Question

A certain neutron star has five times the mass of our Sun packed into a sphere about 10 km in radius. Estimate the surface gravity on this monster.

Short answer

The surface gravity on this monster is $6.63\times {10}^{12}\mathrm{m}/{\mathrm{s}}^2$.

Step-by-step solution

Step 1. Given Data

The mass of the neutron star is $m_{\mathrm{n}}=5m_{\mathrm{s}}$.

The radius is $r=10\mathrm{km}$.

Step 2. Understanding the gravitational acceleration

In this problem, for calculating the surface gravity on the certain neutron star the relation of gravitational acceleration will be utilized.

Step 3. Estimating the surface gravity of the star

The relation of gravitational accelerationis given by,

$g=G\frac{m_{\mathrm{n}}}{r^2}$

Here, G is the gravitational constant.

On plugging the values in the above relation.

$\begin{array}{l}g=\left(6.67\times {10}^{-11}\mathrm{N}·{\mathrm{m}}^2/{\mathrm{kg}}^2\right)\left[\frac{5\left(1.99\times {10}^{30}\mathrm{kg}\right)}{{\left(10\mathrm{km}\times \frac{1000\mathrm{m}}{1\mathrm{km}}\right)}^2}\right]\\ g=6.63\times {10}^{12}\mathrm{m}/{\mathrm{s}}^2\end{array}$

Thus, $g=6.63\times {10}^{12}\mathrm{m}/{\mathrm{s}}^2$is the required gravitational acceleration.