Desperate attempts are under way to save a baby humpback whale which is trying to bond with yachts in Sydney harbour, after mistaking the boats for its mother.

The two week old calf, which has been abandoned by its real mother, was spotted nuzzling up to a whale-sized boat in the picturesque Pittwater waterway just north of Sydney on Monday.

Rescuers from the New South Wales National Parks and Wildlife Service towed the yacht out to sea hoping to entice the calf to find other whales who would adopt it. Eventually the calf detached itself from the boat, although it remained swimming close to it.

However today the baby whale had returned to the Pittwater basin, where spotted swimming “rather energetically” around other yachts in the area.

The race is now on to save it, but wildlife experts are pessimistic about their chances.

The calf, which needs urgently to find a mother to suckle to, is in “grim danger” if it does not find a substitute,said John Dengate, a spokesman for the New South Wales National Parks and Wildlife Service. The only option is for the calf to find another pod of whales with a mother who can adopt it.

“We’ve wracked our brains to think of some kind of captive approach we can do, by taking it in and rearing it ourselves, but it seems to be impossible in Australia, and possibly around the world,” Mr Dengate said.

Baby whales suckle for 11 months on vast amounts of high fat milk and put on approximately 2 pounds a day. To raise this calf by hand, someone would have to take it in and feed it a special formula of whale milk substitute. They would also have to have the capacity to house it until it is grown to its full adult size of 40–50 ft (12-16m), with a weight of approximately 79,000 pounds (36,000 kg).

“It is pretty much an impossible ask,” Mr Dengate said. “It’s just heartbreaking, the only thing we can do is monitor the little fella and hope he finds a new mum.”

Whales are quite often spotted in and around Sydney Harbour and along the coastline of eastern Australia. In July and August (the height of Australia’s winter), humpback whales traditionally take part in their northern migration, where they are spotted up and down the coast as they head towards Hervey Bay in Queensland, where they mate and have babies.

In September and October – prime whale watching time in Australia - they migrate south again in small groups with their calves in tow, to the colder feeding grounds of the Southern Ocean.

Mr Dengate said at least one or two humpback whale calves usually wash ashore each year. Just last month one was found washed up at Ballina in northern NSW.

“There’s not much more time this little thing can survive without being fed,” Mr Dengate said. “It’s a grim situation.”

Times recommends

• Energy-saving ideas from switched-on professor
• Rooks are as clever with tools as chimpanzees
• Burping of the lambs blows roast off menu