(a) Comparison between MacLaurin (violet) and the numerically computed solution at first (red), second (green), and third (blue) order. The Jacobi ellipsoid case is expected for ﹩\tfrac{{{\rm{\Omega }}}^{2}}{\pi G\rho }=0.374﹩ but is not represented here. (b) Absolute difference between the equatorial radius δa = a_ML − a₃ (polar radius δc) computed from the MacLaurin equation and Clairaut’s equations numerically solved at first (red), secod (green), and third (blue) order. The results in δa are plotted with lines, whereas the results of δc are represented with the red cross line at first order, the green square line at second order, and the blue circle line at third order. The horizontal line represents 2.5 km whereas the vertical line represents e = 0.67. The radius of the body is assumed to be 500 km.