After the introduction of astronomy by the Ancient Greeks and of rocketry by the Chinese no significant work was done that contributed to man's eventual arrival in space until the European Renaissance.
By this time astronomy had arrived in Europe via Arab translations of the Ancient Greek's work and rocketry had also reached Europe, probably via the Mongol civilisation.

It should be noted that during this interim period there are frequent reports of development of military rockets until around the 15th century.
However despite this work resulting in some improvement they have to be regarded as modest achievements in the overall picture so we shall not pursue them any further.

Come the 16th century the rocket seemed to become virtually redundant as a weapon of the military and it instead became used almost exclusively in fireworks. The only point worth mentioning here was an achievement of a prominent firework maker, called Johann Schmidlap, who invented a step rocket (a primitive idea of a multi-stage rocket) to allow his fireworks to achieve greater height before they exploded.

Copernican Heliocentric Universe

Copernicus, De Revolutionibus Orbius Coelestium

The 16th century, however, was to produce some extremely significant work in the field of astronomy. In 1533 Nicolaus Koppernigk (Copernicus)(1473-1543) revived the heliocentric theory of the universe. This theory was revolutionary because it was based upon solid evidence in the form of Copernicus' observations of the retrograde motion of Mars and whereas the Ptolemaic geocentric system had always had difficulty explaining this retrograde motion, the heliocentric theory provided a simple answer.
Further to this, the heliocentric theory was able to explain why both Mercury and Venus were always seen in close proximity to the sun (as seen from the Earth), which again made little sense under the geocentric theory.

Originally this system massively reduced the need for epicycles to explain planetary motion, Copernicus then realised some were needed to explain the more subtle irregularities that had been observed, and slowly as more and more were added the greatest single advantage of his system, the simplicity, was eroded away.
If we know now that the heliocentric theory is the correct answer then what was causing these difficulties for Copernicus?
At this stage there was no reason to doubt that the heavens had any imperfections so he continued to cling on to the idea of the planets moving in perfect circles, which of course we now know is not the case.

It is worth pointing out that Copernicus also proposed that the Solar System was very small compared with the whole universe, this was another revolutionary idea for his time.

Despite Copernicus putting his theory together in 1533 it remained unpublished until 1543, the year of his death, as he feared the reaction of the Roman Catholic church, because his theory was contrary to their doctrine of the Earth at the centre of the universe.

Following Copernicus' work came a real revival in astronomy with a great deal of work being produced during the 16th and 17th centuries. The first major figure was undoubtedly Tycho Brahe (1546-1601). He made a massive contribution by carefully measuring the positions of all astronomical bodies thereby compiling the most comprehensive records of astronomy that had been put together up to this point. He was, however, unable to realise the great potential of his work as he lacked the mathematical skills but he did prove that the stars and other celestial bodies were indeed a great distance from the Earth.

His records then passed onto Johannes Kepler (1571-1630) who was to make an outstanding and revolutionary discovery.

Go on to the Dawn of Modern Astronomy and Physics (Kepler)
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