To ascertain something is to determine it with certainty. That’s right, the key idea of ascertain is right there in the word itself: certain(ty). Contrasted with the verb learn, which can imply knowledge come upon without much effort (I just learned the show was canceled), ascertain suggests deliberate steps taken to confirm or verify the truth or particulars of a matter. Perhaps because certainty is harder to come by, we commonly find ascertain used in constructions that showcase its absence, as in long-term effects that are difficult to ascertain.
To call something arduous is to emphasize how much labor or effort it requires, or to call attention to how time consuming and tedious it is. An arduous task, for instance, is one that takes a long time to complete and is generally unpleasant to perform. An arduous journey is one that presents many perils and difficulties and requires great perseverance.
To consider something is to think about it, especially in order to make a decision. To contemplate something is to give it continued attention in a calm, reflective manner. This verb suggests an internal gazing or meditative state similar to the verbs muse and ponder. While the act of contemplation may certainly inform decisions, the verb often wanders free, untethered to aims or outcomes.