In the electric bustle of big-city life, it is easy to forget to look up at the Moon. Transforming an exhibition space into a lunar embassy on London's Southbank over the course of a single lunar orbit, Republic of the Moon inspires us to confront our relationship with the Earth's lone satellite. Presented by The Arts Catalyst, a London-based organization that commissions art that engages with science, the travelling exhibition brings together a diverse collection of projects that weave lunar science and myth, and prod us to think, imagine and smile.

The exhibition leads the visitor through a series of rooms, each featuring the work of an international artist. Liliane Lijn's 'moonmeme' explores her ambition to project a word on the lunar surface that could be viewed from Earth. In a dark room, the word 'SHE' is projected in large block letters on to an image of the Moon, which changes according to the actual Moon's phase. Playing with the feminine symbolism in many cultures that is linked to the cyclic transformation of the Moon as seen from Earth, the letters disappear and reappear slowly over the lunar cycle. On each day of the exhibition, the Moon and the projected letters appear differently. A soundscape of shifting and morphing chants in the artist's voice of the word 'she' emphasizes the transformation that is occurring.

In Katie Paterson's piece 'Earth–Moon–Earth', a self-playing grand piano plays a Moon-altered version of Beethoven's Moonlight Sonata. The original score was translated into Morse code, transmitted to the Moon and reflected back to Earth, where it was retranslated into musical notes. The information lost in the reflection results in eerie gaps in the music. It's easy for the listener to imagine these lost fragments of Beethoven hiding in the shadows of the lunar surface. Paterson's 'Second Moon' project tracks, with a mapping app (www.secondmoon.org.uk), a lunar sample that is travelling anticlockwise around the globe via airfreight carrier at twice the speed of the Moon until September 2014. The lunar sample is displayed in the exhibition whenever it is passing through town.

The Man in the Moone, by Francis Godwin (1562–1633). Credit: © INTERFOTO / ALAMY

'Private Moon' by Leonid Tishkov tells the story of a man whose life companion is a glowing crescent moon. The series of photographs documents Tishkov's travels over the past ten years with his human-sized companion moon, which is present in the gallery, illuminating the photographs on display. The series explores the personal relationship that each of us has with the Moon. In the image of the man sitting alone in his apartment with his private moon, we sense how lonely Earth would feel without its faithful satellite.

Agnes Meyer-Brandis's gaggle of astronaut geese in 'Moon Goose Analogue: Lunar Migration Bird Facility' (www.ffur.de) seems to be, at first glance, a bewilderingly comical finale to a series of thought-provoking pieces. The premise — I dare you not to laugh — is this: the artist raised eleven geese from birth and is in the process of training them at her remote, self-established spaceport in Italy to migrate to the Moon. The geese were imprinted with their purpose in life as future Moon colonists before they even hatched, comforted by a plush moon toy as goslings and given astronaut names such as 'Buzz'. Their astronaut training has included pecking at physics books, flying lessons, high-altitude training in the Alps and anti-gravity exercises in water. The process is explained in a short documentary that accompanies the exhibit.

The geese live at a Moon analogue site that the artist has built for them at the spaceport. Cameras at the analogue site stream video back to a control room in the exhibit space. We can watch the geese pecking about in their command centre and walking around the cratered terrain. They are even conducting an experiment on the growth of a dandelion plant under non-directional gravity. Geese like to eat dandelions, so logically they will need to learn to grow them when they colonize the Moon. We are able to track the progress of the dandelion experiment in the gallery control room in real time.

All this goose-based lunacy was inspired by the 400-year-old book The Man in the Moone by Francis Godwin, in which a man travels to the Moon in a chariot pulled by flying geese. Meyer-Brandis explores the possibility that this book is historical fact rather than an early work of science fiction, and that perhaps geese could relearn their long-lost ability to migrate to the Moon. It's a fanciful idea and indeed a bit silly, and yet this project resonates. We see in these geese an echo of the human experience in space exploration. The images of goose footprints in analogue moon dirt are not unlike those of Apollo astronauts.

Although the lunar embassy in London will have shut its door by the time this goes to press, the art projects continue until the next installation of Republic of the Moon. The art is continually re-energized, as many of the exhibits link directly to the actual Moon, wherever it is in its path around the Earth. You may even find yourself wanting to look up from the city lights and greet the Moon.

Republic of the Moon is a touring exhibition commissioned by The Arts Catalyst with the Foundation for Art and Creative Technology (www.artscatalyst.org/moon). The exhibition was presented at the Bargehouse (Oxo Tower Wharf) in London from 10 January to 2 February 2014.