The story starts with a comet called Gallia, that touches the Earth in its flight and collects a few small chunks of it. The disaster occurred on January 1 of the year 188x in the area around Gibraltar. On the territory that was carried away by the comet there remained a total of thirty-six people of French, English, Spanish and Russian nationality. These people did not realize at first what had happened, and considered the collision an earthquake.
They first noticed weight loss: Captain Servadac's adjutant Ben Zoof to his amazement, jumped twelve meters high. Zoof with Servadac also soon noticed that the alternation of day and night is shortened to six hours, that east and west changed sides, and that water begins to boil at 66 degrees Celsius, from which they rightly deduced that atmosphere became thinner and pressure dropped. At the beginning of their stay in Gallia they noticed the Earth with the Moon, but thought it was an unknown planet. Other important information was obtained through their research expedition with a ship, which the comet also took.
During the voyage they discovered a mountain chain blocking the sea, which they initially considered to be the Mediterranean Sea and then they found the island of Formentera (before the catastrophe a part of the Balearic Islands), where they found a French astronomer Palmyrin Rosette, who helped them to solve all the mysterious phenomena. They were all on the comet which was discovered by Rosette a year ago and predicted a collision course with Earth, but no one believed the astronomer, because a layer of thick fog at the time prevented astronomical observations in other places.
As found by a new research expedition, the circumference of Gallia was 2320Â km. The mass of the comet was calculated by Rosette. He determined it at 209,346 billion tonnes. For the calculation he used spring scales and forty 5-franc silver coins, the weight of which on earth equaled exactly to one kilogram. However, the owner of the scales, Isaac Hakkabut, had rigged the instrument, so the results had to be cut by a quarter.
Involuntary travelers through the Solar system did not have any hope for long-term colonization of their new world, because they were lacking arable land. They ate mainly the animals that were left on the land carried away by Gallia. One strange phenomenon they met was that the sea on the comet did not freeze, even though the temperature dropped below the freezing point (theory that the stationary water level resists freezing level for longer than when a rippled by wind). Once a stone was thrown into the sea, the sea froze in a few moments. The ice was completely smooth and allowed skating and sleigh sailing.
Despite the dire situation in which the castaways found themselves, old power disputes from Earth continued on Gallia, because the French and English officers considered themselves the representatives of their respective governments. The object of their interest was for example previously Spanish Ceuta, which became an island on the comet and which both parties started to consider an unclaimed territory. Captain Servadac therefore attempted to occupy Ceuta, but was not successful. It turned out that the island had been occupied by Englishmen, who maintained a connection to their base at Gibraltar through optical telegraph.
Gallia got to an extreme point of its orbit and then began its return to Earth. In early November Rossete's refined calculations showed that there will be a new collision with the Earth, exactly two years after the first, again on January 1. Therefore, the idea appeared to leave the comet collision in a balloon. The proposal was approved and the castaways made a balloon out of the sails of their ship. In mid-December there was an earthquake, in which Gallia partially fell apart and lost a fragment, which probably killed all Englishmen in Ceuta and Gibraltar. When on January 1 there was again a contact between the atmospheres of Gallia and Earth, the space castaways left in the balloon and landed safely two kilometers from Mostaganem in Algeria.

Question: How did the castaways return to Earth?
Answer: They calculated the time of another collision between Earth and comet and left the comet in a balloon they made from the sails of their ship