The Principle Of Relativity And Planetary Motion

To construct such a new cosmology, there are a number of important topics that must be considered. One of these is the idea of relativity of motion. The watershed in the development of modern astronomy was crossed when Copernicus replaced the ancient geocentric model of the universe with a heliocentric model. Although the relative merit of the two models was initially debatable, the development of Newton’s laws of motion seemed to give overwhelming support for the heliocentric model. This can be argued as follows: If the stars and planets are rotating around the earth once per day, then they should be subjected to tremendous centrifugal forces that will have to be counterbalanced in some way. Isn’t it more reasonable to suppose that the earth, which is much smaller and more compact than the universe as a whole, is rotating on its axis? Likewise, isn’t it more reasonable to suppose that the small earth is orbiting around the massive sun than to suppose that the sun is orbiting around the earth?

This objection can be partially answered by invoking the idea of relativity of motion. Consider two objects, A and B, that are approaching one another at a constant velocity. According to classical physics, there is no physical difference between saying that A is standing still and being approached by B and saying that B is standing still and being approached by A. Thus, as far as physics is concerned, no objection could be raised to either statement.

In classical physics this relativity of motion is not thought to apply to rotation. Imagine an axis running from the center of A through the center of B. Suppose that A is rotating with respect to B on this axis. According to classical physics, rotary motion generates centrifugal force, and thus the actual rate of rotation of A and B can be determined by measuring this force. Thus if A exhibits a certain amount of centrifugal force and B does not, the conclusion of classical physics must be that A is rotating and B is not.

However, the physicist Ernst Mach once made the following argument: Suppose that A and B are the only objects in the universe, and suppose that they are of equal mass. Then why should it be that A shows measurable evidence of rotation and not B? After all, if we say that A is rotating, then what is it rotating with respect to? If B is the only other object in the universe, then A could only be rotating with respect to B. But it could equally well be said that B is rotating with respect to A. Thus Mach concluded that neither A nor B would exhibit centrifugal force if they were the only objects in the universe. He proposed that centrifugal force is generated in one object due to the rotation relative to it of another, much larger object. Thus, Mach maintained that if A is rotating with respect to the rest of the universe, then one could equally well say that the universe was rotating with respect to A and thereby generating centrifugal forces in A. Mach’s argument implies that there are no physical grounds for rejecting the statement that “A is standing still and the universe is rotating around it.”

Here one might object that the rotation of the earth is directly indicated by the Foucault pendulum experiment and the evidence that the prevailing winds are affected by Coriolis forces. Also, the rotation of the earth around the sun is indicated by a number of minute but measurable effects, such as aberration of starlight and the parallax of some stars.
It turns out, however, that Mach’s argument also disposes of these objections. For example, Mach would say that the rotation of the Foucault pendulum can be attributed to the rotation of the massive universe around the earth, just as well as to the rotation of the earth under the pendulum.

If this idea of relativity of motion is granted, one can then argue that the geocentric or heliocentric viewpoints stand on the same footing physically, and we can choose one or the other, depending on what is convenient. In the case of the astronomical siddhāntas, we could argue that the geocentric viewpoint is simply the more practical of the two, since all computations must ultimately be expressed in geocentric terms. And if we intuitively prefer to think of large masses as stationary and small masses as moving, rather than the other way around, then we will prefer the heliocentric viewpoint.

When we turn to the cosmology of the Bhāgavatam, the situation becomes more complex. It is stated that the pravaha wind carries the celestial bodies around the polestar once per day. This can be seen from the viewpoint of relativity of motion in the following way: The pravaha wind is due to a kind of tenuous atmosphere that exists in the region of antarikṣa, or outer space. If we regard the earth as turning on its axis, then the stars are at rest in this stationary atmosphere. In contrast, if we regard this atmosphere as rotating along with the stars, then the stars are being carried by it, but they are still at rest in it. This brings to mind the analogy of the clouds and the wind that Śrīla Prabhupāda uses to illustrate the effects of māyā: Just as the clouds seem to be at rest in the wind that carries them, so people carried by the influence of māyā do not notice this influence.

The situation of Bhū-maṇḍala can be analyzed as follows: As we pointed out in Chapter 3, if Bhū-maṇḍala is located in the plane of the ecliptic, then Bhū-maṇḍala must also rotate daily with the kāla-cakra. The movement of the sun in Bhū-maṇḍala consists of one leftward revolution around Mount Sumeru per year, and both Bhū-maṇḍala, the sun, and the other planets are carried in one rightward rotation per day by the pravaha wind. Here, from the perspective of relative motion, one can regard the earth as rotating and the stars, pravaha atmosphere, and Bhū-maṇḍala as stationary. The sun is then seen to rotate with respect to Bhū-maṇḍala, being carried by its chariot. From the perspective that larger masses should be viewed as stationary, it is reasonable to regard the sun as moving and Bhū-maṇḍala as stationary, since Bhū-maṇḍala is much greater than the sun.

If we then take the covering shells of the universe into account and consider that the pravaha wind is blowing with respect to these fixed coverings, we obtain the following picture: It makes sense to suppose that the pravaha wind and the various celestial bodies are moving with respect to the universal coverings, since the coverings are more massive than the celestial bodies. Likewise, in this picture it also makes sense to suppose that the sun is moving with respect to Bhū-maṇḍala. This, of course, is the picture of celestial motion given in the Bhāgavatam.

As we mentioned in Chapter 3, the idea of relativity of motion is presented by Śukadeva Gosvāmī in his description of the motion of the sun. Mahārāja Pariksit asked him,
My dear lord, you have already affirmed the truth that the supremely powerful sun-god travels around Dhruvaloka with both Dhruvaloka and Mount Sumeru on his right. Yet at the same time the sun-god faces the signs of the zodiac and keeps Sumeru and Dhruvaloka on his left. How can we reasonably accept that the sun-god proceeds with Sumeru and Dhruvaloka on both his left and right simultaneously? [SB 5.22.1]

Here the leftward and rightward movements are the yearly and daily revolutions of the sun about the earth. Śukadeva Gosvāmī replied to this question as follows:

When a potter’s wheel is moving and small ants located on that big wheel are moving with it, one can see that their motion is different from that of the wheel because they appear sometimes on one part of the wheel and sometimes on another [SB 5.22.2].
Śukadeva Gosvāmī explains that in this analogy the potter’s wheel corresponds to the kāla-cakra, which carries the stars and signs of the zodiac with it. The ants correspond to the sun and other planets, which are moving leftward around the wheel while the wheel spins to the right. Thus the idea that motion can be seen differently from different relative perspectives is presented in the Bhāgavatam.

We have discussed these points in some detail to show that Vedic cosmology should not be rejected on the basis of naive arguments regarding the relative motion of the earth, the sun, and the universe as a whole. To fully relate Vedic cosmology to the laws of motion of modern physics, it will be necessary to understand the bearing that structures such as Bhū-maṇḍala and the coverings of the universe have on our understanding of the principle of relativity. Since these structures involve higher-dimensional travel and transformations of time such as that seen in the story of King Kakudmī and Revatī, we do not think that this will be an easy task. But it may well be possible, and the resulting model will no doubt be even more surprising than the quantum theory was to the physicists of the early twentieth century.

We should also note that Einstein’s theory of relativity is required in order to make sense of the heliocentric theory of the solar system. The history of this theory is that in the late 19th century, ether-drift experiments performed by physicists such as Michelson and Morley seemed to indicate that the earth is stationary relative to the ether. Since the ether was then conceived as a highly rigid medium, this seemed to indicate that the earth was stationary with respect to an absolute reference frame. Although many efforts were made to avoid this conclusion, this did not prove to be possible within the framework of classical physics.

The dilemma was resolved only with the introduction of Einstein’s theory, which involved radical changes in physicists’ concepts of space and time, and which has many strikingly counter-intuitive consequences. These include the famous twin paradox, in which a space traveler returns to earth from a year’s journey at nearly the speed of light and discovers that many years have passed. It would take us too far afield to delve into these matters here, but we mention them as an indication that the issue of geocentric versus heliocentric cosmology is not as trivial as it might superficially seem to be.