distance between the centers of the two objects.
In this case, we are interested in the force of gravity at the surface of the neutron star, so we can assume that the mass of the neutron star is concentrated at its center. Therefore, the distance between the center of the neutron star and its surface is equal to the radius of the neutron star (r = 6,000 m).
The force acting on an object due to the gravitational attraction of the neutron star is given by:
F = m * g
Where m is the mass of the object and g is the acceleration of gravity. In this case, we want to find g, so we can rearrange the equation:
g = F / m
Now, we can substitute the expression for F from Newton's law of universal gravitation:
g = (G * m_neutronstar * m_object) / r^2 / m_object
Since we want to find the acceleration of gravity at the surface of the neutron star, the object we're considering is something with mass m_object and negligible compared to the neutron star.
In this case, the mass of the neutron star is given as 2.0 x 10^30 kg, so we can substitute these values into the equation:
g = (6.67430 x 10^-11 N m^2/kg^2 * 2.0 x 10^30 kg) / (6,000 m)^2
Calculating this equation results in the acceleration of gravity at the surface of the neutron star.