f[θ_,β_]=Sin[θ]^2/(1-β Cos[θ])^5

PolarPlot[f[θ,0],{θ,0,2π},AspectRatio->1]

t1=Table[PolarPlot[f[θ,n],{θ,0,2π},AspectRatio->1,PlotRange->All],{n,0,.9,.1}]

γ[β_]=1/Sqrt[1-β^2];
g[θ_,ϕ_,β_]=1/(1-β Cos[θ])^3*(1-Sin[θ]^2*Cos[ϕ]^2/γ[β]^2/(1-β Cos[θ])^2)

SphericalPlot3D[f[θ,0],{θ,0,π},{ϕ,0,2 π}]

SphericalPlot3D[f[θ,.5],{θ,0,π},{ϕ,0,2 π}]

SphericalPlot3D[f[θ,0.7],{θ,0,π},{ϕ,0,2 π},PlotRange->All]

SphericalPlot3D[f[θ,0.9],{θ,0,π},{ϕ,0,2 π},PlotRange->All]

SphericalPlot3D[g[θ,ϕ,0],{θ,0,π},{ϕ,0,2 π},PlotRange->All]

SphericalPlot3D[g[θ,ϕ,.5],{θ,0,π},{ϕ,0,2 π},PlotRange->All]

SphericalPlot3D[g[θ,ϕ,.9],{θ,0,π},{ϕ,0,2 π},PlotRange->All]