The Brisbane Observatory, in Largs, North Ayrshire, was built in 1808 by Sir Thomas Brisbane, an officer in the British Army.
Sir Thomas, born in 1773, was a keen star-gazer, and had studied astronomy and mathematics at the University of Edinburgh.
He helped catalogue 7,385 stars in the southern hemisphere and his work in the 1800s was so significant that a crater on the moon was named after him.
Despite the poor condition of the observatory, hopes are high that it could be restored to its former glory - if £100,000 can be raised.
Campaigners from the Brisbane Observatory Trust say the building is 'internationally significant' and the clock is ticking to save it.
Historian Valerie Campbell, who is also a director of the campaign, said: "We firmly believe that this internationally important 'lost' observatory built by Sir Thomas Brisbane must be saved for future.
"Firstly the building must be brought into a stable and secure condition before any further work is considered.
"The trust's aim is to preserve the observatory and provide controlled access to it.
"We want to involve the community in this effort."
In the 1940s the observatory had a roof and was in good condition - but years of neglect have seen it fall into a state of disrepair.
The trust is keen to raise enough cash to start an archaeological excavation of the interior and vital preservation work, but funding applications have so far proved unsuccessful.
Trust director Martin Maiden said: "Parts of the observatory are in delicate condition where there is a sign of movement in rubble masonry.
"This requires immediate attention to stabilise these sections of the wall.
"We cannot let this piece of the town's history be lost forever."
The observatory was originally designed to house cutting-edge telescopes to enable high precision calculations.
Sir Thomas also built the first observatory in Australia too, after he was appointed Governor of New South Wales in 1821, and sent out to oversee convict settlements.
He established the country's first observatory at Parramatta, west of Sydney, and the city of Brisbane which he founded was named after him.
But he later returned to Scotland, and died in Largs, on January 27, 1860.
Trust treasurer, Eileen Rae, said: "The Brisbane Observatory is in urgent need of stabilisation and repair.
"The cost of doing that is around £100,000.
"In spite of numerous applications being made to a wide range of funding bodies, none of these have been successful yet.
"Unless funding is found very soon, this historic and internationally significant observatory will be lost forever."