A satellite was launched into orbit to monitor the continuously melting glaciers.

Literal

Melt-continue [attributive-の] glacier [object-を] monitor [in-order-to-ために], man-made-satellite [subject-が] orbit [into-に] was-launched-up.

~ために expresses purpose ('in order to'). 溶け続ける is a compound of 溶ける ('melt') + 続ける ('continue') = 'continue melting.' 監視する ('to monitor / watch over'). 打ち上げる ('launch / shoot up') is a compound for rocket/satellite launches. 人工衛星 ('artificial satellite').