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Inclination of moon and earth gives earth four seasons.

Net Inclination of moon and earth is asummed to be zero in the inverse biquadrate gravity system. Degree of inclination is evaluated as orbital plane component of angular momentum.

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