However, things become very different for a SQM planet orbiting a SQM star. Due to its extreme compactness, a SQM planet can spiral very close to its host SQM star without being tidally disrupted. Such a compact system then becomes very efficient in producing strong gravitational waves. Upcoming gravitational wave detectors such as Advanced LIGO and the Einstein Telescope can detect gravitational waves arising from the in-spiral of a SQM planet into its host SQM star.
There are a number of possible mechanisms that can result in the formation of a SQM planet. One mechanism involves newly-born SQM stars that are very hot and exceedingly turbulent. The strong turbulence can eject planetary-mass clumps of SQM. If these clumps remain gravitationally bound, SQM planets are produced. A SQM planet with 1/10th the mass of Jupiter (i.e. 32 Earth masses) would measure only ~1000m in diameter.
J. J. Geng, Y. F. Huang, T. Lu (2015), “Coalescence of Strange-Quark Planets with Strange Stars: a New Kind of Sources for Gravitational Wave Bursts”, arXiv:1501.02122 [astro-ph.HE]