Astronomers will celebrate a remarkable event on 11 July. It will be exactly one year since the planet Neptune was discovered. Readers should note a caveat, however. That year is a Neptunian one. The great icy world was first pinpointed 164.79 years ago – on 23 September 1846. And as Neptune takes 164.79 Earthly years to circle the sun, it is only now completing its first full orbit since its detection by humans. Hence those anniversary celebrations.

And there is much to commemorate – for Neptune's discovery marked a turning point in astronomy. Its existence was revealed, not through a serendipitous observation by an astronomer but by the careful work of mathematicians. They calculated that perturbations in the orbit of Uranus, then thought to be the sun's most distant planet, could only be explained by the existence of another, even remoter world whose gravity was affecting Uranus's path.

The mathematicians – Englishman John Adams and Frenchman Urbain Le Verrier – made their calculations separately. Both agreed, however, where in the sky astronomers would pinpoint the planet causing those perturbations. But they dealt with the information very differently, says historian Allan Chapman of Wadham College, Oxford.

"Adams made a mismanaged attempt to interest the then astronomer royal George Airy while Verrier went public, announcing his prediction in the journal Comptes Rendus. Astronomers in Berlin then turned their telescope to the part of the sky he highlighted – and spotted Neptune."

What followed was equally dramatic. "Society was then undergoing a communications transformation every bit as profound as today's digital revolution," says Chapman. "Packet ships, railways and telegraphs allowed newspapers and journals to be sent across Europe in days. As a result, the Liverpool brewing magnate William Lassell turned his own powerful telescope towards the new planet 10 days later. In fact, only bad weather stopped him doing so earlier. The planet appeared as a blue disc with a white 'star' near it. He had discovered Neptune's moon Triton."

Astronomy was becoming a fast-moving international science – though identifying the exact roles of Adams and Verrier in making the discovery was controversial. France was indignant when Britain demanded retrospective recognition for Adams's part in Neptune's discovery.

As to the nature of the planet, this was only revealed in full in 1989 when the US probe Voyager 2 swept past it and sent back images of a seemingly serene blue world – though later analysis revealed dark spots on its surface that are vast cyclonic storms.

But the real surprise came from Triton, says Professor Carl Murray of Queen Mary, University of London. "We found it had a thin atmosphere and huge streaks of black material across its surface. These are created by geysers of dust and nitrogen erupting from under Triton's icy surface as it is heated by the sun. In other words, even at the edge of the solar system, where temperatures are more than -200C, sunlight can still drive distinctive weather systems. It is quite extraordinary."