Empirical Facts and Scientific Results - Part I Understanding Gravity: Kepler, Newton and Einstein

These Blogs are based on the lectures for a mini course on "Scientific Method for Non-Scientists".

Empirical Facts and Scientific Results - Part I

Understanding Gravity: Kepler, Newton and Einstein

Debi Prasad Choudhary

Los Angeles

Science originates in human mind. It may not be easy to learn what propels mind to consider objects, a profound question that was posed in a great ancient Indian text known as Kenopnished. But, science has achieved many great things in about past 400 years that has improved our living conditions. Only in last ten years, we can reach our destination guided by a talking gadgets and no longer have to carry a map. We can see our loved ones at far away places and talk to them as if sitting in the next chair. We can locate the center of our galaxy and detect what happened soon after the universe was born. All these achievements make us think that there is something profound about science and the way scientists think. Many advocate that scientific thinking; temperament and the method are somewhat superior to all other ways of thinking. Being a practitioner of science for more than past 30 years, people ask me about the scientific method and seek justification and approval of their beliefs from “science”. My response has been random and non-scientific!! In these blogs, I address the issues related to scientific method, its limitations and justification of other methods of human endeavor. Before considering scientific method, let us learn some concrete example of great scientific achievements. I discuss understanding gravity in past about 400 years in this blog. This is an illustration of practicing science through observation of natural phenomena.

Johannes Kepler lived in early 16^th century when understanding the position of earth in the context of rest of the objects in the sky was of great concern, since it decided the power for a class of individuals. Is the earth center of the universe and govern its affairs through few individuals who have direct access to the creator? If that is so than rest of the human being should obey and serve these chosen ones. This question can be addressed by studying the motion of heavenly objects. There are three types of objects in the sky, which rise in the east and set in the west following a definite path. The stars describe simplest sky path. They appear four minutes late every day at the same location in the east sky and many of them seem to circle around a bright star in northern sky, called pole star or “Dhrub Tara” (Constant star). Some of them appear in the east and set in the west and some do not set by the morning. But, all of them repeat the same pattern annually. This pattern is however, not the same for an observer in the southern hemisphere, living say, in Sydney, Australia or Rio De Janeiro in Brazil, where there is no equivalence of a pole star.  As, most of the ancient astronomy was developed in the northern hemisphere, let is confine our story to northern sky for now. The other types of bright objects in the sky are the planets, which appear as non-blinking stars. The background stellar pattern around them change every day. They do not appear in the same location of the sky, although march in a narrow strip from east to west and also known as “wondering stars”.  The sun and the moon are very bright objects, which repeat their sky path in which planets move on annual basis.

About 600 ago, we did not understand the motions of all these objects in the sky in a comprehensive unified model. People thought, stars, planets, moon and sun revolve around the earth in which our Gods and we live. They invented complex geometrical models to describe these motions and predict their path with some success. For the first time, Nicolaus Copernicus of Poland proposed in 1514 that universe consists of eight spheres at the center of which resides the sun and not earth. The outer sphere contains motionless stars and the planets revolve in fixed spheres. Moon revolves around the earth on a sphere. Even though the concept or the idea was revolutionary that interested the Pope of the time, it had little practical consequence because of the basic assumption of circular orbit of the planets around the sun. Its predictive capacity (for the occurrence of eclipse for example) was limited and similar to the geocentric model. Copernicus considered circular orbits, since these are perfect geometrical shapes and did not have compelling reason for any other geometrical path.

About one hundred years later in about 1623 Johannes Kepler, a German Astronomer used accurate positional measurements of planets in the sky to devise laws that described their motion. He said in first two laws that the planets moves around the sun in elliptical and not in circular orbits in such a way that in equal time, equal area of ellipse is covered. As the sun occupies one of the focus of the eclipse, when the planet is nearer to sun it moves faster. The third law related the period of the planets with their distance. Of course there were other observations such as the phase of the planet Venus that also showed that the planets move around the sun. The introduction of elliptical orbit was crucial as it improved the predictability of the model considerably and offered a clear competitive choice to the geocentric model. Although these laws had profound impact by enhancing confidence on heliocentric model of the universe, they were confined to the planets of the solar system alone and did not have the capability of generalized application. The laws were based on purely empirical evidence of the data provided by Tycho Brahe.

The Kepler’s laws found robust foundation of physics after about 50 fifty years later when Sir Isac Newton showed that the motion of any two bodies with masses m1 and m2 separated by a distance r are governed by central forces F = G (m1 X m2)/r², where G is called gravitational constant (numerically: 6.67384 × 10^-11 m³ kg^-1 s^-2). Both the bodies (objects) would move around a central point, situated near the heavier mass, in elliptical orbits. In case of the solar system, the planets do not move around the sun, instead, the sun and planets move around a common point that is situated near the surface of the sun (not at the center of the sun). The Newton’s law of gravitation defined the force F in a quantitative manner that can be used to predict the orbit of any two bodies with masses and led to several new discoveries. We now know why the Kepler’s laws work. Using the Newtonian version of Kepler’s laws, faint and compact White Dwarf stars near bright stars and supermassive blackhole at the center of our galaxy were discovered. We use these laws to launch geostationary communication satellites for navigation. The scope and utility of data based empirical Kepler’s laws were enhanced by using the physics base that treated the planets and stars as simple matter that interact through a force called gravity. This scientific method of extracting systematics of a set of observations (data) and trying to find the underlying physical cause became useful when they provide scope to predict new phenomena to test their limitations.

Finding the common properties of similar phenomena under different situations and understanding them with a simple predictive model central to scientific method. The other aspect is the quest for “beautiful” and “elegant” mathematical explanation of observed phenomena. The General Theory of Relativity of Albert Einstein illustrates such an example. Newtonian mathematical approach is based on observations of experimental results, in which hypothesis are unnecessary. In fact Newton states that “Hypotheses non fingo (I frame no hypotheses). In 300 hundred years after Newton, several conceptual limitations of his theory was encountered as they were applied to study the dynamics of complex and sophisticated systems, chief among them being absence of inertial frame. This is when Einstein’s imaginative approach produced one of the most beautiful descriptions of the world. Einstein states, “Imagination is more important than knowledge. For knowledge is limited to all we now know and understand, while imagination embraces the entire world, and all there ever will be to know and understand.” Einstein proposed that mass and energy shape the space-time geometry, which in turn governs their motion. The consequence of this consideration is that the path of light deviates from the straight line while passing in the vicinity of massive objects, which is now clearly observed. We must note here that there was hardly any need for such consideration from experimental side for Einstein to think in this manner. It is the intuitive generousness that led him to this great discovery.  

Over centuries, man asks questions about its surroundings, some of which are easy and some difficult. Attempting to answer them through generalization of observed results and extending their scope through creative imagination is a vital aspect of scientific method that resulted in a series of discoveries enriching our lives and brought us from caves to modern comfort. The important thing is that any new scientific theory or model must be able to explain the already observed phenomena and predict new results that can be used to test them. The later is an important aspect, absence of which makes a theory unscientific.