History of Heliocentrism!

“Mathematics is the language in which god has written the universe”

-Galileo Galilei

For people who do not know who he was, Galileo is the father of observational astronomy. He was an Italian scientist who was tortured and house arrested till death for his theories supporting ‘Heliocentrism’, the astronomical model in which the Earth and other planets revolve around the Sun along the center of Solar system.

He gave his theory of Sidereus Nuncius in the 17th century, way before anyone else and largely contributed to modern understandings of Astrophysics. Its been 400 years since the start of his work and today we stand in this complex matrix created by Physics and Mathematics trying to understand the working of the Universe.

Math, Math Everywhere!

While we talk of math, it doesn’t have to be always numbers. Angles, trajectories, shapes, orbits, timely appearances of comets and satellites in the night sky, constellations and many more theories have been listed using the Mathematical Universe Hypothesis. Answers to many important questions, from reason of the shape of a water bubble to simulation to find the existence of a black hole, jump out into existence when mathematics is used in understanding physics.

For example, reason of tides, timely appearance of comets, natural satellites and planets such as Neptune and Jupiter were discovered by using radio signals and mathematical relations. Therefore,contribution of mathematics to ‘Theory of Everything’ is as important as physics; as history of mathematics is considered to be history of humanity seeking to understand the universe. Here in this case I tend to specify about paths followed by celestial bodies.

WHY DO CELESTIAL BODIES REVOLVE IN ORBITS OF A TYPICAL SHAPE?

It’s been a very common notion since childhood that our planet and all the other planets along with other celestial bodies in the solar system revolve around the sun which in physical terms is a flaw. All the planets and the sun orbit around their common center of mass known as Barycenter.

Due to higher mass of sun or other parent stars in the universe as compared to that of the planets or celestial bodies, these Barycenters are located quite nearer to the parent star appearing like they are taking an orbit around it. So what do these Barycenters say about the shape of the orbit?

In 1609, a German mathematician and astronomer, Johannes Kepler gave his “Theory of Astronomia Nova” in which he studied the motion of mars to determine how it had an elliptical orbit around the sun and then suggested how all the other celestial bodies had optical shaped orbits around the sun.

Taking a sneak-peek into his work, he describes that if sun’s center acts as one of the focus and Barycenter of Mars the other, then the locus of the center of mars resembled to be that of an Ellipse.

Later, in 1687, Issac Newton with his Laws of gravity (which states that the attraction force between two bodies is directly proportional to its mass and inversely proportional to the square of distance between them.) proved that this relation shows all celestial bodies under the attraction force should travel in orbits of the shape ellipse, parabola or hyperbola. Since parabola or hyperbola are open-ended, he concluded that the orbit is elliptical.

While planets, moons, asteroid belts and the galaxies are known to have orbits, it is a less-known fact that comets have orbits too.

WHAT MAKES COMETS REVOLVE IN ORBITS?

While comets and planets revolve around their parent stars in elliptical orbits, the variation arrives in the eccentricity of the orbits. For example, though Earth revolves around the sun in elliptical path, the distance between Sun and Earth has a maximum variation of 5% but when the path of comets are concerned, Aphelion is almost 30 times as the perihelion; (many short comets have path stretched between Neptune and Mercury).

This is why comets which normally are like any other rock revolving around the star appear to have tails. As a comet gets nearer to the sun, its gases get evaporated, causing an emission of dust and micro-particles which tend to appear as a tail.

HOW WAS MATHEMATICS INVOLVED IN THIS THEORY?

Work over comets started when an English astronomer, Edmund Halley who examined the reports of 3 comets visible from Earth in 1531, 1607 and 1682. He along with Issac Newton worked on the Laws of Gravity to determine that the comets weren’t 3 different ones but was the same comet returning again and would be visible from Earth again in 1758.

Though neither of them survive its return, on the Christmas eve of 1758, the comet returned with a long-tail stretched across the night sky. The comet was named “Halley’s Comet” and it returns to appear in its aphelion every 75 years (74–79 years depending upon the retardation by Jupiter and Saturn).

He compiled his work on 24 comets along Kepler’s 3rd Law of Orbital Motion and Newton’s Laws of Gravity published his theory “Synopsis of the astronomy of comets”. In his work, he found out the maximum distance (perihelion) of the comet through the data collected and also of the aphelion(between Mercury and Venus). By neglecting mass of comet when compared to that of Sun and trying to solve mathematically, periodicity of the comet is determined and the variation can be observed due to pertubation of other celestial bodies.

Not only does the orbits excite humans, but also the nature itself is a complex mathematical matrix. We can observe shapes, recursions, angles, motions, velocities etc. in nature whose origin is unknown but what excites us is the beauty of its presence everywhere.

“If you knew the magnificence of 3, 6 and 9 then you would have the key to universe”- Nicolas Tesla…What does he mean by this? “ We know that planets revolve around the sun in orbits, but we don’t know who puts them in those orbits”- Stephen Hawking…Is mathematics the direction which can help humans run through the maze created by…who say, “They?”