Latitude: planeto-graphic and planeto-centric

Planeto-centric latitude, theta

and the planeto-graphic latitude, phi

R_eq/R_pl

= tan^-1 [ tan( phi

² ]

= tan^-1 [ tan( theta

) ·

² ]

) = R_eq R_pl/ sqrt

[R²_eq · sin²( theta

) + R²_pl · cos²( theta

)]

f = (R_eq - R_pl)/R_eq

e =

[ R²_eq - R²_pl]/R_eq = sqrt

[ 1 - (R_pl/R_eq)²]

S = total area = 2

· R²_eq +

(R²_pl/e) · log_e [ (1 + e)/(1 - e) ]

V = total volume = 4/3

R²_eq · Rpl
If e = 0 then

S = 4

· R_eq · R_eq

CRC Standard Mathematical Tables 26th edition, pg. 129. The volume of an oblate sphere is equal to a sphere with radius <R>.

<R> = (R²_eq · R_pl)^(1/3)

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