Final answer:
An observatory on Moom offers unobstructed views of the universe, advantageous for 360-degree astronomical observations. However, a disadvantage is the limited continuous operation time due to Moom's lack of axial rotation and the requirement of Earth's direct line of sight.
Step-by-step explanation:
An advantage of having an observatory on Moom's surface is the ability to obtain unobstructed views of the universe from every angle as Moom completes its orbit around Earth without axial rotation. This unique characteristic would allow astronomers to observe each part of the sky evenly over time, providing a 360-degree panoramic view of the cosmos unachievable from Earth-based observatories, all without Earth's atmosphere causing distortion or light pollution.
One disadvantage, however, is that since Moom does not rotate and Earth must "see" the observatory at all times, the observatory would not be able to operate continuously. Earth's perspective on Moom changes as both bodies move, causing potential interruptions when Moom's observable location is not facing Earth, thus limiting the available observation time and requiring precise timing for data collection.