Eudoxus and Aristotle intergrated the platonic idea with observations, to create a mathematical viable geostationary solar system, although they didn’t reach a conclution the a wheel within a wheel system as shown about?? Was proposed by Appolonius of Perga (fl. 200 BC), developed by Hipparchus and perfected by Ptolemy (c. 100-178 AD).

The platonic system was accepted by the Christian church, the bible is littered with references to a earth centre universes, and being stationary. ???

As a result of the claps of the roman empire in 476 AD the platomic system remained the best predictions of comic positions for nearly 1500 years. In 622 AD the Islamic Empire extended eastwards into Europe, they translated the work by arestotel, plato ECT!!!!! In to Arabic, this was then later translated into laten, the langue of the European classical scholar, the document crurculated Europe. The acent greeks astronomical tables where still the superior to any created in Europe for many year but there was still no better model.

Regiomontanus (1436-76) was one of the fist people to work on the heliocentric solar system, this idea was used as a tool to calculate the position of the plants and was not taken to be the true arrangement, he couldn’t confurm his heliocentric ideas as there was not good enough tools for odservation available at the time. He worked using his own instruments, but his work was cut short by his untimely death.

In 1473 Nicolaus Copernicus was born in Poland he studied astronomy and mathematics, in his student day debates on the heliocentric solar system where commenly associated with his name

Copernicus didn’t concentrate on observing but on the mathematics devised Pythagoras. He belived that the universe revealed itself through the perfect geometry of planetary orbits. He was forced to reject the Ptolemaic system, because of technical imperfections, in platos ariginal theory all of the plants had a uniform speed, this idea was change so the the obsevation fitted the theory, a hypothetical point called a equant was created where the planet would appear to be moving at a uniform point. Copernicus could not accept this so to keep the perfect cirles and uniform speeds he concluded a heliocentric system. Although opernicus had not taking in to account a elliptical ordits. MATHS BEHIND THIS PLEACE

Copernicus . He concluded that the only way to 'save the phenomena' of perfect circles and uniform speeds was to place the Sun at the centre of the solar system and let the planets revolve around it, as Aristarchus had suggested. Since Copernicus assumed that the orbits of the planets are circular his scheme still needed epicycles to make it work, but the simulation was precise. For the first time, tables of planetary motion could be calculated from heliocentric principles. Furthermore, these tables proved more accurate than those based on the Ptolemaic system.

to support the helilcentric solar system Copernicus took a series of observations other his life. in 1515 Copernicus started to odserve the sun’s path, he descivered that the diurnal point of the Sun’s course has move by over 30 degrees since the odservations taken in Plato’s era. This gave him an indercation that the solar system was not static. DIAGRAM EXP MATHS LOT S

At this stage observations where by eye, using a verity of positioning techniques EEEEEEEEEE

After many years of reluctance on Copernicus part, In 1542 De Revolutionibus was printed, he dedication it to the Pope Paul III, he included the first picture of a sun centred solar system with the moon going around the earth on in turn the earth rotating around the sun.

Copernicus didn’t realise that the planets didn’t take a perfectly spherical orbit, but he work was a revolution for the time. Copernicus died just after De Revolutionibus was put in to circulation, the scientific community over looked it, they thought it was an interesting theory and it was a good calculation ad.

After the work of Copernicus Galileo Galilei entered the scene and was a supported of the heliocentric solar system. When the was young a bright new star in the constellation Cassiopeia appeared. Over a period of observation lasting 18 months, he noted how it first appeared brilliant enough to be seen in daylight, then dimmed and disappeared from sight. This event gave Galileo a new way of thinking, before the stars where thought to be a fixed “sheet” in the sky never changing but this event had made him think that the old rules where wrong.

Though out Galileo life the scienticfic world didn’t like the procpect of change that the heliocent system presented, it couldn’t be tougth as truth, and Galileo openly didn’t in fear of being ridiculed and of persecution by the church. Galileo relised that he would not be able to prove this as truth without more evidence. and this evidence came from the invention of the telescope.

The telescope was a revolutionary device that changed the course of space observation. Its basic roll was to make the a object apair larger then it is.

magnifie the object

How a basic telescope works (keplers)

How a basic Galilean Telescope works

Galileo first attempted at a telescope used a concave(diverging ) and convex (converging) lens in order to create a virtual image that appeared larger then the real one.

the light from the incoming object strike a concave lens (object lens), refraction of the light accurse, focusing the light on a central point, the light then spreads again, is refracted by another concave lens then the photons of light stimulate the retina of the eye.

The larger the lens the greater the magnification of the image. Galileo did not realise how to calculate the magnification of his telescope but we now now that magnification = F/f

from the utilisations of the telescope, many discoveries where made, that enforced the heliocentric idea, and apposed the idea of a perfect cosmos:

the surface of the Moon was not perfectly smooth, it was as full of lofty mountains and deep hollows.

there where stars that had never been seen before, with the improving resultion of telescopes it are clear that only a fraction of the stars in the sky where visable to the naked eye.

The discovery of 4 moons of Jupiter, the idea of other planets havng moons aes quite monumenta, the earth was kinsided to be special because of its moon. He found dark patches on the sun now know as sunspots, again proving that the sun if not perfect, it changes with time

Most importantly he discovered that Venus had faces just like the moon, this was prof that the heliocentric system had to be true as this observation fitted. But didn’t fit the geocentric method, thus disproving the accepted theory by coXXXXXXXXX

as the diagram shows the faces for the heliocentric match those of take by the observations. They where not those of the geocentric shown to the left.

Galileo finally published his work, but was persecuted by the church for teaching Copernican theory opposed Holy Scripture, after many years of not printing his finding Galileo finally printed it, he was then imprisoned for his beliefs.

Galileo believed himself that heliocentric system was try so he tried t owork out why the bodies stay in a orbit.

Though experiments by rolling a body down a ramp Galileo relised that there was content accretion on the body, because the time it took to travel a quarter of the way down the ramp was half the time it took to travel down all of the ramp. This gave the ground work for Newton’s Laws and Gravitation.

Newton developed laws of motion that enable him to help explain why things stay in orbit

Newtons 1st law: A body at rest remains at rest, or a body in uniform motion remains in uniform motion, unless acted upon by an external force

Newtons 2nd law: The acceleration of an object is proportional to the force acting on an object. The constant of proportionality is the mass:

F=ma (a=dv/dt)

Newton’s 3rd Law When any two objects interact, the force exerted by the first object on the second is equal and opposite to the force exerted by the second on the first. Or, for every action (force), there is an equal and opposite reaction; that is forces are mutual and act in pairs.

From these 3 laws it is possible to draw up a law for the interaction of 2 bodies,

Newton’s Law of Gravity

Each body has a mass, this mass creates a force, though the interaction particals now known as gravitons, the more massive a body is the more gravations created so the strounger the force it creates.

If one body is orbiting another in a circle then its centrail petail and centafugal force must be equal,

This can then be worked out to be F = GMm/r2

It is r2 because, as the area round a sphere increases it increase by the radios squared.

From Newton’s first law it is clear that there is a conseation of momentum

Momentum = mV = constant

Kepler’s second law states that there is conservation of angular momentum:

mVr = constant

Kepler’s 3rd law and Gravity

As

F = GMm/r2

F= ma

a= v2/r

a= f/m= GMm/r2m = GM/r2

so v2= GM/r

as v = distance /time = circumference /period for orbit

v = 2пr/p

v2 = 4п2r2/p2

GM/r = 4п2r2/p2

p2= ( 4п2 /GM) r3