Millimeter-sized objects trapped at a liquid surface distort the interface by their weight, which in turn attracts them towards each other. This ubiquitous phenomenon, colloquially called the “Cheerios effect” is seen in the clumping of cereals in a breakfast bowl, and turns out to be a highly promising route towards controlled self-assembly of colloidal particles at the water surface. Here, we study capillary attraction between levitating droplets, maintained in an inverse Leidenfrost state above liquid nitrogen. We reveal that the drops spontaneously orbit around each other – mirroring a miniature celestial system. In this unique situation of negligible friction, the trajectories are solely shaped by the Cheerios-interaction potential, which we obtain directly from the droplet’s dynamics. Our findings offer an original perspective on contactless and contamination-free droplet cryopreservation processing, where the Leidenfrost effect and capillarity would be used in synergy to vitrify and transport biological samples.