To complete Puzzle #9: Observatory you will first have to reach level 4. Once you have this requirement have a master scientist make the saw. Once the saw has been made have a scientist look for 2 whale bones in the whale skeleton pond and take them to the crafting bench. Drop a builder on the saw so he goes and cuts a tree trunk lighter. Now have a master scientist draw up plans for the framing of the observatory. Drop two adults to carry the lighter log to the observatory at the top of the map.
At this point you need to drop a master builder on the crafting hut and select bamboo which is then taken to the observatory to create a frame. This needs to be done 3 times. Drop two adults on the two statues (sun and moon) so they carry them to the observatory. Then craft an unpolished mirror in the crafting hut. Afterwards drop a scientist on the crafting hut and select the unpolished mirror so he takes it to the observatory.
At the observatory drop the scientist on the mirror so he polishes it. Drop the scientist again so he affixes it to the log. Now drop a master scientist on the trunk above the oven so he makes a wooden cog which is then taken to the observatory. If you now drop a master builder on the observatory they will repair and finish the observatory. Once done drop a master scientist on the observatory and they will research.
Check out our Puzzle #10: Reservoir page to get the solution for the next puzzle.