Geocentric view
This simulation shows the planets' paths relative to the Earth as they appear to move against the background of the stars. The simulation is calculated using exactly the same Newtonian (even heliocentric) laws as the other simulations - we've just displayed the results as they appear relative to the Earth.

Three views are displayed; an overall view of this Earth-centred model of the universe, and a pair of views from Earth towards a celestial body of your choice; one tracing the object's apparent motion, the other a close-up showing the Sun's shadow and changes in visual size. [The close-up views from Earth show the planets at all the same magnification - and the Moon and Sun at a lower magnification. Apart from Earth itself, all celestial objects are displayed without orbiting moons or surface detail.]

In this simulation the Earth spins (try zooming in to see it) - whereas in a full-blooded geocentric model the Moon, Sun, planets and stars all circle the Earth once a day in addition to the movements shown here.

Planetary motion
Instead of following (relatively simple) elliptical orbits around the Sun (today's heliocentric model) - the planets take a more complex wandering path around the geocentric model's fixed Earth. Each planet's overall motion is to circle the Earth in the same west-to-east direction - but each also regularly backtracks in a period of "retrograde motion".
Geocentric theory (elaborated by Claudius Ptolemy ~ 90-170 AD) explains this strange motion with the idea that each planet, in addition to circling the Earth (on a "deferent" circle) also moves around a smaller "epicycle".
Diagrams of Ptolemy's Planetary models illustrate some of the intracacy of the theory.
Alfonso X of Castille and Leon (1221-84) complained on having the Ptolemaic system explained to him: "If the Lord Almighty had consulted me before embarking upon Creation, I should have recommended something simpler."

In his 1543 deathbed publication of "On the Revolutions of the Heavenly Bodies" the Polish astronomer Copernicus proposed a heliocentric model, reviving the ideas of Aristarchus of Samos (200 BC). Copernicus' heliocentric model didn't need epicycles to explain retrograde planetary motion (but he did use them to make his planets' circular paths a closer match to the ellipical reality).

Overcomplexity wasn't Ptolemy's geocentric theory's only problem - it seriously misrepresented the motions of certain planets - as Galileo observed with a telescope in the early 1600s.
What did Galileo see (you don't need a telescope to observe it in the simulation) and how did it conflict with Ptolemy's model?

Which celestial bodies don't exhibit retrograde motion? Why don't they?

What was Tycho Brahe's (1546-1601) model of the universe and why did he adopt it?

Links:

The Scriptural Basis for a Geocentric Cosmology

The universe of Aristotle and Ptolemy

The Copernican Model:A Sun-Centered Solar System

Ancient Greek astronomy

The heliocentric revolution

Renaissance Astronomy and the Acceptance of the Heliocentric Model

Ptolemaic system

Ptolemy

Diagrams of Ptolemy's Planetary models

Copernicus Suggests a Heliocentric Cosmology

Copernicus and the Aesthetic Impulse

Renaissance astronomy