All of us know the effects of the mysterious force called gravity. However, the question 'what is gravity' is not easy to answer at all. The reason is that we don't really understand what this force actually is (if it is a force at all).

The 'Giants'

It would have been nice if we could have popped the question 'what is gravity' to the 'gravity-giants' like Kepler, Newton and Einstein. Maybe they could explain the characteristics and effects of this phenomenon properly and we could then (perhaps) answer the question.

Kepler could not explain gravity, but amazingly, he worked out the details of how the orbits of the moon and planets can be described mathematically. This is known as the Kepler laws of planetary motion, as described later, but it does not answer the question 'what is gravity'.

Newton, reportedly while observing an apple falling from a tree, got an inspiration that allowed him to work out how the force of gravity can be described mathematically. It later became apparent that there are some scenarios where Newton's mathematical description does not quite hold, but it still the simplest way of describing gravity. It does however also not answer the 'what is' question.

Einstein later worked out how the force of gravity is not quite a force, but rather an artifact of the natural movement of objects through curved four-dimensional spacetime. Einstein reportedly got the inspiration for this imaginative leap in understanding of gravity by contemplating a man falling off a building. Such a falling man would not experience any force while he is falling, at least not before hitting the ground and suffering severe forces.

Kepler's Gravity (1605)

Johannes Kepler's noted his three laws of planetary motion in 1605, by studying the precise measurement of the orbits of the planets by Tycho Brahe. He found that these observations followed three relatively simple mathematical laws, i.e.

1. The orbit of every planet is an ellipse with the Sun at one of the two focus points.

2. A line joining a planet and the Sun sweeps out equal areas during equal intervals of time.

3. The squares of the orbital periods of planets are directly proportional to the cubes of the major axis (the "length" of the ellipse) of the orbits.

However, the physical explanation of this behaviour of the planets came almost a century later when Sir Isaac Newton was able to deduce Kepler's laws from his laws of motion and his law of universal gravity, using his prior invention of calculus.

Newton's Gravity (1687)

In his 'Principia' of 1687, Isaac Newton included his famous three laws of motion and the law of 'universal gravitation', which can be briefly stated as:

1. An object in motion will remain in motion unless acted upon by a net force.

2. Force equals mass multiplied by acceleration.

3. To every action there is an equal and opposite reaction.

4. The force of gravity is proportional to the product of the two masses and inversely proportional to the square of the distance between the point masses.

Double one of the two masses and the force of gravity will also double. Double the distance between the masses and the force of gravity will be four times weaker.

Newton was uncomfortable with his own theory of gravity and in his words, never "assigned the cause of this power. He was unable to experimentally identify what produces the force of gravity and he refused to even offer a hypothesis as to the cause of this force on grounds that to do so was not sound science.

It is now known that Newton's universal gravitation does not fully describe the effects of gravity when the gravitational field is very strong, or when objects move at very high speed in the field. This is where Einstein's general theory of relativity rules.

Einstein's Gravity (1916)

In his monumental 1916 work 'The Foundation of the General Theory of Relativity', Albert Einstein unified his own Special relativity, Newton's law of universal gravitation, and the crucial insight that the effects of gravity can be described by the curvature of space and time, usually just called 'space-time' curvature.

It is reasonably easy to accept that space can be curved – after all, we all know that a disk has a curved edge, but how can time be 'curved'? The secret lurks in the way that space and time is combined into space-time. Normally, a space-time diagram is drawn with a straight horizontal spatial axis and a straight vertical time axis. Just bend the two straight axes a little and we have curved space-time.

The horizontal axis of the diagram represents space and the vertical axis time (actually time multiplied by the speed of light) - hence it is a spacetime diagram. The mass M disturbs the spacetime in such a way that it causes the spacetime path of a particle P to be curved towards the mass.

At a particular radial distance r from the mass, the particle P follows a curved path that has a center at a distance R from the particle, defining a point called the center of spacetime curvature.

Although it may look like it, this diagram does not represent a particle in orbit around the mass, or around the center of curvature. Because it is a spacetime diagram, it represents the flow of time PLUS the movement of particle P towards the mass M - i.e., the particle is starting to fall directly towards the mass.

The radius of spacetime curvature is indicated on the diagram as R. As you will spot, the radius of curvature has something to do with the acceleration that the particle will suffer - the centripetal acceleration towards the center of curvature.

If we plug in real values, like Earth's mass as M, the gravitational constant G and the radius of Earth as r (with c the speed of light, what else?), we find that the centripetal acceleration is just about the acceleration of 1g that keeps us firmly on the surface of Earth. The tiny difference is due to Earth's rotation, Earth's uneven density and the fact that Earth's is not a perfect sphere.

The above holds well for weak gravity fields and low speed movement, i.e., the Newtonian limit of general relativity. In strong gravity fields, the curvature of spacetime and the effect of velocity must be catered for. They both have the effect of lengthening the radius of curvature of the path of the particle. The diagram below illustrates this shift in the position of the center of curvature in an exaggerated fashion.

Essentially, the center of curvature drops below the x-axis, firstly due to curved space-time and then also due to velocity. The resultant radius of curvature is hence modified by a relativistic factor, which is rather difficult to express in simple terms.

In essence, the original (quasi-Newtonian gravity) radius of curvature is shortened - first by a gravitational time dilation term end then by a velocity time dilation term. This causes the acceleration of a radially falling object, as experienced by the free falling object to be larger than what Newton predicted.

Einstein came the closest of the three 'giants' in answering the question 'what is gravity?'

Summary

So, what is gravity? The truth is that at the most fundamental level, no one really knows. This page covered the basics of Newton's and Einstein's gravity in terms of the gravitational acceleration that is caused by curved spacetime and velocity. We may have to wait for
'quantum gravity'
to be completed before we will know a better answer to the topical question: 'what is gravity?'.

A more complete picture of gravity is presented in the eBook Relativity 4 Engineers.

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