From Geocentrism to Heliocentrism and Fluid Dynamics

Geocentric Theory

Aristotle proposed the following:

• The Earth is round and immobile at the center of a celestial sphere, which houses the stars.
• The planets and stars rotate in a celestial sphere with uniform circular motion around the Earth.

Ptolemy improved Aristotle's theory. The Ptolemaic theory was based on circular orbits but later included eccentric orbits and epicycles to describe the movement of the planets. He maintained that the Earth was the center of the universe.

Heliocentric Theory

Copernicus and Galileo, who demonstrated this theory with a microscope he had built, proposed the heliocentric theory. However, Copernicus did not reveal his theory until the 16th century. It affirmed the following points:

• The Sun is at the center of the universe.
• The Moon revolves around the Earth.
• The planets orbit the Sun in elliptical orbits.
• The Earth has two movements: rotation on its axis and translation around the Sun.

Kepler's Laws

• First Law (Law of Orbits): Planets have elliptical orbits around the Sun.
• Second Law (Law of Areas): The speed of a planet depends on its orbital position, sweeping out equal areas in equal times.
• Third Law: The square of a planet's orbital period is proportional to the cube of its average distance from the Sun.

Fluid Dynamics

Pressure is the force exerted per unit area. It is measured in Pascals (N/m²).

Mathematical Proof of P = ρgh

-----------------------> P = g • h · ρ

F = m_L · g = ρ_L · v · g = ρ_L · S • h · g

ρ = m / v

m = ρ · v P = F / S = ρ_L · S • h · g / S = ρ_L • h · g

v = S • h

Fundamental Principle of Hydrostatics

P₁ = ρ · g • h₁

P₂ = ρ · g • h₂

P₂ - P₁ = ρ · g · (h₂ - h₁)

Flotation

• Pressure > E (Weight of fluid displaced) ----> Sinks ----- ρ_c > ρ_Liquid
• Pressure = E (Weight of liquid displaced) ---> Balance ---> ρ_c = ρ_Liquid
• Pressure < E (Weight of liquid displaced) ---> Floats ---> ρ_c < ρ_Liquid

Archimedes' Principle

Archimedes' principle states that a body wholly or partially submerged in a static fluid will experience an upward buoyant force equal to the weight of the volume of fluid displaced by that body.

Pascal's Principle

In a fluid, pressure is transmitted equally in all directions.

P = F / S

P₁ = P₂

P₁ = F₁ / S₁

P₂ = F₂ / S₂

F₁ / S₁ = F₂ / S₂