Was Galileo wrong?

rogerinnh · Feb 11, 2005

Galileo Was Wrong In a famous experiment Galileo dropped two balls of different weights from a balcony on the Tower of Pizza, both of which hit the ground at the same time, thereby proving that heavier objects fall at the very same rate as lighter objects, in contrast to the common wisdom that the heavier object should fall faster. But was he right? A “thought experiment” has long been used to corroborate Galileo’s experiment. The thought experiment is quite simple. Consider two objects of identical masses. Drop them separately. They will fall at the same rate, since they are of identical mass. Now tie the two masses together and drop them. Will they now drop faster merely because they are tied together? The presumed answer is “of course they will not drop faster”. And the presumed conclusion is that heavier (more massive) objects fall at the same rate as lighter (less massive) objects. Yet, … Consider another thought experiment. Take a ball and drop it, here, on Earth. You’ll find that it falls at approximately 32 feet per second per second. Take that same ball up to the Moon and drop it. The Moon’s gravity is one-sixth that of the Earth’s, so that same ball is going to fall at a much lower rate. Now consider that all motion is relative. We described the motion in this experiment from the perspective of the Earth, when we dropped the ball here on Earth, and we described the motion from the Moon’s perspective when we dropped it on the Moon. But it is just as valid to describe these motions from the perspective of the ball that we’ve been dropping. When we hold the Earth and ball apart (by our hand keeping the ball away from the Earth, our feet pressing against the Earth to keep it away from the ball) and we then release the ball (take away the body holding the two apart) the Earth and the ball move towards each other at 32 feet per second per second. From the ball’s perspective the Earth, which is a hugely mass

robnissen · Feb 11, 2005

You are wrong, not Galileo. I have to go way back to high-school physics, but I believe the answer to your paradox, is that while the larger masses do assert a stronger attraction on each other, the larger mass, also has a higher inertia. The higher inertia, exactly cancels the higher mass, and all bodies do (in a vacuum) fall at the exact same speed.

siarad · Feb 11, 2005

Are you trying to say the combined gravity field squeezed between them is more concentrated therefore causing them to fall faster?

larper · Feb 11, 2005

<blockquote>In reply to:<hr />The gravitational field around the combined object is greater than the individual gravitational fields around the individual objects. When you put the two objects together you are not only adding them physically together, you are adding the gravitational fields of the two objects.<hr /></blockquote> So, a string tied between two objects causes their gravitational fields to interact. Amazing. So this is string theory, eh?<img src="/images/icons/rolleyes.gif" /> <div class="Discussion_UserSignature"> Vote Libertarian </div>

pizzaguy · Feb 11, 2005

Two signs this guy is a bit loose on the facts... 1) "Tower of Pizza" 2) We have two identical objects and simply tie them together. How could they possible fall faster merely by being tied together. Because it’s the gravitational field around an object that determines how fast it falls (relative to another object’s gravitational field). The gravitational field around the combined object is greater than the individual gravitational fields around the individual objects. When you put the two objects together you are not only adding them physically together, you are adding the gravitational fields of the two objects. And that greater, composite gravitational fields pulls more strongly on the other object (the Earth) than either of the objects individually. Bla bla bla .... I already tried Galileo's experiment as a young boy. We went to Cedar point and I dropped an apple and a rock from the skycar, they hit virtually at the same time from a height of just over 100 feet. (My big sister about freaked out over that one - the place is too busy now to do it again...) <div class="Discussion_UserSignature"> Note to Dr. Henry: The testosterone shots are working! </div>

Astrosag · Feb 11, 2005

That is precisely correct.

Astrosag · Feb 11, 2005

Did he drop them or roll them down a very smooth incline? I don't think he dropped them.

nacnud · Feb 11, 2005

An incline is problematic due to the difference in angular momentum between two spheres of different mass but equal size. I don't think the knowledge available in Galileo’s time was sufficent to compensate.

Saiph · Feb 12, 2005

After newton however, it is easy to design a lighter sphere with the same angular momentum. You just have to know how hollow to make it. Thus the experiment can be done today. <div class="Discussion_UserSignature"> --------------------SaiphMOD@gmail.com -------------------"This is my Timey Wimey Detector. Goes "bing" when there's stuff. It also fries eggs at 30 paces, wether you want it to or not actually. I've learned to stay away from hens: It's not pretty when they blow" -- The Tenth Doctor, "Blink" </div>

JonClarke · Feb 12, 2005

Gallileo was wrong about quite a few things, and was just as inflexible as his aristolean opponents. His refusal to accept Kelper's ellipical orbits, and his ideas on the tides are just two. Gallielo also had a sheer genius in being able to antagonise people who were originally sympathetic. The pope for example. In many ways be got what he deserved. This does not diminish from is greatness, however, but it is useful to remember that those who disagreed with him were not idiots either. At its heart was a clash of method - induction (Gallileo) vs deduction (the aristoleans) - complicated by a clash of personalities. Jon <div class="Discussion_UserSignature"> Whether we become a multi-planet species with unlimited horizons, or are forever confined to Earth will be decided in the twenty-first century amid the vast plains, rugged canyons and lofty mountains of Mars Arthur Clarke </div>

pizzaguy · Feb 13, 2005

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ Quite a post - I see we have a REAL historian here! <img src="/images/icons/smile.gif" /> James Burke says that Galileo was "an arrogant, egotistical exhibitionist ... who must have known himself that even HE got some things wrong." <div class="Discussion_UserSignature"> Note to Dr. Henry: The testosterone shots are working! </div>

rogerinnh · Feb 13, 2005

Robnissen says: “I believe the answer to your paradox, is that while the larger masses do assert a stronger attraction on each other, the larger mass, also has a higher inertia. The higher inertia, exactly cancels the higher mass, and all bodies do (in a vacuum) fall at the exact same speed.” So, let’s see. I take the Moon and hold it a few feet above the Earth and release it. Since the inertia of the Moon exactly cancels the Moon’s gravitational field it will fall at 32 feet per second per second. Now I do the “opposite” and take the Earth and hold it a few feet above the Moon and release it. The Earth’s inertia cancels its gravitational field and the Earth falls towards the Moon at, well, whatever the acceleration is on the Moon, considerably less than 32 feet per second per second. But then which is it? Both of these situations are identical: the Earth and Moon are held apart and then released. Do they fall together at the Earth’s gravitational rate or the Moon’s gravitational rate? I’d suspect that they fall together at a rate somewhere in between those two rates, meaning that a falling body falls at an acceleration that is at least somewhat determined by the masses of the falling body and the body to which it is falling. Certainly the acceleration is primarily determined by the more massive object. If I drop a ball on the Earth then the rate at which the ball falls is primarily determined by the mass of the Earth. But as the size/mass of the ball is increased (Moon sized, Jupiter-sized, …) the ball’s mass comes more into play and the rate at which the ball falls will be different when compared to the small-ball’s rate. If this weren’t true, then any two objects, when allowed to fall together, would fall at exactly the same rate. And we know that that is not the case. So, it would seem that more massive objects do indeed fall at a different rate than less massive objects. And the error in this logic is ..... ?<</safety_wrapper>

JonClarke · Feb 13, 2005

Thanks pizzaguy. Aurther Koestler's "The sleep walkers" has an excellent section on Galileo. Owen Gingerich also written extensively on the period, I heard a lecture he gave about his trial which was perhaps the best lecture I have ever heard. Owen wrote an article in Scientific American about 20 years ago that is well worth reading, plus a lots of more recent stuff on the period from Copernicus to Newton. Cheers Jon <div class="Discussion_UserSignature"> Whether we become a multi-planet species with unlimited horizons, or are forever confined to Earth will be decided in the twenty-first century amid the vast plains, rugged canyons and lofty mountains of Mars Arthur Clarke </div>

robnissen · Feb 13, 2005

Massive objects do NOT fall at a different rate than less massive objects. If you drop a ball from a height of 1000 miles, and you "drop" the moon from a height of 1000 miles, and you have a marker at 500 miles, both objects will reach that marker at the EXACT same time. The only difference between the two, is that the moon will pull the earth up towards it, so that the moon might fall 900 miles (I'm not going to bother to do the math to see exactly how far the moon pulls the earth towards it) before it hits the earth, whereas the ball, because (for all intents and purposes) it does not pull the earth towards it, must fall 1000 miles before it hits the earth. But until the moon hits the earth, the moon and the ball fall at the EXACT same speed. Gallileo was right.

JonClarke · Feb 14, 2005

Acrually Steve, it was primarily a matter of logic. The aristoleans believed that only what could be proved by deductive logic was true. Inductive reasoning was at best an unreliable guide. Therefore stimply looking at something through a telescope or carrying out an experiment did not prove very much at all. They were they were right, from a the position of pure logic. What Galileo did was argue (and try to show) that for understanding the physical world a weight of inductive evidence combined with a coherent explanation, while not sufficient for a formal proof, was enough to provide valuable insights into the way the world was. Since Galileo's day we now realise that induction is not enough and that hypotheses must be capable of testing and falsification. However we are still closer to Galileo's position than to his forebears and most of his contemporaries. In fact, it was the coherence of the theory that swung the day for heliocentricism, not just empirical observation. The final verifiation of the heliocentric solar system dud not come until the 18th century with the measurement of stellar aberration. Galileo rejected Kelper not because he knew that planets moved in three dimensions, but because he was still wedded to the Aristolean circular orbits. For this reason he also dismissed Tycho's very accurate measurements of positional astronomy. While there were conservates then as now, Galileo did not help his case by sheer bloody mindness, arrogance, and at times rudeness. This does not mean he was not a great thinker, a man of consderable scientific insight and faith, and a powerful observer. But we should not ignore his flaws or dismiss his contemporaries either. I think you underestimate Kelper's laws. They are very accurate in describing planetary motion, vastly superior to anything previous and, with modification by Newton, were more than adequate until the the problem of Mecurcy's orbit came to ligh <div class="Discussion_UserSignature"> Whether we become a multi-planet species with unlimited horizons, or are forever confined to Earth will be decided in the twenty-first century amid the vast plains, rugged canyons and lofty mountains of Mars Arthur Clarke </div>

pizzaguy · Feb 14, 2005

I think you underestimate Kelper's laws. They are very accurate in describing planetary motion, vastly superior to anything previous and, with modification by Newton, were more than adequate until the the problem of Mecurcy's orbit came to light. Problem? This is news to me, anything I should be worried about? In other words, ... please continue. <img src="/images/icons/smile.gif" /> <div class="Discussion_UserSignature"> Note to Dr. Henry: The testosterone shots are working! </div>

nacnud · Feb 14, 2005

Keplers laws, and Newtons laws that followed them can not explain the precession of the perihelion of the orbit of the planet Mercury. This precession is small; the unexplained portion is on the order of one angular second per century (an arc-second per century). See about halfway down on this page for more It wasn't until General relativity came along that the problem was sorted out.

rogerinnh · Feb 14, 2005

My thanks to both Tigerbiten and x_snipe for clarifying the issue here and verifying that object masses are indeed involved in the determination of how fast objects "fall together". Tigerbiten provided the precise formula. He makes the statement that "So as long as M >> m then small differences in m make no practical difference in the force between them", 'M' being the mass of the more massive object and 'm' being the mass of the less massive object. The key word here is "practical". In any given application the difference between the force for a small object and that of a (slightly) larger object may be irrelevant, but it is still there, even if it's immeasurably small. It's one of those things that are taught in schools (all objects fall at the same rate) that are not quite true. I would much rather science be taught accurately (give them the whole equation, not just an approximation to it) than teach them something that's not quite right. There are many issues like this, "facts" that are taught in science classes that are not quite right.

larper · Feb 14, 2005

<blockquote>In reply to:<hr />There are many issues like this, "facts" that are taught in science classes that are not quite right. <hr /></blockquote> First, if you try to give students the whole equation, they would be overwhelmed. What do you do, introduce 7th graders to General Relativity and tell them that everything else can be derived from that? Secondly, the statement "All objects fall at the same rate" is a correct statement given Galileo's time and general understanding of how the world worked. It took Newton to realize that gravity was a force and that the apple has an effect on the earth just as the earth has an effect on the apple. But, the statement "The acceleration due to gravity at the earth's surface is 32ft/sec/sec" is correct no matter the size of the object being accelerated. Thus, the statement "all objects fall at the same rate" is simply more correctly stated as "all objects at the surface of the earth are subjected to the same acceleration." In science and math, you have to teach the fundamentals first, or you will alienate the student. <div class="Discussion_UserSignature"> Vote Libertarian </div>

silylene old · Feb 14, 2005

Personality issues aside, Galileo's new physics was far better and more scientific than anything which had proceeded him, except for some of Da Vinci's work. I wouldn't be so certain. What about Al-Khwarizmi's 9th century Kitab al-Jabr wal-Muqabala, which is arguably the most influential science/math work in history? http://www.ms.uky.edu/~carl/ma330/project2/al-khwa21.html <div class="Discussion_UserSignature"> <div class="Discussion_UserSignature" align="center">- - - - - - - - - - - - - - - - - - - - - - </div><div class="Discussion_UserSignature" align="center">I really, really, really miss the "first unread post" function. </div> </div>

robnissen · Feb 14, 2005

Once again another informative post from silylene. I knew where calculus came from, I did not know where al-jabr (algebra) came from. Thx for the link.

Saiph · Feb 14, 2005

and the statement that all things fall towards an object at the same rate is true now, if you completely consider the switch you make in teh frame of reference. F=MA Fg= GMm/r^2 So, MA = GMm/r^2 or A = Gm/r^2. M is the mass of the falling object, m is the mass of the object considered stationary. M drops out if you consider it to move. So when you switch from one body being stationary to the other, you also switch the equations used, from A = GM(1)/r^2 to A = GM(2)/r^2. Note the change in the "attractor" labeled M(1) vs M(2). The accelerations are not the same between the two frames. I.e. the earth does not fall towards the ball at the same rate the ball falls towards it. However all balls fall towards the earth at the same rate, and all earths, and balls, fall towards the "falling ball" at the same rate. This is a very good thing. Otherwise every time someone dropped a ball from head height, the earth would lurch ~4 meters in a single second from many peoples reference frames. <div class="Discussion_UserSignature"> --------------------SaiphMOD@gmail.com -------------------"This is my Timey Wimey Detector. Goes "bing" when there's stuff. It also fries eggs at 30 paces, wether you want it to or not actually. I've learned to stay away from hens: It's not pretty when they blow" -- The Tenth Doctor, "Blink" </div>

JonClarke · Feb 15, 2005

Steve, I suggest you read the writers of the period - and historians Owen Gingerich who research them - like more carefully. Deductive logic WAS supreme method for determining truth. What Galileo and Copernicius before him suggested was that inductive logic was sufficient in natural philosophy. Observational science astronomy, biology, geology, palaeontology, archaeaology are still strongly inductive today, relying on inference and accumulated data. Deductive logic is largely useless in such fields. Aristotle got many things wrong, but he was also a good observer who got many things right. Much the same as Galileo, his observations proved better than his physics. It is also misleading to over emphasise the influence or Aristotle as well, or the degree to which his idweas were held by the scholastics. Theye were in fact intensely debated. BTW, although contemporary celestial mechanics has indeed improved in Kelper, Kepler's laws are still good enough approximations to be used in in introductions to the courses. Jon <div class="Discussion_UserSignature"> Whether we become a multi-planet species with unlimited horizons, or are forever confined to Earth will be decided in the twenty-first century amid the vast plains, rugged canyons and lofty mountains of Mars Arthur Clarke </div>

silylene old · Feb 15, 2005

Nothing much came of Al-Kwarizimi's work. *boggle* In addition to inventing algebra, Al-Kwarizimi was also the individual who brought the use of the "zero" to European culture, and expound on its value in this book (which now only exists as its Latin translation) Algoritmi de numero Indorum His astronomical book Sindhind Zij describes the calcuations inmaking calendars; calculating true positions of the sun, moon and planets, tables of sines and tangents; spherical astronomy; astrological tables; parallax and eclipse calculations; and visibility of the moon; a related manuscript, attributed to al-Khwarizmi, describes spherical trigonometry. His works were translated no less than 7 different times into Latin and other European languages by the 12th Cnetury. "Algebra" was the transliterated title of one of the Latin translations. All subsequent math and physics is based upon Al-Kwarizimi's masterpieces works. As the historian Allard said, Al-Khwarizmi's algebra is regarded as the foundation and cornerstone of the sciences. In a sense, al-Khwarizmi is more entitled to be called "the father of algebra" Historian Kahn said: "In the foremost rank of mathematicians of all time stands Al-Khwarizmi. He composed the oldest works on arithmetic and algebra. They were the principal source of mathematical knowledge for centuries to come in the East and the West. The work on arithmetic first introduced the Hindu numbers to Europe, as the very name algorithm signifies; and the work on algebra ... gave the name to this important branch of mathematics in the European world... The historian Sarton said: "... the greatest mathematician of the time, and if one takes all the circumstances into account, one of the greatest of all time...." <div class="Discussion_UserSignature"> <div class="Discussion_UserSignature" align="center">- - - - - - - - - - - - - - - - - - - - - - </div><div class="Discussion_UserSignature" align="center">I really, really, really miss the "first unread post" function. </div> </div>

JonClarke · Feb 16, 2005

Steve Galileo not a mathematician? Mathematics was the only subject he did well in as a student. His first job after dropping out was lecturing mathematics and tutoring it privately. He then applied (unsuccessfully) for the chair in mathematics at the university of Bologna, and then held chairs in the discipline first at the university of Pisa and then at the university of Padua. Galileo subsequently became personal mathematician to the Grand duke of Tuscany. He was first and foremost a mathematician, physics was a hobby. Another reason why the professional physicists looked down on him. He did experiments, but not as rigorous as later scientists, admittedly partly because of limits in available instruments. However, despite this, and his telescopic observations, in many ways he was still strongly rationalistic, hence his rejection of elliptical orbits, despite their superiority. In fact he never mentioned Kepler's work, even though he had to have been aware of it. Science is certaionly rational and therefore logical. However a great many issues in science cannot be couched in simple deductive logic. For example organic evolution, or plate tectonics were not arrived at through simple deduction, but by the weight of evidence (induction), carefully tested and compiled into a coherent theory. Virtually nothing that Aristotle discovered is taught any more, except as a sidelight? Let's see, Aristotle discovered the hydrological cycle, recognised that land and sea changed places, commented on the great antiquity of the earth compared to the span of human history, made detailed observations on anatomy of many organisms that were not surpassed until the use of the microscope, described the social organisation of bees, and introduced a system of taxonomy that was not significantly improved until Linnaeus. I am going to have check my dates, it is a while since I lectured on this stuff, and my lecture notes have disappeared . B <div class="Discussion_UserSignature"> Whether we become a multi-planet species with unlimited horizons, or are forever confined to Earth will be decided in the twenty-first century amid the vast plains, rugged canyons and lofty mountains of Mars Arthur Clarke </div>

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