describe the main differences between the earth centred model of the universe and the sun centered modeland epalin the meaning of retrograde motion...

The Earth was once thought to be the center of not only the solar syster but of the universe.  These beliefs, dogmaticaly supported by the Catholic Church were accepted as fact and any question of their validity was considered herasy, a crime that could result in torture and death.  Then came along Gaileo who built a device to look at things closely - a microscope of sorts.  In his tinkering he noticed that positioning two lens' in front of one another and pointing it up at the darkened sky he was amazed to see the heavenly bodies from a new perspective.

Ashrof, you nearly answered your third question with your second one.  Galileo began to make consistant daily observations of the night sky and saw that the behavior of the planets, which were larger and closer than the stars were different than all the rest of the countless stars.  As stars seemed to cross the night sky together sort of like a big sheet with pin holes of light, the planets were seen to make circles and elipses, which is now called retrograde motion.  Carefull analysis of this(there is math involved,however your question is directed at the astronomy involved) led Galileo to conclude that the planets were circling the sun - not the Earth and if they were circling the sun then surely the Earth must be doing the same.  Further observations with Galileo's telescope and improvements to it led to the science of astronomy.

Naturally the Church was dipleased at Galileo and his notions because up until then it was a matter of Church dogma and faith that said since "Man" is God's finest creation it follows that everything else revolved around him and his home, namely Earth - known as the Earth centered model of the Universe. With all we have come to learn through astronomy and space study we now understand that we live in a sun centered solar system which resides on the fringe of a spiral galaxy known as the Milky Way and the universe consists of countless galaxies,stars,nebulas,black holes,pulsars, quasars and so much more yet to be discovered.  I hope I have anawered you question Ashrof,

Yours truely, Paul Agogliati