# Modern Version of Galileo’s Leaning Tower of Pisa Experiment

Friends,

Galileo’s leaning tower of Pisa experiment is one of the most famous and important experiments in the history of science. In today’s VERITAS article we will examine the status of that experiment today.

The question that you may ask is: that experiment was done. Why do we need to examine its modern status? The answer is that in scientific method there is no final answer to anything. So experiments need to be repeated again and again. And new experiments should be an improvement over previous ones. For a history of the scientific method read my book: Pilgrims of Episteme: Story of the Scientific Method.

Before we start, lets recall Galileo’s experiment and understand its significance. Aristotle believed that if two objects, one heavier and the other lighter were dropped together, the heavier one will fall faster and therefore reach the ground first. The problem with Aristotle was that he was a great philosopher but he did not like to experiment. So he just imagined that the heavier object would fall faster and formulated his “theory” of gravity. The problem with the world was that they just followed what Aristotle said- and they believed that he had to be right- for nearly 2000 years! But Galileo was different. He wanted to test this and so in 1589 he went up to the top of leaning tower of Pisa and dropped a wooden and a lead ball. The balls landed at the same time much to the astonishment of Aristotelian teachers.  This experiment is extremely important because it formed the basis of Newton’s theory of gravity and also the equivalence principle which formed the basis of Einstein’s general relativity.

Now some historians doubt whether this experiment actually took place. But Galileo had done several other experiments and shown that gravity causes the same acceleration in all falling bodies. Galileo had also created a thought experiment to show that a heavier body and a lighter body will fall at the same rate. Here is how it goes: if we say that a heavier body falls faster than a lighter one then what would happen if the heavier and the lighter body are tied together using a string? Would the light body not slow down the fall of the heavier body? But this cannot be right because the combined weight of the two bodies is a sum of their individual weights. So it should fall at a speed greater than either of them. So this is a paradox because we get different answers depending on how we approach the problem and we have logical inconsistency.  The only way to solve the paradox is to reject the assumption that the heavier body would fall at a faster rate. Therefore all bodies fall at the same rate irrespective of their weights.

This is a nice thought experiment but the ultimate test of all science is experiment. In this VERITAS I want to tell you the status of this experiment today. When we say that all bodies fall at the same rate, this is a scientific theory. An experiment can NEVER say something like that. An experiment can only state the limits or accuracy to which this theory( or any other theory) has been verified.  So the aim of experimental scientists is to keep creating better experiments to test a theory to a greater limit or accuracy than previous experiments.

The modern version of Galileo’s experiment does not measure the rate of fall of two balls. It measures the rate of fall of Earth and Moon towards the sun! So the experiment is done on a massive scale. And this experiment has been going on for over three decades and will continue to give us new data for many years to come. The name of the experiment is Lunar Ranging Experiment. And this is how it was done: Apollo 11, 14 and 15 missions to the moon from 1969 to 1971 left hundreds of corner-cube retroreflectors  on the surface of the moon.  A corner cube retroreflector is a device that has the property that it reflects any incident light back in the direction from where it came, no matter what its incident angle was.

For more than 30 years laser pulses have been sent from earth to the moon. Each pulse lasts 200 pico seconds and such laser pulses are sent 10 times each second. These laser pulses strike the retroreflectors and return back to earth where they are detected. From this  we can calculate the distance between Earth and Moon to the precision of a few mm!

By observing the return times of the pulses, scientists have confirmed that the moon and Earth fall or accelerate towards the sun at the same rate – to the precision of 1.5 X 10 ^ -13.  If the rate of fall of the earth and moon was different, it would have shown in the results of this experiment as deviations in trajectory and therefore distance between Earth and the moon.

So we know that the theory that all masses accelerate equally under the influence of a gravitational field is true to the accuracy of the 13th place of decimal. This is one of the most accurate experiments done in the history of science. But we still keep doing more experiments and keep improving the accuracy of the Lunar Ranging experiment because even if we find that this principle is not valid to a place of decimal after the 13th, we will reject the theory, and consequently reject Einstein’s general relativity and look for a better theory of gravity.

In this article I had made reference to the equivalence principle which forms the basis of Einstein’s general relativity which is the currently accepted theory of gravity. Let me briefly describe this very interesting principle. Einstein noted that if a person falls in a gravitational field and only observes objects around him, he would think that he is weightless ie does not experience any gravitational field. To illustrate the principle, lets take a person and a few objects( say a cup, a ball and paper) and put them in a closed box. Now lets drop this box from a great height on Earth( or any planet). While the box is falling, the man, the objects inside the box and the box itself are all falling at the same rate( as shown by Galileo’s experiment and its modern version- the Lunar Ranging experiment). Since the man, the box, the ball, the paper and the cup are falling at the same rate, the man would not think that he or any other object is moving at all- the relative velocity of these objects with respect to each other is 0. Now lets place the same box( with the same objects) in outer space, far away from any gravitational field. Since there is no gravitational field, the man, the box and the other objects are at rest with respect to each other. So the man feels weightless. Einstein said that no experiment can distinguish between these two scenarios- the box freely falling on Earth and the box floating about in outer space are equivalent to each other for all objects inside the box. This principle is one of the central assumptions of Einstein’s general relativity- and we have see that this too is based on Galileo’s experiment and its modern version – the Lunar Ranging experiment.

Kanwar

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Go wondrous creature, mount where science guides

go measure earth, weigh air, state the tides,

instruct the planets in what orbs to run

correct old time, regulate the sun

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