Following in the footsteps of Frank Wild, Shackleton's right-hand man, The Guardian's Bella Bathurst heads towards Antarctica – a magical land of towering icebergs and fascinating wildlife.

Everyone who has gathered here in Ushuaia, at the southernmost tip of Argentina, has an agenda – needs, desires, something they hope the ice will show them.

Most passengers have paid richly for the privilege: tickets start high and end somewhere in the upper atmosphere. There are several twitchers, and a couple of bucket-list completionists knocking off the last of their seven continents. Some are after the full box-set of penguins, and some are just seeking a place where the world can't reach them. One couple walked into the travel agent's planning a trip to Africa and walked out with a ticket to the end of the world. The rest have reason to be here – scientists hitching a ride, polar experts, and those in search of Frank Wild.

A century ago, on 14 December 1911, Roald Amundsen raised the Norwegian flag at the South Pole. Because he's foreign and because he succeeded, it won't be his achievement that the British mark; it will be Scott's heroic failure, and Shackleton's great escape.

When the Weddell Sea ice crushed Ernest Shackleton's expedition vessel, the Endurance, during the Imperial Trans-Antarctic Expedition of 1914-16, his men took to the lifeboats and rowed their way to Elephant Island. There Shackleton left his second-in-command, Frank Wild, in charge of the main group while he and five men set off in the James Caird to find help 800 miles away in South Georgia. They succeeded; Shackleton, Wild and the rest finally returned to Britain ragged, malnourished, but alive and sane.

Back among the mapped territories, however, Shackleton lost his way. In photographs his face is young but his eyes are lightless. Five years later he contacted Wild – by then living and farming in South Africa – and asked if he'd like to act again as his second-in-command. The two balanced each other so well they almost became a single entity. "It is hardly necessary to write about him," Shackleton wrote of Wild in his book South. "He is my second self. I love him. He has been a tower of strength to me."

The Quest Expedition's aims were unsettled, but most of the original team came anyway. On 5 January 1922, just as they reached South Georgia, Shackleton died. With the blessing of his widow Emily, he was buried in the cemetery by the old Norwegian whalers' church at Grytviken.

Wild returned to South Africa and died there in 1939. Over the years, various attempts were made to publish his memoirs or write his biography, but none succeeded. Wild's achievements were as astounding as the Boss's: he was involved in five separate polar expeditions and remains one of only two people to have been awarded the Polar Medal four times. But myths clouded his later life: he'd lost all his money, he was a drunk, a waster, he was nothing without Shackleton. There were fights over his memoirs and, after his death, his medals. His ashes went missing.

Something about Wild seemed very resistant to completion – until now. On board the ship are Wild's new biographer Angie Butler, six of Wild's descendants who have flown in from Australia, Shackleton's granddaughter Alexandra, a Canterbury GP named Mike Wain who bought Frank Wild's Polar Medals at auction, and a small wooden box classified as hand baggage containing the now-recovered ashen remains of Frank Wild himself. We're here to do Shackleton backwards – from the Falklands to South Georgia to Elephant Island to the Antarctic Peninsula, with a ceremony at Grytviken to mark Wild's final reunion with the Boss. But in all other respects, our experience will be utterly different to theirs.

The ship we're on, the Akademik Ioffe, also has a history. Built and ice-strengthened in Finland to a Russian spec in 1989, it was designed for "hydro-acoustic research" – Cold War code for sonic mapping and surveillance, and for submarine detection. Silent, stable and thoroughly Soviet, the Ioffe is one of about 25 ships currently offering trips to the Antarctic to around 25,000 passengers a year. That figure alone explains almost everything about the way the poles have changed in the century since the Endurance was crushed. For those first explorers, the Antarctic was as foreign as the moon; now it's a holiday destination.

And so we unmoor. All our associations beyond the horizon recede and now we have nothing to do except examine our bizarre new climate. Days at sea begin to take on a recognisable routine: breakfast, lunch and dinner plus a nutrient-rich diet of lectures given by the expedition's respective experts. By the end of these 18 days we will have been fully briefed on the great explorers, the breeding habits of the cape petrel and the 47 names for ice. In between, there is the chance to be seasick or to stand enchanted for hours watching the sea rolling and unfolding as the albatross and the petrels swing beatless over the stern.

The Falklands look like the Hebrides; same diagonal vegetation, same proportion of sheep to people, same ability to seduce or assault with equal vigour. Shackleton never really got the point of this place. Staying at the governor's house on Port Stanley while trying to organise a vessel to rescue the men left on Elephant Island, he could not conceal his frustration. "The street of that port is about a mile and a half long," he wrote in South. "It has a slaughter-house at one end and the graveyard at the other. The chief distraction is to walk from the slaughter-house to the graveyard. For a change one may walk from the graveyard to the slaughter-house." His granddaughter Alexandra has a more patriotic view of the place. An abrupt, patrician figure, very definite, very English, she corrects anyone who offers a less-than-Empire view of the Falklands.

The Wilds, by contrast, are relaxed about their ancestor. The family's stock of prints by Frank Hurley, the expedition's photographer, got traded or swapped between them (in one case for a pack of cigarettes) and several of the original glass-plate negatives that Hurley snatched from the sinking Endurance were broken when they were kids playing tag in the laundry room.

"Scott and Shackleton have had their day," says Julie George, Wild's great-niece. "Now there's more of an emphasis on the unsung ones. I'll be really interested to see what it was about the Antarctic that kept pulling Frank back – what he called the 'call of the little voices'.''

South Georgia has six whaling stations. The only one that is still accessible is in Grytviken, where the few buildings still in use – the old Norwegian church and the world's most southerly post office – stand surrounded by the machinery once used by the whalers. Picturesque and macabre, the skeletal tanks and irrelevant engines dominate the bay. Shackleton was buried at Grytviken with full honours by his companions and the Norwegian whalers; now his right-hand man will be buried beside him. "Here you go, Frankie boy," says Julie fondly, placing the casket down on the altar.

The congregation sits: the Wilds, Alexandra Shackleton, Angie Butler, most of the Ioffe's passengers and crew, a group of British Antarctic Survey staff, and the full two-person might of the South Georgian authorities. Out of the church and on the way to the graveyard, the congregation sidesteps elephant seals sleeping like speed bumps across the track. Wild's ashes are placed in a new grave besides Shackleton's. For as long as the Boss has lain here, there has been a tradition that all ships' companies arriving in Grytviken toast him with a nip of whisky; the tradition is now extended for the first time to Wild.

The days on either side are bookended by wildlife. South Georgia has one of the largest king penguin rookeries in the world, home to about 250,000 birds all simultaneously laying, gestating, moulting, eating and singing tuneless intergalactic folk songs to each other. King penguin chicks take a year to go from egg to fully watertight penguin, and for most of that time they stand around on the beach smacking each other and mugging their parents for food. Finally, when the chicks are wider than they are tall and almost too fat to stagger into the sea, they vanish.

In the meantime they are photographed. Only those who have been here many times before don't fall victim to the conviction that nothing in life has been experienced unless it's been recorded in six formats. On top of that there are the penguin counters. Ron Naveen, head of the science and education foundation Oceanites, used to be a lawyer but chucked it in and came south. Since then he has been counting gentoo, adelie and chinstrap populations, his theory being that penguins are the canaries of global warming. 

On Elephant Island, Frank Wild was left in charge of 22 men while Shackleton set off for South Georgia. They found shelter under the two remaining lifeboats in a cove with a calving glacier at one end and the sea at the other. Thick pack ice meant it was four and a half months before Shackleton got through. When the Yelcho finally arrived, Wild was serving out lunch, "which was particularly good that day, consisting of boiled seal's backbone, limpets and seaweed".

Now the cove is unreachable; the glacier has receded and the sea has advanced. Still, we stand there on the bow, well-fed and warmly clothed, as remote from Wild's experience as if we were still in London or Sydney.

And then, finally, the place itself. "Welcome to Antarctica," says Prossin, as often as possible. "The coldest, highest, driest, windiest, darkest, loneliest place on the planet." And somehow, despite the penguin origami and the Soviet broadcasts, despite all the distance between us and Shackleton, this place is still astounding, and still unimaginable.

Unimaginable because it's vast – 10% of the world's continental surface, unimaginable because it doubles in size every winter, unimaginable because everything here somersaults the ordinary laws of physics. Waterfalls flow upwards, storms stay petrified, snow shrieks.

Going out in the Zodiacs, we slide past icebergs shaped like galleons, castles, symphonies. "People come down here for the wildlife," says author and guide David McGonigal. "But they return for the ice." Over millennia, the air in glacier ice is pressed out, compressing the water into an essence of itself. So the deeper the blue, the older the berg. In these abstract fragments is contained a record of ourselves and our planetary history like the rings on a 1,000-year-old tree.

This is the engine room; this is the place where climate and weather come from, where the world is made and unmade. Zipping from shore to ship to island on the Zodiacs, even the numbest of passengers stops taking photographs and listens. Ice snaps, birds cry and once in a fabulous while, a glacier or an iceberg calves with a sound like the end of time.

Does any of this connect to the journeys that the great explorers made? Not really. Reaching Antarctica is both too different and too usual now. But it does act as a reminder that part of what we reach for in Shackleton and Wild's story is not just that they got out, but that they came back. "What the ice gets," Shackleton said as he stood watching the Endurance crack and fall, "the ice keeps."

Bella Bathurst; the Guardian.

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