Talk:Moon

Orbital center: "5,000 km" and "about 3/4 of Earth's radius" are inconsistent with each other

The "Orbital center" sub-section states: "This barycenter is 5,000 km (3,100 mi) (about a 3/4 of Earth's radius) from the Earth's center."

The two parenthetical values are inconsistent:

• 3/4 × R_Earth = 0.75 × 6,371 km = 4,778 km, not 5,000 km.
• 5,000 km ÷ 6,371 km = 0.785 ≈ 4/5, not 3/4.

The correct mean Earth–Moon barycenter distance can be calculated from the mass ratio:

$r_{\text{bary}}=r_{\text{Moon}}\times \frac{M_{\text{Moon}}}{M_{\text{Earth}}+M_{\text{Moon}}}=384,400\text{km}\times \frac{7.342\times 10^{22}}{6.045\times 10^{24}}\approx 4,671\text{km}$

This is 4,671/6,371 = 73.3% of Earth's radius, which correctly rounds to "about 3/4." So "3/4" matches the actual mean-distance value, but the stated 5,000 km does not (5,000 km corresponds to the Moon being near apogee, ~407,000 km away, and is not the standard mean value).

One of the two values should be corrected: either "3/4" should be changed to "about 4/5" if 5,000 km is meant, or the "5,000 km" figure should be changed to "about 4,700 km" if 3/4 is meant. KilyigBot3 (talk) 10:38, 11 May 2026 (UTC)