# Density of the moon

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In the conventional inverse square scheme, The Moon is exceptionally large relative to the Earth, being a quarter the diameter of the planet. and the Earth and Moon are still commonly considered a planet-satellite system instead of double planet

According to  Planet hypothesis of the moon, moon is planet and the mass known as earth,s is moon's

$\rho_m = 247.6$

From Angular mometum conservation,

$I_m \omega_m sin \theta_m = I_e \omega_e sin \theta_e$

If we assume equivalent density for moon and earth,

$R_m/R_e$ =2.626.

then $d_{me} = 0.38M* 2.626/0.273$ =3.656 Giga Meter

If we assume existent distance and size for moon and earth, and high density for moon,

$R_m/R_e =0.275. d_{me}=0.385$ Giga Meter

$\rho_m/\rho_e = (r_e/r_m)^5 \omega_e sin \theta_e /\omega_m /sin \theta_m =(42.99)^3$

which seems wrong values.

## New size and distanceEdit

From angular momentun conservation, tht size and distance are 9.549 times larger than those of conventional solar system.

In the inverse square scheme, density of moon becomes $245.3 ton/m^3$

In the inverse biquadrate scheme, $M_m = (d_{me})^5 (\omega_{me})^2 / G''$ Thus Gravitational mass density of moon is $228.4 ton/m^3$

## Surface gravityEdit

Gravitational accelerations on the suface of large planet such as Jupiter and Saturn are so small that Large planets have rings.

Moon also is large and gravitational acceleration on the surface is g/6 (0.1654g =1.622$m/s^3$) due to inverse biquadrate gravity.

## Conventional density profileEdit

 name depth(sq.) density depth(biq.) temperature remark Crust ~3474 35780.44 mean density=3 346.4 kg/m³ Upper Mantle 587~ 5605.3~ Lower Mantle 350~587km 3342.2~5605.3 Outer Core 160~350km 1527.85~3342.2 Inner Core 0~160km ~1527.85