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Wikipedia gives the following physical dimensions for the Moon:

Physical characteristics

Mean radius        1737.1 km  (0.273 of Earth's)
Equatorial radius  1738.1 km  (0.273 of Earth's)
Polar radius       1736.0 km  (0.273 of Earth's)

In all cases, the proportion of Earth's equivalent measurement is 0.273. If these figures are accurate, why aren't these numbers (0.273) different from each other at this scale? Obviously, if measured to enough decimal places, differences will appear.

The Moon has less gravity and rotates at a different speed from the Earth. Why don't these cause variability in the different radius measurements? Do they cancel out? It is a coincidence? Is there something about the Earth-Moon dynamics that means over millions of years these proportions gradually equalise?

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    $\begingroup$ Obviously, if measured to enough decimal places, differences will appear. Indeed, there are differences, but 3 significant digits is not enough to see that. The values (with more decimal places) would be 0.272657; 0.272509; 0.273095. If you calculate the flattening, you can also easily see the difference: Earth's flattening is 0.00335, while the Moon's is 0.00121. If you scaled the Earth to match the Moon's equatorial radius, its polar radius would be 1732.3, quite a significant difference. $\endgroup$ – FSimardGIS Jan 25 at 2:55
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Why is the difference from a perfect sphere the same for the Earth and the Moon?

It isn't, as soon as you look one more digit further.

From NASA's Earth Fact Sheet and Moon Fact Sheet which I found here

                             Moon (km)   Earth (km)      Ratio     (rounded)
Mean radius (volumetric)     1737.4       6371.000      0.27270      0.273
Equatorial radius            1738.1       6378.137      0.27251      0.273
Polar radius                 1736.0       6356.752      0.27310      0.273

If you would like to compare the Moon and Earth parameters further, see the Moon Fact Sheet:

nssdc.gsfc.nasa.gov/planetary/factsheet/moonfact.html

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    $\begingroup$ Thank you! I've updated the Wikipedia page from NASA's site now. $\endgroup$ – CJ Dennis Jan 25 at 7:16
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    $\begingroup$ @CJDennis that is excellent; thanks! $\endgroup$ – uhoh Jan 25 at 7:54

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