Gravitational force |Fundamental Forces of Physics - Part 1

Four Fundamental Forces of Physics - Part 1  : An overview of Gravity - Newton's law of Gravitation and Einstein's explanation of gravitational force as the curvature of spacetime.

    In the entire universe all the forces, all the phenomena, all the interactions that you see from the microscopic subatomic level to intergalactic distances can all be traced or broken down into four fundamental classifications. These are -

1. Gravitational force, 

2. Electromagnetic force, 

3. Strong interaction force and 

4. Weak interaction force. 

In this part we are going to discuss about the Gravitational Force.

Gravitational force | Newton's law of Gravitation | Gravitational force equation | Einstein's Gravity 

    Let's get straight into it. The first force we are going to discuss is the gravitational force. Most of the macroscopic and large-scale behavior of nature is a result of the gravitational force or gravity.

What is Gravity? 

    In a sentence we may define gravity as an attraction force that acts on a body which has a particular mass or inertia. 

Newton’s Law of Gravitation:

    The first scientific explanation for natural gravitational force was given by Sir Isaac Newton.    

    Sir Isaac Newton discovered gravity in1687, when, as legend tells, an apple fell from a tree and struck him in the head. It’s likely that events didn't transpire in quite this way, but the story is a good one.

Statement of Newton's Law of Gravitation :

    Any particle of matter attracts any other particle in the universe, along the line joining them, with a force which is directly proportional to the product of the masses of the particles and inversely proportional to the square of the distance between them.

    If and are the masses of the interacting particles, at a distance r , then the Gravitational attractive force between them is given by,

Or,  

------------------- (1)

 

Where, G is the universal gravitational constant and the negative sign indicates that the force is an attractive force.

    Thus gravitational force is directly proportional to the product of masses of two objects and inversely proportional to the square of distance between them.

Definition of Gravitational Force Constant (G) :

    If put  =   = 1 in the equation (1) and also r=1 then we find that F=G (Numerically).

    The Gravitational constant G is thus numerically equal to the force of gravitation between two unit(point) masses when they are separated by unit distance.

  

        - Using this very simple model of Newton one can not only explain why ‘The Apple’ falls to the ground but also the moving of Earth around the Sun, the behavior of asteroids and comets and satellites around the solar system can be explained .

    In this way, the very simple model of the gravitational force given by Sir Isaac Newton was successful in explaining a large number of natural phenomena.

    For example, the reason we can stand on the surface of this planet called Earth is gravity. Without gravity we would not be able to stand on this surface because the earth is spinning on its own axis and without gravity we would be flying across space. If I throw something it falls down due to this same force.

    This is also responsible for the tides. We see tides because of the motion of the Moon around the earth and the Earth's rotation. The water Bodies keep on changing their height regularly on the surface of earth, this is because of the moon's gravitational attraction.

    The earth itself would not be a round planet without gravitation. The masses of the solar nebula came together as a collection to create all the objects known as planets, stars or asteroids because of gravity. In fact it is gravity which gives the structure the solar system. All the planets revolve around the Sun because of gravitational attraction.


    All the solar systems revolve in the form of a galaxy with respect to some kind of a core because of gravitation force.

    The same gravitational attraction also leads to the existence of our Sun. Sun was originally a collection of gases spread out in space called nebulae. They came together because of gravitational interaction. Now these gases have been concentrated in a certain region in space and there is very much gravitational pressure, that pressure leads to a huge amount of temperature, that leads to nuclear reactions. ( These reactions happen because of different reasons but the pressure which is necessary to induce nuclear reactions is coming from gravitational pressure.)

Gravitational Force of Earth:

    Since the gravitational force is directed towards the center of mass of the objects therefore Earth's gravitational force is directed towards its center of mass. Since Earth is assumed to be spherical, therefore the center of mass of Earth lies at its geometrical center. This force pulls the object towards it's center this is the reason why objects fall on earth in a vertically downward direction.

    If earth attracts an object towards itself then that object also attracts the earth towards itself with equal force. This means that earth and the object both should move towards each other. But we always see that object move towards the earth. We never see earth moving towards the object. Why? 

    It is so according to Newton's second law. The force acting on the body results in change in acceleration. This acceleration is given as the force divided by mass of the body. g = F/M . 

    In case of gravitation the acceleration of the object with smaller mass will be greater as compared to acceleration of object with higher mass. It is because the answer of F / M will be greater for smaller masses.

    It means the objects move towards each other with different accelerations, since the mass of earth is very large therefore the gravitational force results in negligible acceleration in it. Thus it appears that the earth is at rest and the object is moving towards it. 

     Acceleration due to gravity on the surface of earth is written as g. it is defined as the acceleration produced in a body as a result of gravitational force acting on it. 

Properties of Gravitational force:

1. First of all it is always attractive i.e. it always attracts it never repels.
2. The gravitational force is conservative in nature.
3. It is the weakest force among the four fundamental forces but very important of them.
4. The gravitational force has an infinite range. It can act at short distances, it can also act at very high very large intergalactic distances.

    However, the gravitational force is usually not responsible for interactions at the subatomic level. In subatomic dimensions, when we are discussing the interactions of protons and electrons and neutrons, the mass is very small and other forces are dominant. Gravity is almost negligible here.

    Still there were few phenomena which were not successfully explained using this model.

    one Of them was the orbit of Mercury. Usually in Newton's law of gravitation, the kind of orbit that we see in this solar system, is an elliptical orbit or a circular orbit. But in the case of the Mercury the The orbit is not exactly an ellipse but rather it looked like an ellipse rotating with time with respect to one of its focus.

    Then, there was something which is confusing and not being explained by Sir Isaac Newton's law of Gravitation. About 100 years ago a new theory of gravitation was given by Albert Einstein. In his theory of general relativity he explained gravity in a slightly different manner. This theory was very much successful in explaining the perturbations in the orbit of mercury as well as in predicting so sudden very strange behavior with respect to the gravitational force. 

Einstein’s Gravity:

    Now Einstein defined gravity not as a force acting between two masses but rather as a consequence of the curvature of space-time.

    Everything that we know about in the universe exists in a space-time continuum. This space-time continuum, according to Einstein, depends appreciably on the mass present at a particular point. So, mass has a capacity of affecting the space-time continuum in a particular region which leads to gravitational effects.


    Basically, objects want to move in the shortest path, this is also known as geodesic.


    In the presence of a heavy mass space-time continuum gets curved or distorted. These geodesics that represent the shortest path between any two points in the continuum is not always a straight line but rather they become curved. It can be shown by a very simple example of a heavy mass on some kind of elastic surface.

    

    

    It is not an exact representation but it gives an idea about it. If there is an object moving on this plane shown in the above figure it will try to move in a straight line but if this particular thing of the plane gets curved then the object’s motion will also get affected. According to Einstein this phenomenon is called gravity.

    Einstein says that gravity is nothing but the consequence of the curvature of the space-time continuum that is created by the presence of some kind of a nearby heavy mass. This explanation is the modern explanation of gravity. This definition not only explained what Newton's law of gravitation could not explain but also it predicted many other very interesting phenomena such as - gravitational lensing, gravitational redshift, gravitational time dilation, existence of black holes etc.


    In other words, time increases proportionately with the curvature of space near a gravitational field, compared to empty space, to keep the speed of light constant in both reference frames. This is why time is considered distorted by gravity along with space. It is really just a part of the same fabric called space-time. This has some massive implications.

    It implies that the observer experiencing no gravity at all, sees the clock in a gravitational field running slower. This means that the clocks on earth run slightly slower than clocks on the international space station. This effect has been confirmed by many experiments, and is taken into account in order to keep the clocks of GPS satellites in sync with the clocks on earth.    

    You should know that although General relativity is an astounding achievement by one the greatest scientists of all time, it does not answer everything. Questions remain.

    Although it tells us how gravity works, it doesn’t tell us what exactly it is. Why do massive objects distort space time? What is the underlying connection between mass and space-time?

    It also predicts regions of space where space time can get so distorted that nothing escapes including light. This is called a black hole. But it shows that within these black holes lies something that seems impossible, and that is a mass concentrated to an infinitely small point with infinite density. This is called the singularity and is theorized to exist within the black hole. General relativity fails to work at this singularity. But infinities like this in science usually indicate some sort of incompleteness of theories rather than things that actually exist.

    To figure this out what happens at these really small scales, we need our old friend Quantum mechanics. But alas, the equations of quantum mechanics make no sense in terms of singularities, or in terms of general relativity.

    So for now the two theories remain incompatible. If we can bring these two theories together, and truly understand how gravity behaves at the tiniest scales, we may answer the question of what gravity actually is. We will need a new theory to figure this one out – and that theory is called quantum gravity. We will discuss it in detail.

    Hope you have got an idea about the gravitational force and its importance in our world.