2.2  Gravity and the model

This section is a brief description of the science history and the classical physics of gravity and the model used by the program and model limits.

2.2.1  The classical physics of gravity

Men would have always been known why heavenly bodies move so as it looks like in the sky. Up to the 16^th century, the geocentric world conception held the field, by which Earth is in the center of the universe. Ptolemy (reigned from ca AD 83 to ca AD 161) summarized and expanded the doctrines of Greek astronomy then in being. His chef-d'oeuvre Almagest and his tables or other pieces were so definite and relatively precise that they held out contrary to other opinions.

Copernicus (1473 - 1543) issued his principal book titled New Almagest, in which he places the Sun in the center of the universe. In his view, only the Moon revolves around the Earth, taking one turn about the Sun in a year and about its own axis in 24 hours, and fixed stars are much farther than planets. This book flew abroad within the scientific domain and the heliocentric world concept started to shake the geocentric world concept impugned unsuccessfully to that time.

Data of planetary observations with an unaided eye from Tycho Brahe (1546 - 1601) were amazingly precise: deviations came to not more than 2 angular minutes. Johannes Kepler (1571 - 1630) built up his three laws from these data:

1. Planets revolve around the Sun on an elliptic orbit, in one of whose focal points is the Sun.
2. The radius vector drawn from the Sun to the planet rubs against equal areas in equal periods.
3. The square of the circulation duration T for the planet is proportional to the cube of its distance in the mean R as measured from the Sun. Thus the relationship T² / R³ is constant for all planets.

It was Kepler's revolutionary innovation that he broke away from the stationary orbit indisputable by everyone to that time.

Giordano Bruno (1548 - 1600) became a passionate follower to Copernicus to boldly make a stand for his opinion openly advocating it. More and more powerfully, Church took actions against the new doctrines and their propagators, employing all means of power in its final bitter fight. As early as in his youth, Giordano Bruno was accused of heresy, therefore he run away to wander throughout Europe, teaching at famous academies and criticizing the dogmas of the Church. Finally he was captured, sentenced and on 15 February 1600, burnt at the stake.

The great scientist of his age, Galileo Galilee (1564 - 1642) was also a follower to Copernicus. Galilee was the first in using a telescope to observe the sky, and what he saw there and descried was not only utterly absorbing, but on the other hand, heretical. There are four moons around the Jupiter, spots on the Sun, stars incorporating the Milky Way, mountains and valleys on the Moon is not reconcilable with the teaching of the Church. Galilee was arrested and forced to withdraw his view what he did.

Due to the heliocentric world concept, a satisfactory explanation could be given of the loop motion of planets. The Sun, the Moon and for the most part the planets too rove their celestial way compared to fixed stars from the west to the east, but sometimes a planet or another moves backward with its orbit looping in the sky. To eliminate this problem, the ancient Greeks introduced spheres and eccentric circles. Copernicus did still use epicycle, for instance in the case of the Mercury.

Thanks to Kepler, computing the orbits has much simplified and became precise. At this time, scientists were interested in why the Sun is in the midst and why orbits are like that Kepler described it, to what effect an elliptic path generates.

The so many whys were answered by Isaac Newton (1642 - 1727) in his book Philosophiæ Naturalis Principia Mathematica issued in 1687. The Principia confirmed Newton as one of the greatest all-time genius, canceling Aristotle's 2000-year learning about the dualism of earthly and celestial laws. In this work, he describes his three laws of motion, laying the foundations of dynamics:

1. All bodies keep their linear steady motion or steady state so long as another body forces them to change it. (low of inertia)
2. Resultants of the forces acting on a body change the momentum of that body. If the mass of a body is constant, then  (Resultants of the forces acting on a body equals to the product of the mass and acceleration of that body)
3. If body A and B exerts force to each other, then the magnitude of the force exerted by body A to B is the same and its direction is opposite to the force exerted by B to A (law of action and reaction)

Moreover, the Principia contains Newton' theory of gravity, by which the same force attracts bodies toward the Earth, than the one holding the planets on their orbit. Universal gravity is an attraction force between any two particles¹ in the universe, whose magnitude is computed with the formula on the inverse square of the distance:

Where m₁ and m₂ is the mass of the two bodies, r is the distance between bodies, G is the constant of gravitation, whose value measured experimentally is:

Newton's theory explains the three Kepler's laws, serving as a base for mechanics and by it, it is easy to compute the position of a body after dt time, if its current radius and velocity vector and its mass as well as the radius vector and the mass of the forces acting on it are known.

Computation is detailed in section Compute position.

2.2.2  The model

A model is an aid for understanding physical reality. Phenomena in the world are often so complicated that their principles can not be revealed directly, we are forced to create models and study them. On modeling, things insignificant for the study are ignored, and those significant are stressed, which is referred to as abstraction. During abstraction, phenomenon to be observed is easy to simulate by using the heuristic method. Consequently, this model reflects reality only in part, with good approximation for significant elements and ignoring the insignificant ones.

Gravity models gravitation. The following list encompasses the differences between real gravity and the model used by this program.

1. Natural phenomena are continuous (or considered so), while the computer computes with discrete data of finite accuracy.
2. This model is only of two dimensions.
3. (As to our present knowledge), gravity is described correctly by the general theory of relativity, this model uses the classical mechanics.

The limitation described in the first point is unavoidable, only model accuracy can be improved e.g. by reducing the time unit (naturally, it shall not reach zero), but velocity of the simulation will slow down proportionally.

The second limitation is only in technical sense. This program uses two-dimension model due to the higher processing rate alone. In certain cases, the three-dimensional computerized representation of a physical process can be even disturbing, as you think in two dimensions for the most part, surface of a paper sheet, blackboard or screen is plane as well.

The limitation described in the third point was incorporated in the model also due to velocity. Einstein's formulae are more complicated and time-consuming than the simple Newton's formulas.

However, only the first limitation will probably remain in the model of a later version of Gravity.

1 By the theory of relativity, this is supplemented so that in space and time, the two bodies shall be “near” to each other in the same universal time. Viz. gravity drive travels also at light speed. In Newton's mechanics, this drive will immediately be exerted anywhere in the universe, with its speed infinite.