Question

How thick a layer would Earth form as it wraps around the neutron star’s surface? Assume that the layer formed by Earth has the same average density as the neutron star. (Hint: Consider the mass of Earth to be distributed in a spherical shell over the surface of the neutron star and then calculate the thickness of such a shell with the same mass as Earth. The volume of a spherical shell is approximately its surface area times its thickness: Vshell=4πr2×thickness. Because the shell will be thin, you can assume that its radius is the radius of the neutron star.)

Answer 1

Step-by-step explanation:

Let the radius of the neutron star be R.

Its surface ares a will be 4πR² . Let the thickness required be t .

The volume of the envelop of thick shell

4πR² t .This must be the volume of the sphere

= 4/3 πR³

mass = 4/3 πR³ ρ where ρ is the density of the star. ρ will also be density of shell's envelop. So mass of envelop

= 4πR² t .

Given that

mass of envelop = mass of the earth

4πR² t ρ = 4/3 πR³ ρ

R = 3t