'apsidally' originates from Greek via Latin: from Greek 'ἁψίς' (hapsis) meaning 'arch' or 'vault', which became Latin 'apsis'. The adjective-forming suffix '-al' produced 'apsidal' (relating to an apse or apsis), and the adverbial suffix '-ly' yielded 'apsidally'.

'apsidally' changed from Greek 'ἁψίς' to Latin 'apsis', then into Medieval/Modern Latin and Old/Middle English forms such as 'apse' (for the architectural recess). From the adjective 'apsidal' in English the adverb 'apsidally' was formed by adding '-ly'.

Initially it referred specifically to the apse (an architectural arch or recess); over time the root broadened to include the orbital sense 'apsis' (nearest/farthest orbital point), and the modern adverb can be used for either architectural or astronomical contexts.