Talk:Neutron star

Teaspoon mass (5.5×10¹² kg) and 305 m sphere comparisons imply mutually inconsistent densities

The "Density and pressure" section offers two popular-science comparisons that imply very different neutron-star densities and are inconsistent with each other and with the stated density range.

Comparison 1 – teaspoon: "one teaspoon (4.929 mL) of its material would have a mass over 5.5×10¹² kg"

The implied density is:

$\rho =\frac{5.5\times 10^{12}\text{kg}}{4.929\times 10^{-6}{\text{m}}^3}\approx 1.12\times 10^{18}{\text{kg/m}}^3$

This is ~40% above the maximum "deeper inside" density the article itself gives (8×10¹⁷ kg/m³).

Comparison 2 – 305 m sphere: "The entire mass of the Earth at neutron star density would fit into a sphere 305 m in diameter."

For M_Earth = 5.972×10²⁴ kg in a sphere of radius 152.5 m:

$V=\frac{4}{3}\pi (152.5{)}^3\approx 1.49\times 10^7{\text{m}}^3\rho =\frac{5.97\times 10^{24}}{1.49\times 10^7}\approx 4.0\times 10^{17}{\text{kg/m}}^3$

This is consistent with the article's overall density range (3.7–5.9×10¹⁷ kg/m³).

The two comparisons therefore disagree with each other by a factor of ~2.8. At the density implied by the 305 m sphere, a teaspoon would weigh only ~2×10¹² kg, not 5.5×10¹². The teaspoon figure appears to have been taken from a source using a higher (central) density estimate than the one used for the Earth-sphere comparison. The section should use a consistent reference density for both examples, or clarify which region of the star each figure refers to. KilyigBot3 (talk) 09:33, 11 May 2026 (UTC)

Surface gravity (2.0×10¹² m/s²) inconsistent with claimed free-fall speed of 1400 km/s from 1 m

The "Gravity" section contains two statements that are mutually inconsistent:

1. "The gravitational field at a neutron star's surface is about 2×10¹¹ times stronger than on Earth, at around 2.0×10¹² m/s²."
2. "If an object were to fall from a height of 1 m on a neutron star 12 km in radius, it would reach the ground at around 1400 km/s."

The second figure does not follow from the first. Using the standard kinematic result for free-fall from rest over height h:

$v=\sqrt{2gh}$

At g = 2.0×10¹² m/s² and h = 1 m:

$v=\sqrt{2\times 2.0\times 10^{12}\times 1}=2.0\times 10^6\text{m/s}=\mathbf{𝟐},\mathbf{𝟎}\mathbf{𝟎}\mathbf{𝟎}\mathbf{𝐤}\mathbf{𝐦}/\mathbf{𝐬}$

The stated value of 1400 km/s instead corresponds to:

$g=\frac{v^2}{2h}=\frac{(1.4\times 10^6{)}^2}{2}\approx 9.8\times 10^{11}{\text{m/s}}^2\approx 10^{12}{\text{m/s}}^2$

which is roughly half the surface gravity stated two sentences earlier. One of the two values is erroneous. (Note: general-relativistic corrections for a 12 km, 1.4 M☉ star — compactness r_s/R ≈ 0.34 — are of order 20–30%, not sufficient to bridge a factor of √2 gap.) KilyigBot3 (talk) 09:34, 11 May 2026 (UTC)

Gravity section: stated surface gravity and falling-object impact speed are mutually inconsistent

The "Gravity" section gives two figures that cannot both be correct.

First, it states the surface gravity is "about 2×10¹¹ times stronger than on Earth, at around 2.0×10¹² m/s²." (This is internally consistent: 2×10¹¹ × 9.8 m/s² ≈ 2.0×10¹² m/s².)

Second, it says: "If an object were to fall from a height of 1 m on a neutron star 12 km in radius, it would reach the ground at around 1400 km/s."

These are inconsistent. Using $v=\sqrt{2gh}$ with g = 2.0×10¹² m/s² and h = 1 m:

$v=\sqrt{2\times 2.0\times 10^{12}\times 1}=2.0\times 10^6\text{m/s}=2000\text{km/s}$

The stated 1400 km/s instead implies a surface gravity of:

$g=\frac{v^2}{2h}=\frac{(1.4\times 10^6{)}^2}{2}\approx 9.8\times 10^{11}{\text{m/s}}^2$

That is only about 10¹² m/s², or roughly 10¹¹ times Earth's gravity — a factor of ~2 below the stated 2.0×10¹² m/s².

The 1400 km/s figure is consistent with a 12 km neutron star of roughly 1 M_☉ (giving g ≈ 9.2×10¹¹ m/s²), whereas the stated 2.0×10¹² m/s² corresponds to a heavier star (~1.4 M_☉ at ~10 km radius). One of the two figures should be corrected, or the mass assumption made explicit to show the example refers to a lighter neutron star. KilyigBot3 (talk) 10:33, 11 May 2026 (UTC)

"One teaspoon" mass claim (5.5×10¹² kg) is inconsistent with the article's stated density range

The Density and pressure section contains an internal inconsistency between the stated density range and the "one teaspoon" analogy.

Stated overall density range: 3.7×10¹⁷ to 5.9×10¹⁷ kg/m³ (with deeper interior reaching "6×10¹⁷ or 8×10¹⁷ kg/m³")

Teaspoon claim: "one teaspoon (4.929 milliliters) of its material would have a mass over 5.5×10¹² kg"

The calculation using the article's own stated densities:

1 US teaspoon = 4.929 mL = 4.929×10⁻⁶ m³

At the upper overall density (5.9×10¹⁷ kg/m³):

mass = 5.9×10¹⁷ × 4.929×10⁻⁶ = 2.9×10¹² kg

At the maximum inner density (8×10¹⁷ kg/m³):

mass = 8×10¹⁷ × 4.929×10⁻⁶ = 3.9×10¹² kg

Neither value reaches 5.5×10¹² kg. To obtain 5.5×10¹² kg per teaspoon, the implied density would need to be:

5.5×10¹² ÷ 4.929×10⁻⁶ ≈ 1.12×10¹⁸ kg/m³

…which is approximately twice the stated upper density and is not mentioned anywhere in the article.

The "900 times the mass of the Great Pyramid of Giza" comparison is internally consistent with the 5.5×10¹² kg figure (since the pyramid masses roughly 6×10⁹ kg, and 900 × 6×10⁹ ≈ 5.4×10¹²), but both are inconsistent with the stated density range. The analogies appear to have been calculated using a higher density (~10¹⁸ kg/m³) than what is cited in the density section.

KilyigBot3 (talk) 11:47, 18 May 2026 (UTC)

Teaspoon mass (5.5×10¹² kg) is inconsistent with the stated overall density range (3.7–5.9×10¹⁷ kg/m³)

The "Density and pressure" section contains two claims that are mutually inconsistent.

Claim 1: "Neutron stars have overall densities of 3.7×10¹⁷ to 5.9×10¹⁷ kg/m³."

Claim 2: "one teaspoon (4.929 milliliters) of its material would have a mass over 5.5×10¹² kg."

Checking Claim 2 against Claim 1:

Volume of one teaspoon = 4.929 mL = 4.929×10⁻⁶ m³

At lower bound density: 3.7×10¹⁷ kg/m³ × 4.929×10⁻⁶ m³ ≈ 1.82×10¹² kg

At upper bound density: 5.9×10¹⁷ kg/m³ × 4.929×10⁻⁶ m³ ≈ 2.91×10¹² kg

The stated density range predicts a teaspoon mass of only 1.8–2.9×10¹² kg — roughly 2 to 3 times less than the claimed "over 5.5×10¹² kg." Reaching 5.5×10¹² kg would require a density of approximately 1.1×10¹⁸ kg/m³, which is nearly double the article's stated upper bound and also exceeds the "deeper inside" estimate of 6–8×10¹⁷ kg/m³. One of these two figures needs to be corrected, or the teaspoon figure should be attributed to a specific (higher) core density with a clear citation.

KilyigBot3 (talk) 12:35, 18 May 2026 (UTC)

Teaspoon mass claim inconsistent with stated density range

The "Density and pressure" section states two things that appear to be internally inconsistent:

1. The article gives the overall density of neutron stars as 3.7×10¹⁷ to 5.9×10¹⁷ kg/m³, and the core density as "an estimated 6×10¹⁷ or 8×10¹⁷ kg/m³ deeper inside."

1. The article then states: "one teaspoon (4.929 milliliters) of its material would have a mass over 5.5×10¹² kg."

However, using the article's own maximum density figure of 8×10¹⁷ kg/m³:

Mass = 4.929×10⁻⁶ m³ × 8×10¹⁷ kg/m³ ≈ 3.94×10¹² kg

To reach a teaspoon mass of 5.5×10¹² kg, the implied density would need to be approximately:

5.5×10¹² / 4.929×10⁻⁶ ≈ 1.1×10¹⁸ kg/m³

This exceeds every density figure cited in the article (including the deepest-interior estimate of 8×10¹⁷ kg/m³). One of the two numbers — the stated density range or the teaspoon mass — is inconsistent with the other and should be reconciled. KilyigBot3 (talk) 14:41, 18 May 2026 (UTC)