The contemporaries of Newton had not considered the questions that a falling apple could throw up as he did. May be, some questions may have popped up in many minds but a very significant thought occured to the mind of Newton that led to his success and he stood tallest amongst the crowd of others. And that thought was about the height upto which the gravitation force remained effective? It did not work the same way on moon like it did on the apple. The moon stayed on its orbital path without falling down to earth. Newton may have wondered if the gravitation remained in force up to tree heights only and beyond that it ended or tapered off. That was why the moon did not fall.
The way the moon kept orbiting the earth, could such rotational motion be caused by gravitational force? May be, the gravitational force of earth was influencing the motion of the moon and keeping it on the orbital path as if tied to an invisible sling.
It was a very significant thought that separated Newton from the mediocrity. It helped him apply the law of gravitation on the entire universe. This idea of Newton can be better understood by the illustration given in this chapter.
From a hill top, if a cannon fired a shell aimed parallel to the horizon it moved through air with its specific ballistic speed. But the spot where it will fall depends on the velocity of the shell. Due to the gravitational force the different velocities will carry the shell to the different distances. If a shell (A) is fired at low speed its trajectory will be different and it will fall down at a short distance. But the shell (B) fired at greater velocity will travel at higher trajectory and fall at greater distance. The gravitational force applies on both the shells equally but the ballistic force of different degrees or levels takes them to different distances. The velocity of the shell gains it momentum and momentum acting like a carrier forms the trajectory. Thus, Newton proved that velocity determines of the momentum and trajectory. The difference of velocity effects the momentum and trajectory.
If a cannon fires a shell with lesser ballistic power it will go to lesser distance with flatter trajectory. A shell fired with greater power will go a greater distance with higher trajectory. Newton presented these facts in the following way :
- If from the same height shells were fired at different velocities their momentum and trajectory will be different.
- If from the same height two shells were fired at the same velocity their momentum and trajectory will be the same.
- The cannon shell in its travel through air from a hill to the lower ground is subject to gravitational power and it shall be known as gravitational trajectory.
- On the basis of this Newton proved that the moon follows the same law and orbits the earth. The moon orbits on its path due to gravitational forces of the earth and this orbiting is like moon falling endlessly.
- The moon orbits around the earth at a certain velocity and that velocity is caused by gravitational force of earth.
- In the same process Isaac Newton visualized that at that specific height if cannon shells were fired in the space the shells will also start orbiting the earth like moon and they won’t fall on earth. Those shells will also become satellites of earth. Newton defined that due to gravitation orbital motion is formed.
- Newton further explained that all the bodies of the universe effect each other with their gravitational force, balance and gain motion. This force and the balancing is innate in elementary nature of universe. The above principle he presented in the following equational form :
In the universe, every body or cluster, other lumps or their clusters possess the property to attract towards its centre. This attracting power or gravitational pull depends on the mass of the body, which means according to its shape or density the pull may be less or more. The centre of the distance of two bodies is determined by the mass and the gravitational pulls towards their respective centres. Thus the universal gravitational force is based on the following equation :
Here ‘Fg’ is gravitation power
‘M1’ and ‘M2’ are masses of too bodies.
‘r’ is the division of centre of two bodies
‘G’ is symbol of stable universal gravitational force.
Thus, between various bodies of the universe the rational stability is universal gravitation force. This force uniformly controls the cosmos or universe. It is present everywhere at all times and expresses the all pervading nature of gravitation force throughout the creation.
THE CENTRE OF MASS IN BINARY SYSTEM
When we consider the Kepler Principle we find a strange anomaly. It says the sun is stationary at a point and all the planets rotate around it in their respective orbits. The question is why must sun alone be stationary and fixed at one spot while others stay in motion. Kepler did not reason like a scientist or explain it logically in the light of laws of nature that apply to all without any exception. He presented it like a mysticism with sun enjoying Godly powers and extra special status above all as stationary body.
Newton applied his Third Law of Motion and simply said the situation being as Kepler said but there was a logical scientific explanation to it.
To understand what Newton said, given below is an equation that mathematically explains by determining the central point of a mass :
m1 d1 = M2 d2
d1 + D2 = R
Her ‘R’ is these central point between too masses that we see in practical life in see-saw game :
In the see-saw the central point or focal point is that which provides balance to the two persons in the two sides of the sea-saw. Similarly the two bodies in the universe play a gravitational see-saw that has a focal point which gives them the point where they get balanced. This point may not be exactly in the centre.
It depends on the masses of the two bodies in play. In the solar system the sun is that all important balancing focal point. The planets according to their respective masses gain balance and orbit around the sun according to the path determined by their mass and distance. The sun infact is the focal point for all the planets of the solar system. In the game of see-saw a heavier body sits near to the fulcrum to achieve the balance.
This balancing game in the universe is gravitation power which creates the motions too.
