# Latitude: planeto-graphic and planeto-centric

Planeto-centric latitude, and the planeto-graphic latitude,

Req/Rpl
= tan-1 [ tan()/2 ]
= tan-1 [ tan() · 2 ]
R() = Req Rpl/[R2eq · sin2() + R2pl · cos2()]
f = (Req - Rpl)/Req
e = [ R2eq - R2pl]/Req = [ 1 - (Rpl/Req)2]
S = total area = 2 · R2eq + (R2pl/e) · loge [ (1 + e)/(1 - e) ]
V = total volume = 4/3 R2eq · Rpl
If e = 0 then
S = 4 · Req · Req

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

<R> = (R2eq · Rpl)(1/3)

 ReqKm RplKm Req/Rpl f e Km Venus 6051.0 6051.0 1.000000 0.000000 0.000000 6051.00 Earth 6378.5 6356.0 1.003540 0.003527 0.083920 6370.99 Mars 3393.0 3375.0 1.005333 0.005305 0.102869 3386.99 Jupiter 71492.0 66854.0 1.069375 0.064874 0.354316 69911.33 Saturn 60268.0 54364.0 1.108601 0.097962 0.431658 58232.01 Uranus 25559.0 24973.0 1.023465 0.022927 0.212906 25362.16 Neptune 24820.0 24274.0 1.022493 0.021998 0.208597 24636.66 Titan 2575.0 2575.0 1.000000 0.000000 0.000000 2575.00