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Imagine a neutron star could be broke into pieces.

How big would be the piece matching Earth's mass?

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    $\begingroup$ Why are people answering this question and not upvoting it? If a question is sufficiently good enough to warrant an answer, then it certainly warrants an upvote. $\endgroup$
    – zephyr
    Aug 21, 2018 at 17:00

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The question has no answer. The minimum mass for stable neutron matter is about 0.1 solar masses (see my answer here) and so is much more massive than the Earth.

As neutron stars become less massive they also become less dense, so your question is unanswerable at that level too, since we cannot put a figure on the density of something that cannot even exist in principle.

If your question is merely what radius is a spherical object that has a similar density to a typical neutron star, can you not do $$\frac{4\pi r^3}{3} \rho = M_{\rm Earth}$$ to find $r$?

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Volume is mass divided by density.

Earth's mass = 5.972x10²⁴ kg.

Neutron star's density = 10¹⁷ kg/m³.

The sought volume of a neutron star's piece with Earth's mass is then Earth's mass divided by neutron star's density, which makes 59720000 m³. This is a cube with the side length of 390.87 m or a sphere with radius of 242.48 m.

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    $\begingroup$ With that density of a neutron star we'd get a cube with the side length of roughly 271 m or a sphere with radius of 168 m. $\endgroup$
    – SergiusPro
    Aug 20, 2018 at 12:04
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    $\begingroup$ @MikeG In astronomy we don't quibble over factors that are off by less than 10x ;-) $\endgroup$
    – user1569
    Aug 20, 2018 at 13:21
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    $\begingroup$ Understood, but if the density isn't known with 1 significant digit, then the volume isn't known with 4 significant digits. $\endgroup$
    – Mike G
    Aug 20, 2018 at 15:05
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    $\begingroup$ This assumes that the density of the piece would remain constant, which I doubt. In general, more massive neutron stars are smaller, and less massive ones are larger. Of course, that doesn't tell us what would happen to relatively small chunks of a neutron star, but it does tell us that we shouldn't assume uniform density. $\endgroup$
    – HDE 226868 ♦
    Aug 20, 2018 at 15:56
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    $\begingroup$ Earth-mass chunks of neutron star material don't exist and cannot exist. $\endgroup$
    – ProfRob
    Aug 20, 2018 at 19:10

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