Galileo, Astronomy, and Physics
Galileo Galilei
There was another man, working at around the same time as Kepler, who made an even greater contribution to the dawn of modern astronomy and single-handedly pioneered modern mathematical physics. This was a man who laid down virtually all the groundwork for Newton and his name was Galileo Galilei (usually referred to only as Galileo). He has been called by some as the father of both modern astronomy and modern physics and certainly his role as a pivotal figure in the development of both these sciences is beyond question.
On top of this he was also the pioneer of modern experimental scientific method.
It was Galileo that finally provided proof of the Copernican theory, and thus confirming Kepler's work to be correct.
He also had time to lay down the foundations of correct understanding of dynamics and of gravity.But we are getting ahead of ourselves here.
Galileo's Telescope
Before Galileo began so much of his ground breaking work in astronomy an invention was to come along and help him out, that invention was the telescope and in the arms of Galileo it was the instrument that was to revolutionise the science of astronomy, allowing Galileo to peer into the heavens and see at a magnification many times what any human had seen before.
The discovery of the telescope is usually credited to Hans Lippershey in 1608, although there is some evidence that there was one or possibly even two people before him to invent a telescope, but this evidence remains very much inconclusive, so we shall not break from tradition here!
Galileo and Astronomy
So back to Galileo, in 1609 (about the same time as Kepler was about to publish his first two laws) from only simple reports of this new invention, Galileo, using his skills, was able to construct a vastly superior model to Lippershey's telescope and is said to be the first to use the refracting telescope. Some of his early observations included:
The Moon was not smooth but actually covered in mountains and craters.
The planets were discs not points of light.
The Milky Way was composed of an enormous number of stars (agreeing with Copernicus' idea of the universe being much vaster than previously thought, also destroying the only argument for the Taychoic system, by providing reason for why, in a heliocentric system there would appear to be no stellar parallax).
As a collective what these observations did was to raise the issue of the credibility of the Ptolemaic system, how could Aristotle and Ptolemy's work be trusted to be correct when there was so much of the universe they didn't know?
Galileo's early observations convinced him of the accuracy of the Copernican system and he began to argue strongly for it, basing his arguments on his observations with his telescope.
In this work there are 3 further observations in particular that deserve special mention:
His observations of the Moons of JupiterGalileo used the so called Galilean moons to prove a major argument against the Copernican system was incorrect.
The argument suggested that given the moon orbited the Earth, if the Earth then orbited the Sun, the Moon would be left behind. With the discovery of the moons around Jupiter it was clear that a planet could orbit a body without leaving behind any moons that were in turn orbiting it.
Observations of Sunspots
With the observation of Sunspots not only did Galileo prove that the Sun was not perfect (remember at the time the held ideas continued to be Aristotle's theory that God made all the celestial bodies and so they must be perfect) but he also observed that these imperfections were moving. This implied that the Sun was rotating on an axis which meant it was more feasible for the earth to be rotating (the idea of the Earth rotating in the Copernican model was one of the greatest arguments against it as such rotation could not be felt).
Galileo's view of SunspotsFrom Galileo's own sketches
A 2001 view of SunspotsCourtesy of SOHO/MDI
Observations of the Phases of Venus
Galileo's most important achievement in astronomy was demonstrating that the planet Venus, as seen from the Earth, went through a complete set of phases just like the Moon, which he first noticed in 1610.This wasn't just ground breaking it was earth shattering, it provided conclusive evidence that was consistent with the Copernican model but not with the Ptolemaic model.How? Well if the Earth was the centre of the Universe then due to the position of the Earth, Venus and the Sun, we would only ever see Venus in crescent phases because Venus would always be between the Earth and the Sun (see Ptolemaic system below).
The Ptolemaic System
The Copernican SystemGalileo identified that Venus went through a full cycle of phases, as viewed from the Earth, which meant that sometimes Venus must be on the opposite side of the Sun from Earth (see the Copernican system above), thus disproving the Geocentric theory of the Universe. So long after Copernicus' discovery finally there was empirical evidence to allow a definitive test, which proved Copernicus' and Kepler's work to be correct and the Ptolemaic model that had been held to be correct for 1500 years to be wrong!
Galileo Publishes His Work
In 1632 Galileo published his work Dialogue Concerning The Two Greatest World Systems. This latest work, supporting the Copernican model and proving the geocentric system wrong was not received well by the Roman Catholic Church! Indeed they were incensed by this work as it was contrary to scripture, contrary to the very foundations of religion. Of course a century before Copernicus himself and delayed the publication of his work for fear of the reprisal of the church, and it appears that his fear was justified.
In 1633 Galileo was summoned to Rome and quickly convicted of heresy, he was forced to make a public confession of his error in judgement and withdraw his support for the Copernican model, he was also forbidden to publish any further work and sentenced to life imprisonment. Due to his age, however, he was permitted to serve his sentence under house arrest.
Galileo's 'Ears of Saturn'
As a point of interest Galileo also discovered what he called the 'ears' of Saturn (of course we now know these to be rings but Galileo's telescope was not powerful enough to determine this).
Galileo and Physics
After Galileo's conviction in Rome, publicly at least, he lost interest in astronomy and he concentrated his efforts on his other life long work in the pioneering field of mathematical physics. In 1638, he managed to have his final work, Discourse on Two New Sciences smuggled out of Italy and published in the Netherlands. This work detailed his findings on the correct understanding of dynamics, gravity and, putting the two together, of projectiles.
Yet again Galileo was to challenge the long held theories of Aristotle.
In his early work in this field he performed inclined plane experiments, in which he studied both gravity and inertia.
He was studying the Law of Fall from as early as 1604 and was using inclined planes because in his initial experiments he found that objects in free fall accelerate too quickly for accurate measurement so he began using these planes to effectively slow down the rate of fall, therefore allowing him to make accurate time and distance measurements.
Aristotle had previously said that bodies falling in the same medium will fall at a speed proportional to their weight. Galileo believed this to be incorrect he suggested that all objects in a medium without resistance (e.g. on the Earth's surface but ignoring the effects of air resistance) will all gain equal amounts of velocity in equal intervals of time (uniform acceleration), regardless of weight (in other words all objects will fall at a constant rate and further to this, this rate will be the same for all objects no matter their weight).
After long experimentation he found that as the seconds past the distance the object would travel would increase in ascending odd numbers i.e. 1, 3, 5 ,7 ,9 etc (in other words in the third second the object will travel a distance of 5 units, but the total distance travelled in all 3 seconds of the experiment is 5+3+1=9units) from this he realised that the distance covered is directly proportional to the square of time taken (see table).This was one of his startling discoveries, that laid down the groundwork for some famous work to be done in the not too distant future.
Galileo's Law of Inertia
On inertia Aristotle had formulated the principle of impetus from his observations that most objects do not remain in motion after a force that is acting upon them is moved is removed. So he suggested that any object in motion will not remain so unless the force that is acting upon it does so constantly, if a force was removed the impetus would run out. What Aristotle actually believed was that the natural state of any object is at rest and so any object at rest will remain so unless acted upon by a force. Using just observation it is clear why Aristotle would think this
way, although this concept clearly has shortcomings.
Take, for example, an arrow travelling through the air, how could this arrow continue on its path after the force (the bow string) was removed?Aristotle's principle should mean that the arrow would not remain in motion after the force acting on it was removed. This is an often quoted example because it this was particularly troublesome to the Greeks (their actual reasoning for why it remained in motion had something to do with the arrow creating a vacuum behind it and air rushed into the vacuum to push the arrow along!).
With use of inclined planes Galileo realised that this was wrong because Aristotle had failed to take into account a hidden force (of course frictional force). He worked out that this force was acting in the opposite direction to motion and that if this force was decreased (by using oil, grease etc) then the object in motion would move further before stopping.
From this Galileo was to formulate his Law of Inertia:
An object in a state of motion possesses an inertia causing it to remain in a state of motion unless acted on by an external force.
Another way to state this is: if the frictional force is reduced to zero and a force is applied to an object so that it is pushed at a constant velocity after that force is removed the object will continue at that velocity forever, unless of course a new force acts on it at a later time.Clearly then Galileo demonstrated that a object's natural state was not at rest, as Aristotle had believed, but in fact in motion, and rest was just a special case where velocity was zero, though there was still forces acting on it.
These principles are simply taken for granted now, just as many of Galileo's achievements are, but it must be remembered at the time, as foolish as it seems to us now, everyone believed Aristotle's principles and Galileo's work was totally revolutionary. Clearly his work laid down the principles of the modern day understanding of dynamics.Galileo and Projectiles
Then Galileo went on to study projectiles, where he brought together his work on falling bodies and inertia and added the principle of Superposition. This stated that if a body is subject to two influences, each producing a characteristic type of motion, the object will respond to each, without modifying its response to the other. Or in simpler terms, referring to the diagram (right), a diagonal motion (V) may be spilt into its vertical (Vy) and horizontal (Vx) vectors and these two vectors can be treated separately.Before Galileo it was believed that when a projectile was launched it would continue until its impetus (horizontal motion) was lost and then fall towards ground. (Aristotle believed that the projectiles were pushed along (horizontally) by an external force transmitted through the air, see the example of the arrow above).For Galileo though projectiles move both horizontally and vertically at the same time, and that the motion can be separated into these two components (principle of Superposition). So what Galileo achieved here was to realise that the object was subject not only to horizontal force that caused acceleration but also to a vertical acceleration.
The horizontal component is described by Galileo's principle of inertia (contrast to impetus) so, providing no force acts on it after launch (in this case no air resistance) the horizontal velocity will remain constant (i.e. horizontal acceleration is zero), so the horizontal distance is clearly proportionate to the time taken to cover it.The vertical component causes constantly accelerated motion (don't forgot it is a vector so the direction is important, in this case downwards towards the Earth) so the vertical distance is proportional to the square of time taken (from his law of fall).
By treating the components separately when Galileo combined the calculations for the components he predicted that the path of a projectile would be a gently curving arc called a parabola and he proved this by experimentation. He showed that the projectile would always follow this path regardless of launch angle and launch velocity. (Obviously there is resistance in real world experiments, but the effect of air resistance is not that great and experimentation results are very similar to what would be predicted using the mathematics).
Galileo's Projectile work
Galileo stands as one of the all time great scientists, not only for his discoveries and his pioneering techniques but also for the fact that he had the courage to stand up and fight against tradition, public opinion and the church for what he believed in.
Science truly owes Galileo Galilei a debt of incredible gratitude.
There was another man, working at around the same time as Kepler, who made an even greater contribution to the dawn of modern astronomy and single-handedly pioneered modern mathematical physics. This was a man who laid down virtually all the groundwork for Newton and his name was Galileo Galilei (usually referred to only as Galileo). He has been called by some as the father of both modern astronomy and modern physics and certainly his role as a pivotal figure in the development of both these sciences is beyond question.
On top of this he was also the pioneer of modern experimental scientific method.
It was Galileo that finally provided proof of the Copernican theory, and thus confirming Kepler's work to be correct.
He also had time to lay down the foundations of correct understanding of dynamics and of gravity.But we are getting ahead of ourselves here.
Galileo's Telescope
Before Galileo began so much of his ground breaking work in astronomy an invention was to come along and help him out, that invention was the telescope and in the arms of Galileo it was the instrument that was to revolutionise the science of astronomy, allowing Galileo to peer into the heavens and see at a magnification many times what any human had seen before.
The discovery of the telescope is usually credited to Hans Lippershey in 1608, although there is some evidence that there was one or possibly even two people before him to invent a telescope, but this evidence remains very much inconclusive, so we shall not break from tradition here!
Galileo and Astronomy
So back to Galileo, in 1609 (about the same time as Kepler was about to publish his first two laws) from only simple reports of this new invention, Galileo, using his skills, was able to construct a vastly superior model to Lippershey's telescope and is said to be the first to use the refracting telescope. Some of his early observations included:
The Moon was not smooth but actually covered in mountains and craters.
The planets were discs not points of light.
The Milky Way was composed of an enormous number of stars (agreeing with Copernicus' idea of the universe being much vaster than previously thought, also destroying the only argument for the Taychoic system, by providing reason for why, in a heliocentric system there would appear to be no stellar parallax).
As a collective what these observations did was to raise the issue of the credibility of the Ptolemaic system, how could Aristotle and Ptolemy's work be trusted to be correct when there was so much of the universe they didn't know?
Galileo's early observations convinced him of the accuracy of the Copernican system and he began to argue strongly for it, basing his arguments on his observations with his telescope.
In this work there are 3 further observations in particular that deserve special mention:
His observations of the Moons of JupiterGalileo used the so called Galilean moons to prove a major argument against the Copernican system was incorrect.
The argument suggested that given the moon orbited the Earth, if the Earth then orbited the Sun, the Moon would be left behind. With the discovery of the moons around Jupiter it was clear that a planet could orbit a body without leaving behind any moons that were in turn orbiting it.
Observations of Sunspots
With the observation of Sunspots not only did Galileo prove that the Sun was not perfect (remember at the time the held ideas continued to be Aristotle's theory that God made all the celestial bodies and so they must be perfect) but he also observed that these imperfections were moving. This implied that the Sun was rotating on an axis which meant it was more feasible for the earth to be rotating (the idea of the Earth rotating in the Copernican model was one of the greatest arguments against it as such rotation could not be felt).
Galileo's view of SunspotsFrom Galileo's own sketches
A 2001 view of SunspotsCourtesy of SOHO/MDI
Observations of the Phases of Venus
Galileo's most important achievement in astronomy was demonstrating that the planet Venus, as seen from the Earth, went through a complete set of phases just like the Moon, which he first noticed in 1610.This wasn't just ground breaking it was earth shattering, it provided conclusive evidence that was consistent with the Copernican model but not with the Ptolemaic model.How? Well if the Earth was the centre of the Universe then due to the position of the Earth, Venus and the Sun, we would only ever see Venus in crescent phases because Venus would always be between the Earth and the Sun (see Ptolemaic system below).
The Ptolemaic System
The Copernican SystemGalileo identified that Venus went through a full cycle of phases, as viewed from the Earth, which meant that sometimes Venus must be on the opposite side of the Sun from Earth (see the Copernican system above), thus disproving the Geocentric theory of the Universe. So long after Copernicus' discovery finally there was empirical evidence to allow a definitive test, which proved Copernicus' and Kepler's work to be correct and the Ptolemaic model that had been held to be correct for 1500 years to be wrong!
Galileo Publishes His Work
In 1632 Galileo published his work Dialogue Concerning The Two Greatest World Systems. This latest work, supporting the Copernican model and proving the geocentric system wrong was not received well by the Roman Catholic Church! Indeed they were incensed by this work as it was contrary to scripture, contrary to the very foundations of religion. Of course a century before Copernicus himself and delayed the publication of his work for fear of the reprisal of the church, and it appears that his fear was justified.
In 1633 Galileo was summoned to Rome and quickly convicted of heresy, he was forced to make a public confession of his error in judgement and withdraw his support for the Copernican model, he was also forbidden to publish any further work and sentenced to life imprisonment. Due to his age, however, he was permitted to serve his sentence under house arrest.
Galileo's 'Ears of Saturn'
As a point of interest Galileo also discovered what he called the 'ears' of Saturn (of course we now know these to be rings but Galileo's telescope was not powerful enough to determine this).
Galileo and Physics
After Galileo's conviction in Rome, publicly at least, he lost interest in astronomy and he concentrated his efforts on his other life long work in the pioneering field of mathematical physics. In 1638, he managed to have his final work, Discourse on Two New Sciences smuggled out of Italy and published in the Netherlands. This work detailed his findings on the correct understanding of dynamics, gravity and, putting the two together, of projectiles.
Yet again Galileo was to challenge the long held theories of Aristotle.
In his early work in this field he performed inclined plane experiments, in which he studied both gravity and inertia.
He was studying the Law of Fall from as early as 1604 and was using inclined planes because in his initial experiments he found that objects in free fall accelerate too quickly for accurate measurement so he began using these planes to effectively slow down the rate of fall, therefore allowing him to make accurate time and distance measurements.
Aristotle had previously said that bodies falling in the same medium will fall at a speed proportional to their weight. Galileo believed this to be incorrect he suggested that all objects in a medium without resistance (e.g. on the Earth's surface but ignoring the effects of air resistance) will all gain equal amounts of velocity in equal intervals of time (uniform acceleration), regardless of weight (in other words all objects will fall at a constant rate and further to this, this rate will be the same for all objects no matter their weight).
After long experimentation he found that as the seconds past the distance the object would travel would increase in ascending odd numbers i.e. 1, 3, 5 ,7 ,9 etc (in other words in the third second the object will travel a distance of 5 units, but the total distance travelled in all 3 seconds of the experiment is 5+3+1=9units) from this he realised that the distance covered is directly proportional to the square of time taken (see table).This was one of his startling discoveries, that laid down the groundwork for some famous work to be done in the not too distant future.
Galileo's Law of Inertia
On inertia Aristotle had formulated the principle of impetus from his observations that most objects do not remain in motion after a force that is acting upon them is moved is removed. So he suggested that any object in motion will not remain so unless the force that is acting upon it does so constantly, if a force was removed the impetus would run out. What Aristotle actually believed was that the natural state of any object is at rest and so any object at rest will remain so unless acted upon by a force. Using just observation it is clear why Aristotle would think this
way, although this concept clearly has shortcomings.
Take, for example, an arrow travelling through the air, how could this arrow continue on its path after the force (the bow string) was removed?Aristotle's principle should mean that the arrow would not remain in motion after the force acting on it was removed. This is an often quoted example because it this was particularly troublesome to the Greeks (their actual reasoning for why it remained in motion had something to do with the arrow creating a vacuum behind it and air rushed into the vacuum to push the arrow along!).
With use of inclined planes Galileo realised that this was wrong because Aristotle had failed to take into account a hidden force (of course frictional force). He worked out that this force was acting in the opposite direction to motion and that if this force was decreased (by using oil, grease etc) then the object in motion would move further before stopping.
From this Galileo was to formulate his Law of Inertia:
An object in a state of motion possesses an inertia causing it to remain in a state of motion unless acted on by an external force.
Another way to state this is: if the frictional force is reduced to zero and a force is applied to an object so that it is pushed at a constant velocity after that force is removed the object will continue at that velocity forever, unless of course a new force acts on it at a later time.Clearly then Galileo demonstrated that a object's natural state was not at rest, as Aristotle had believed, but in fact in motion, and rest was just a special case where velocity was zero, though there was still forces acting on it.
These principles are simply taken for granted now, just as many of Galileo's achievements are, but it must be remembered at the time, as foolish as it seems to us now, everyone believed Aristotle's principles and Galileo's work was totally revolutionary. Clearly his work laid down the principles of the modern day understanding of dynamics.Galileo and Projectiles
Then Galileo went on to study projectiles, where he brought together his work on falling bodies and inertia and added the principle of Superposition. This stated that if a body is subject to two influences, each producing a characteristic type of motion, the object will respond to each, without modifying its response to the other. Or in simpler terms, referring to the diagram (right), a diagonal motion (V) may be spilt into its vertical (Vy) and horizontal (Vx) vectors and these two vectors can be treated separately.Before Galileo it was believed that when a projectile was launched it would continue until its impetus (horizontal motion) was lost and then fall towards ground. (Aristotle believed that the projectiles were pushed along (horizontally) by an external force transmitted through the air, see the example of the arrow above).For Galileo though projectiles move both horizontally and vertically at the same time, and that the motion can be separated into these two components (principle of Superposition). So what Galileo achieved here was to realise that the object was subject not only to horizontal force that caused acceleration but also to a vertical acceleration.
The horizontal component is described by Galileo's principle of inertia (contrast to impetus) so, providing no force acts on it after launch (in this case no air resistance) the horizontal velocity will remain constant (i.e. horizontal acceleration is zero), so the horizontal distance is clearly proportionate to the time taken to cover it.The vertical component causes constantly accelerated motion (don't forgot it is a vector so the direction is important, in this case downwards towards the Earth) so the vertical distance is proportional to the square of time taken (from his law of fall).
By treating the components separately when Galileo combined the calculations for the components he predicted that the path of a projectile would be a gently curving arc called a parabola and he proved this by experimentation. He showed that the projectile would always follow this path regardless of launch angle and launch velocity. (Obviously there is resistance in real world experiments, but the effect of air resistance is not that great and experimentation results are very similar to what would be predicted using the mathematics).
Galileo's Projectile work
Galileo stands as one of the all time great scientists, not only for his discoveries and his pioneering techniques but also for the fact that he had the courage to stand up and fight against tradition, public opinion and the church for what he believed in.
Science truly owes Galileo Galilei a debt of incredible gratitude.
posted by Ric Caric at 7:48 PM
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