Energy change due to gas drag for each orbit, as a function of its minimum approach distance to the planet with ζ = 3 × 10 ⁻⁹. Panels (a) and (b) show the results for and (30, 0), respectively. Red pluses and green crosses represent prograde and retrograde trajectories (see the text for their definitions), respectively. Blue asterisks show energy change in the case without gas drag, that is, errors in our numerical integration. Dashed and dotted lines show the analytic results for the prograde and retrograde shear-dominated cases, respectively. The solid line shows the analytic result for the dispersion-dominated case.