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.)

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Physics

Jonah

21 October, 01:55

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.)

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Bradley · Answer 1

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