Now we can see where is the gravitational focal point between the two bodies. For example, we may take two bodies of dissimilar mass, one big and another small. We shall find that the focal point is nearer to the bigger mass and away from the smaller one. The following equation pictures the solar system more vividly. The sun is massive compared to any other solar planet. The focal point would be very near to the sun in the case of any planet. So, being at the very focal point it has to be in stable position but not perfectly. That was also the initial thought of Kepler, thus, through the sun all the planets going their stable orbital paths but the resultant reaction makes the sun unstable.
In another situation if we take two bodies having similar and equal masses we can safely assume that the focal point of gravitation between them would be in the centre. Hence the two bodies (planets) will orbit the sun in parallel path. Gravitation will be responsible for it and it will provide them the motional force. Every planet (body) orbits according to the focal point of gravitation. It can be seen through the following equation:
m1 = m2 d1 = d2 = d2
This condition is used normally for twin stars. The twins are almost equal in size and mass. Their gravitational power is also equal. They will both orbit on the parallel path at equidistance from the centre of force in space. Such twin stars have equal mass as a common factor and in defining this Newton upgraded the third law of Kepler to a large extent.
This upgraded definition ‘Java Applet’ can be seen at work in the space. There are a number of planets and stars that confirm to this principle.
We can see analogous situation around us in play grounds where children play see-saw. If the kids playing at are of equal weight the focal point will be in the centre of the see-saw plank. But sometimes we see a fat and heavy boy at play against a light and smaller boy. In such situations the focal point of balance would be closer to the fat boy. If the two players want to have playing balance the fat boy will have to sit nearer to the centre. It proves the centre of the force and balance are nearer to the heavier mass. Acting on this principle the heavenly bodies maintain balance and gain the orbital paths.
A demonstration of Kepler’s law is available on the computer that will help you see and understand the calculations orbital path timings and the concept of the focal points of gravitation between the bodies or the masses. In a subsequent section Kepler’s third law as upgraded by Newton is discussed.
