Employing high order constellations is inevitable in order to achieve high spectral efficiency in satellite communication systems. In DVB-S2X standard, constellations with up to 256 points have been included. However, optimizing such high order constellations is a difficult task. In this paper, we study circular constellations obtained as the image of the QAM under the radial map. Constellations with 16, 64 and 256 points are shown to have a mutual information very close to the peak power limited capacity for a large range of SNR values. For constellations with 256 points gains of at least 0.5 dB can be obtained with respect to the DVB-S2X standard. To have a more realistic view, we also consider the effect of the phase noise on our proposed constellations.