What is the magnitude of the gravitational field at the surface of a neutron star whose mass is 1.64 times the mass of the Sun and whose radius is 9.1 km?

Smith

To find the magnitude of the gravitational field at the surface of a neutron star, we can use Newton's law of universal gravitation.

The formula for the magnitude of the gravitational field is:

g = GM / R^2

Where:
g is the magnitude of the gravitational field,
G is the gravitational constant (approximately 6.674 x 10^-11 N m^2 / kg^2),
M is the mass of the neutron star, and
R is the radius of the neutron star.

In this case, the mass of the neutron star is given as 1.64 times the mass of the Sun, which we can denote as Msun. The radius of the neutron star is given as 9.1 km, which we need to convert to meters.

Step 1: Convert the radius from km to meters:
9.1 km = 9.1 × 10^3 meters

Step 2: Calculate the magnitude of the gravitational field:
g = (G * M) / R^2

Given that the mass of the Sun (Msun) is approximately 1.989 x 10^30 kg, we can calculate the mass of the neutron star as:
M = 1.64 * Msun

Substituting the values into the formula, we get:
g = (6.674 × 10^-11 N m^2 / kg^2 * 1.64 * 1.989 × 10^30 kg) / (9.1 × 10^3 m)^2

Now we can evaluate this expression to find the magnitude of the gravitational field at the surface of the neutron star.