Some adjectives formed with either -ic or -ical endings have exactly the same meaning in general use:
botanic/botanical electric/electrical mythic/mythical zoologic/zoological
But in other cases the meaning is different, and you will need to check to make sure you are using the correct form:
an astronomic rise in prices [a large increase] astronomical calculations [calculations made in astronomy]
comic [relating to comedy] comical [amusing]
economic issues [relating to the economy] economical with the housekeeping [keeping costs down]
a historic building [important because of its history] historical data [in the past]
Check formal names (such as those of gardens, zoos, societies and precincts) that contain interchangeable forms:
Australian National Botanic Gardens Royal Tasmanian Botanical Gardens
The -ly adverbs derived from these adjectives are always based on those with the -ical ending, whatever the meaning:
astronomically botanically economically historically
The same alternatives occur with -istic and -istical:
statistic/statistical/statistically mechanistic/mechanistical/mechanistically