Question

If Earth’s Moon were replaced with a typical neutron star, what would the angular diameter of the neutron star be as seen from Earth?

Answer 1

Answer:

$0.00005202\ \text{rad}=0.003^{\circ}$

Explanation:

d = Diameter of typical neutron star = 20 km = 20000 m

D = Distance between Earth and Moon = $384.4\times 10^6\ \text{m}$

Here, $D>>d$ so we use small angle approximation

$\delta=\dfrac{d}{D}\\\Rightarrow \delta=\dfrac{20000}{384.4\times 10^6}\\\Rightarrow \delta=0.00005202\ \text{rad}=\dfrac{0.00005202\times 180}{\pi}=0.003^{\circ}$

The angular diameter of the neutron star would be $0.00005202\ \text{rad}=0.003^{\circ}$ from Earth.