Sir Isaac Newton said, “Gravity must be caused by an agent acting constantly according to certain laws; but whether this agent is material or immaterial, I have left to the consideration of my readers”.

As far as we know big bang is the birth of the universe with an infinite amount of energy. It was extreme temperature and ghostly empty space expanding without any stoppage. Overtime as space was continued cooling down slowly the formation of the matter started. Some kind of force of attraction embedded in the energy started formatting visible elements and objects such as hydrogen, atoms, molecule, gas, star, planets, sun, galaxy, water, air, fish, other creatures and us. You must have noticed that even the tiniest insect knows how to survive in a hostile environment.  From the beginning of the human race, our brains started to take shape for survival. Our ancestors looked at the sky and stars with boundless curiosity. They developed many ideas by looking at the natural phenomenon. Ancient philosophers and astronomers started to believe in the force of attraction among planets and stars. Intrinsic force must exist between two objects, that is the reason why coalescing started. Is it the force of gravitation, the so-called attraction? The human race observed planets and other large celestial objects as being round in shape. Naturally, serious attention was given to circular shape. The mathematician derived area of a circle is proportional to radius squared. Volume is proportional to three to the power of the radius. Thrust and appetite of knowledge drove the human race a constant search in nature. Who else could be our best teacher – it has to be nature, a God’s gift.  Numerous scientific developments happened since the start of our existence. If we look closely – even an inanimate object tries to survive in a stable state. A mountainside rock strongly grips the ground not to fall. Stability starts at the micro-level in an atom. Many astronomers grappled with many ideas and slowly mathematics had been developed from the observation of planetary movement. A great many ancient astronomers, scientists observed the natural phenomenon and postulate the idea of gravitation.

Greek philosopher Aristotle in the 4th century BC believed in gravity force.  Around 6 century AD, Indian mathematician Aryabhata used in a geocentric model which referred to gravity as a force; He theorized an eccentric elliptical model of movements of the sun, moon and other planets. Indian philosopher and mathematician Brahmagupta was eloquent about gravity as an attractive force.

Around 14 century AD, the Idea of acceleration came from Islamic scientists Sina and al-Baghdādī, their ideas were a falling object accumulates incremental power so caused successive increments of velocity.

Mountains of observed data from movements of planets and stars were logged by astronomers and scientists for thousands of years. These data were the gift to the next upcoming astronomers during that time.

Kepler (around 1610) is the best known for his 3 laws of planetary motions. Let us look closely at his idea and mathematics behind it. He formulated – ‘Orbital period square’ is proportional to the ‘cubic root of the radius of the orbit’. This is known as Kepler’s third law. His teacher was Tycho Brahe not very familiar to us, throughout his life he logged results of his observation of planetary movement. Kepler had used this data and came up with his three laws.

From ancient times the human being observed that sun rises and sets, they encountered day’s light and night’s dark. Slowly they started to realize the uniformity in natural phenomena. It appeared to astronomers that planetary movements are circular.

Kepler looked deeply into planetary movement and found it is not exactly circular, but it is elliptical, Kepler observed that the sun holds its position in one focus. This is the first law of Kepler. This proved the concept of Indian mathematician Aryabhata at 600 AD. Please note that compare to other planets, earth orbit around the sun is less elliptical, almost circular fashion.

Kepler observed planet velocity was not constant, but the swiping area of a planet (such as the earth) swept centered the sun is constant with respect to time. This is the second law of Kepler. These three laws became the foundation of Newton’s law of Gravitation.

In the early 17th century, Galileo noticed that all objects tend to accelerate equally in free fall. Subsequently, the existence of the gravitational constant was explored by various researchers from the mid-17th century,

What is the cause of the formation of particles from micro atom to planets? A simple fall of an apple on Newton’s lap caused a revolutionary idea of Newton’s law of universal gravitation. A deep observation is the mother of invention. He thought if apple can fall from a small tree, other objects can fall from a tall tree, so the object is pulled by some force. This is the force of earth’s gravity. Actually apple and Earth experienced a force of attraction mutually. Force of attraction by an apple is insignificant compared to the force of attraction by huge Earth, so its net effect is falling apple. Obviously masses of the two objects are the determining factor of the effect of the gravitational force. Moon and earth pull each other, its visible effect is ocean tide. Experiment by NASA has proved that the surface of the moon slightly bugles toward earth due to the gravitational effect between sun and earth.

About 70-80 years later after Kepler’s laws, (1680) Newton formulated in a simple equation by inductive reasoning which says “The force is proportional to the product of the two masses and inversely proportional to the square of the distance between them.” His equations proved Kepler’s laws of planetary movement.

F = G (m1 m2/r²)

Where F is the resultant gravitational force acting between two objects, m1 and m2 are the masses of the objects, r is the distance between the centers of their masses, and G is the gravitational constant.

It is so hard to conceive that when you and I are close it produces a gravitation attraction. In reality, even two micro-objects has this inherent force of attraction. This must be the cause of coalescing of matter and formation of the planet and us.

During the era, 1700 scientific development was accelerated in electric and magnetism. Scientists in mid-1700 came to realize that electric force between two charged objects diminishes with distance and assumed it may obey inverse square law. Some of the scientists and philosopher namely Aepinus, Cavendish, Coulomb were notable in this area.

After a long wait of 80 years, Newton’s law of gravitation was lab tested by Cavendish (1800). His device was able to measure the effect of the gravitational attraction between two objects and calculate the exact value of the gravitational constant (G). Value of G is 6.674×10−11 in unit m3⋅kg−1⋅s−2

Scientists and Physicists were surprised by the Coulomb’s law of electrical force; it had been proved that electrical force between two charged bodies follows Newton’s law of gravitation. The electric force is inversely proportional to the square of the distance between the charged bodies. Coulomb’s law uses the electrostatic constant (K) in place of the gravitational constant (G).  The value of K is 8.99×109 N·m2·C−2.  We can safely conclude that a gravitational force was inherent in nature even in a macroscopic object such as atoms, molecules, etc.

We use term weight and mass. Both are same for our normal daily life. Physics defines weight is the effect of gravitational force on the mass. A simple illustration is as follows:

Courtesy of Google

The weight of the mass at earth is proportional to the acceleration due to gravity at the earth’s surface. Acceleration due to gravity at the moon will be quite different so the weight will be different for the same mass.

This is where I wanted to complete the article. For completeness, it would make sense to talk about the new concept of gravity.

Gravity concept got a new spin from modern quantum physics. General Relativity theory gave a new concept of gravity. So it is important to understand the gravity concept in the light of general relativity. Newton’s math still very useful for general physics as it did a good job of predicting the movement of everything from projectiles to planets. But for better accuracy use of general gravity would make more sense.

There are 4 fundamental forces of nature –Electromagnetism, Gravitation, Strong interaction and Weak interaction.

Gravity force is weakest of all, about a thousand times weaker among four fundamental interactions of nature and any physical entity. As a consequence, it has no significant influence at the level of subatomic particles. In contrast, it is the dominant force of interaction at the macroscopic level and is the cause of the formation, shape, and trajectory of astronomical bodies. Just imagine the weakest force has more influence in keeping the balance of the universe.

Only when objects are a distance apart like earth in relation to the moon, sun, planets and even GPS satellites Einstein’s  Gravity concept and equation are accurate than the Newtonian equation. The general relativity theory considers gravity not as a force, but as a consequence of the curvature of spacetime.  Newtonian Gravity concept didn’t consider acceleration. Einstein Gravity concept added the effect of acceleration.

Einstein felt x, y, and z coordinate is not enough to define for any entity/object, time factor must be added in the calculation. He realized space and time (spacetime) as an integral part of the entity.

Einstein’s general theory of relativity says –

Time and space are neither flat nor fixed; they are curved and distorted by mass and energy.                 The gravitational effect is minuscule due to the acceleration when objects are close.  Thereby concept and equation of Newtonian Gravity are quite appropriate to use at close orientation. So, every day’s physics is fine.  Truly speaking using the classical equation gives only a fractional error with a faraway star. However, Einstein equations are much more accurate than classical equations. The serious argument of GR lasted for a few years until mathematician Grossmann proved the concept of the theory of relativity. Today GR equations are needed for GPS and us at the earth’s surface as calculation demands much more accuracy for GPS technology to work with time correction.

It took years for Einstein to succeed in showing that matter and spacetime mutually interact to mimic Newton’s idea that masses attract each other. Physicist John Archibald Wheeler worded the idea of Einstein’s gravity later, “mass grips spacetime, telling it how to curve, and spacetime grips mass, telling it how to move”. Confused!? I am.

Some background behind light bending due to the gravitational force as follows:-

Scientists Johann von Soldner (1804) and Henry Cavendish(1784) had calculated light bending based on Newtonian theory and the corpuscular model of light. Those calculations had good accuracy of bending due to the bending of light around the sun. But their calculation had the error of about one-half the value from calculated value by general relativity (GR) and it had been confirmed by experiment.

Einstein’s gravitational equation is very complex. His argument,  reasoning, and views of gravity are as follows:

Acceleration and gravity are not distinguishable. Light bends due to gravity. Photon has no mass so the Newtonian equation didn’t consider the effect of the photon.

His idea is movement of mass distorts the space. Bigger the mass is more the distortion of space. Imagine the entire universe is layers of trampolines. Any movement associates with time will displace the trampoline that is space. So his thinking was not only x, y, z coordinates but added time (t) for space. It is so complex that it took ten years to develop the mathematical equation which is called the Einstein field equation. For an object moving in space it is easy to draw a graph with one axis (say x) and other (t). A constant movement will be a straight line. But gravity creates acceleration. So it will be a curved line. So Einstein thought space is curved space. So spacetime became a single entity in the calculation. Newton thought gravitational force between sun and earth creates centripetal force and earth moves around the sun to remain stable. It is absolutely right. But the small error in prediction by Newton equation, Einstein thought Sun is so massive it warps the space and earth follow the curved space path and his sets of complex equations (10) are the best way to explain gravity and planetary motion in the universe.

The field equation is as follows, to understand even the basic aspect of the equation a good understanding of tensor mathematics, Christoffel, Ricci curvature, curvature scaler, stress energy-momentum, and the cosmological constant are needed.

R_μγ – ½ g_μγ R + g_μγ Λ = 8πG/C⁴ T_μγ

The left side of the equation relates to the curvature of the spacetime (It tells mass and energy how to move)

The right side of the equation relates to mass and energy. (It tells spacetime how to curve)

To understand more read advanced physics. I will add a small write up with a few details of the Field equation as shown above. Stay tuned…