We give a first rigorous characterization of Operational Design Domains (ODDs) for Machine Learning (ML)-based aeronautical products. Unlike in other application sectors (such as self-driving road vehicles) where ODD development is scenario-based, our approach is data-centric: we propose the dimensions along which the parameters that define an ODD can be explicitly captured, together with a categorization of the data that ML-based applications can encounter in operation, whilst identifying their system-level relevance and impact. Specifically, we discuss how those data categories are useful to determine: the requirements necessary to drive the design of ML Models (MLMs); the potential effects on MLMs and higher levels of the system hierarchy; the learning assurance processes that may be needed, and system architectural considerations. We illustrate the underlying concepts with an example of an aircraft flight envelope.