The answer to the question of why the role of Syriac in transmitting Greek science into Arabic is negligible in astronomy but important in philosophy and medicine lies in the history of Syriac science. There was little imperative to transmit Greek astronomy into Syriac because Babylonian astronomy was dominant and received in Syriac. Conversely, there was an imperative to transmit Greek philosophy, due to the lack of anything comparable in Syriac and a need that arose in the late fifth century. Medicine is an in-between case—there was a well-established Mesopotamian medical system, yet Greek sources were translated and integrated with it. This integration was rejected by Arab translators, the effects of which impacted modern scholarship. This analysis explains why influence varies by field and highlights how the modern study of the Syriac sciences has neglected their Mesopotamian background and focussed on how they received and transmitted Greek sources.
For Mandaic see Rochberg“Babylonian Origins” pp. 243–245who presents compelling evidence that suggests that the Mandaeans possessed at least partial translations of the earlier cuneiform material; for more examples see also Bhayro “Cosmology in Mandaean Texts.” For Jewish Aramaic see Ben-Dov Head of All Years who discusses this phenomenon in great detail; see also Bohak and Geller “Babylonian Astrology” who present a case involving a later medieval Jewish text and add: “This is not simply a general case of borrowing general ideas motifs or words but we have here a concrete example of a collection of accurate renditions of the same concepts being transmitted through similar or even identical wording while crossing linguistic and geographic boundaries” (p. 620).