κ=-4+3 (Sqrt[3])-6 ArcCoth[(Sqrt[3])]+Log[27] ;(* Objętość ekstremalnego modelu Roche'a o promieniu równikowym (Subscript[R, e])=1 *)

N[κ,32]

w2=Block[{ε=2/3},RegionPlot[{Legended[r^2+z^2<κ^(2/3),"Kula\no identycznej objętości"],Legended[1/Sqrt[r^2+z^2]+r^2(1/ε-1)>1/ε&&-1<r<1,"Ekstremalny\nmodel Roche'a"]},{r,-1,1},{z,-1,1},PlotPoints->132,Epilog->{{Dashed,Line[{{-1,2/3},{1,2/3}}],Text["2/3",{0,2/3},{0,-1}]},{ Arrow[{{0,0},{0,2/3}}],Text["(Subscript[R, p])",{0,1/3},{-1,0},BaseStyle->FontSize->16],Arrow[{{0,0},{1,0}}],Text["(Subscript[R, e])",{1/2,0},{0,-1},BaseStyle->FontSize->16]}}]]

Manipulate[Plot[Sqrt[ϵ^2+x^2],{x,-1,1},PlotRange->{0,1}],{ϵ,0,1}]

Realistyczny model  gwiazdy https://en.wikipedia.org/wiki/Achernar  Eri http://ester-project.github.io/ester/

ε=1-3/4 Ω^2/(2Pi G ρ)

ε/.{Ω->2Pi/Quantity[1,"Days"],G->Quantity[1,"GravitationalConstant"],ρ->Quantity[1,"EarthMass"]/(4/3Pi Quantity[1,"EarthMeanRadius"]^3)}

1-%

1/%

Quantity[1,"EarthPolarRadius"]/Quantity[1,"EarthEquatorialRadius"]//N

1-%

1/%