Chapter 10, Section 10.7, Figure 10.25

Start by defining a function that returns the orbital radius, r, for a given semi-major axis, a, eccentricity, e, true anomaly, f and longitude of pericentre, ϖ.

r[a_,e_,ϖ_,f_]:=a(1-e^2)/(1+e Cos[(f-ϖ) °]);

Plot radius as a function of longitude for Pandora.

pa = Plot[r[141700,0.0042,22,t],{t,0,360}]

Plot radius as a function of longitude for Prometheus.

pr = Plot[r[139350,0.0024,173,t],{t,0,360}]

Plot radius as a function of longitude for the F-α strand.

fα = Plot[r[140089,0.0026,230,t],{t,0,360}]

Plot radius as a function of longitude for the F-β strand.

fβ = Plot[r[140176,0.0026,230,t],{t,0,360}]

Plot radius as a function of longitude for the F-γ strand.

fγ = Plot[r[140219,0.0026,230,t],{t,0,360}]

Plot radius as a function of longitude for the F-δ strand.

fδ = Plot[r[140366,0.0026,230,t],{t,0,360}]

Display all the orbits together.

Show[pa,pr,fα,fβ,fγ,fδ, 
     PlotRange->{{0,360},{138900,142500}},
     Frame->True]