In our Jyothisha Shastra, we believe that Bhumi is stable and that the Sun revolves around it. Ayanam means path, way. When the sun moves towards the northern direction, it is Uttarayanam and when it travels towards the southern direction, it is Dakshinayanam. The respective transition periods are considered Punya kalam. During these Punya kala-s, tharpanam, and Tiruvaradhanam must be performed. The Agamas must certainly have mentioned this. Azhwars and Acarya-s do appear to have dealt with this subject. If we get to know, will inform you.