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Author Topic: Was Galileo wrong?  (Read 5678 times)

Offline DoctorBeaver

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Was Galileo wrong?
« on: 14/03/2006 01:07:21 »
I know there's a thread in another forum about Galileo's experiment, but I thought this would be better here. I've been putting my warped little beaver brain to work again and I've come up with a rather puzzling thought.
According to Galileo, objects will fall at the same rate. But will they? What if you had 2 objects of identical weight; 1 a sphere, the other a very long cone. If you held them so that the bottoms were level and then let go, would they actually land at exactly the same time?
Surely, gravity would have more of an effect on the sphere. There would be a certain proportion of the mass of the cone further from the ground than the sphere. Therefore there would be a stronger gravitational attraction between the Earth and the sphere at any given point in its descent than between the Earth & the cone at the same time. Wouldn't that cause the sphere to accelerate faster and hence hit the ground before the cone?
Ignore any effects of air resistance, that isn't important in this thought experiment. I'm talking about, and only about, gravitational attraction.

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another_someone

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Re: Was Galileo wrong?
« Reply #1 on: 14/03/2006 02:12:54 »
You thought experiment does not contradict Galileo, it merely makes some erroneous assumptions.

You assume that two objects, where the gaps between the lowest point of the objects and the Earth is identical, will take the same time to drop to the Earth.  This is demonstrably an erroneous experiment.

If one takes an extreme example – take two identical balls with 3 foot of  string attached.  Hold both balls three feet above the ground.  Now unwind the string on one ball, so it just touches the ground.  Now drop the balls – which ball and string will touch the group first – clearly the strong of the ball with the string unwound was already touching the ground before the experiment started.

The only valid measure is to measure the centre of gravity.  More accurately, the experiment should be that two bodies should be dropped such that at the start of the experiment the centre of masses of the two objects are aligned, and at the end of the experiment, you should measure the centre of mass (which means you should not really be measuring an impact on the ground, but measure it as it passes through a line in space close to the ground).



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Offline G-1 Theory

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Re: Was Galileo wrong?
« Reply #2 on: 14/03/2006 12:33:26 »
The Galileo's experiment was done on eather the first or secund Moon landing with a 3# hammer and An egle father. and they broth landed at the same time.
The eagle father reminded me that it was the first moon landing.


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Offline DoctorBeaver

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Re: Was Galileo wrong?
« Reply #3 on: 14/03/2006 12:49:52 »
quote:
You assume that two objects, where the gaps between the lowest point of the objects and the Earth is identical, will take the same time to drop to the Earth. This is demonstrably an erroneous experiment.


That's exactly the opposite of what I said. My thought was that the object with more mass at the bottom would accelerate faster and hence hit the ground 1st.

quote:
The Galileo's experiment was done on eather the first or secund Moon landing with a 3# hammer and An egle father. and they broth landed at the same time.


Did they? I don't remember any instruments capable of measuring in nanoseconds being used; and that's what the difference would have been.
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« Last Edit: 14/03/2006 12:53:13 by DoctorBeaver »
 

Offline G-1 Theory

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Re: Was Galileo wrong?
« Reply #4 on: 14/03/2006 12:59:06 »
quote:
Originally posted by DoctorBeaver

quote:
You assume that two objects, where the gaps between the lowest point of the objects and the Earth is identical, will take the same time to drop to the Earth. This is demonstrably an erroneous experiment.


That's exactly the opposite of what I said. My thought was that the object with more mass at the bottom would accelerate faster and hence hit the ground 1st.

quote:
The Galileo's experiment was done on eather the first or secund Moon landing with a 3# hammer and An egle father. and they broth landed at the same time.


Did they? I don't remember any instruments capable of measuring in nanoseconds being used; and that's what the difference would have been.
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Well if see the experiment I am sure you will see that the hammer had more mass at the bottom. I am remember it right he held the hammer between two fingrs at the handles end with the 3# head down and the feather was held strite out. so the hammer head did have more mass at the bottom.

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Offline G-1 Theory

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Re: Was Galileo wrong?
« Reply #5 on: 14/03/2006 13:25:23 »
Come on people;

I am not to tell anyone that they are wrong. I am here heple with your answers and try to show some you things that I have learn over the years.

Iam a retired invesitagetor, that has over the last 16 years turned my investators skills to one of my many hobbies that is physics, I a will asure you that I am not trying to cut anyone down for their believes are. BUT THEORY DO NOT BECOME FACTS JUST DO TO THE FACT THAT TIME HAS PASTED.
 
And at no time do I beleive that anyone SHOULD TEACH A THEORY AS FACTS.

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Offline DoctorBeaver

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Re: Was Galileo wrong?
« Reply #6 on: 14/03/2006 14:54:42 »
G1 - I'm not disputing that the hammer & the feather certainly appeared to land at the same time. The difference (if there actually was 1) would have been too short to be noticeable to the human eye; or even to high-speed cameras that were then available.
 

another_someone

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Re: Was Galileo wrong?
« Reply #7 on: 14/03/2006 16:35:07 »
quote:
Originally posted by DoctorBeaver

That's exactly the opposite of what I said. My thought was that the object with more mass at the bottom would accelerate faster and hence hit the ground 1st.




But it still comes back to the fact that if you calculate the centre of gravity correctly, and take measurements as if you were dealing with a point mass at the centre of gravity, then trhe actual distribution of mass should not matter, since that distribution would be allowed for when calculating the centre of gravity.



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Offline Dr B

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Re: Was Galileo wrong?
« Reply #8 on: 14/03/2006 18:04:06 »
DoctorBeaver:  Is your point that the acceleration due to gravity decreases with height above the planet.  Thus the top of your elongated cone is in a weaker field than the bottom.  The bottom is pulled down more strongly than the top and the object is stretched.  This difference is less on the concentrated sphere.  Am I also correct in thinking that you do not want to measure any real difference - you are happy with a theoretical difference.  In which case I guess you are correct!  Anyone else?

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Offline Hadrian

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Re: Was Galileo wrong?
« Reply #9 on: 14/03/2006 19:56:41 »
Limerico di Galileo© [13 stanzas]
          by Martin J. Murphy

While watching a cannonball's motion,
Galileo conceived of the notion
That natural laws,
Not a mystical Cause,
Ruled the physical world's locomotion.

Though its own view was mostly confused,
The Church was not greatly amused
With this flaunting of Deo
By old Galileo
And ordered it quickly defused.

So the Pope sent some priests who inquired
If it wouldn't be best he retired?
"Undoubtedly you know
What we did for Bruno;
Do you also wish to be fired?"

He asked an old Cardina;'s opinion:
"Pray tell me, Your Grace, if you will then,
Does this mean what I think?
That henceforth I must shrink
From discussing my clever perception?"

Said Bellarmine, "No, it is not a ban;
If you want to keep teaching of course you can.
They merely have said
To take care where you tread
And smile when you say thing Copernican."

Unbeknownst to our venerable dissident
The records said something quite different.
When the Pope saw the note
The inquisitors wrote
He lost what remained of his temperament.

The message the Vatican sent
Was blunt in its stated intent
"Recant all this heresy
Quick or we'll harass thee,
Now until your life has been spent."

In facing the dread inquisition,
Few men could defend their position;
So it shouldn't surprise
When we are apprised
Of old Galileo's decision.

"Explaining celestial motion
Needs more than just faith and devotion.
But to save my poor head
I'll recant what I've said
(Though I'll secretly keep to my notion)".

So our friend the illustrious Florentine
Spent his last years in Vatican quarantine,
Locked up in his home
By the prelates of Rome
For being a cosmical libertine.

The Church caused a major imbroglio
By correcting Copernicus' folio
Yet it couldn't discern
The abuse it would earn
In forbidding the whole Dialogo?

By killing Sidereus Nuncius
For the news that their views were defunctus,
The renaissance ended
And darkness descended
Upon the Dominican dunces.

In spite of the Vatican's dissuasion
Galileo still rose to the occasion.
Though once deemed heretical,
He proved more prophetical
Than those of a clerical persuasion.


What you do speaks so loudly that I cannot hear what you say.
 

Offline DoctorBeaver

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Re: Was Galileo wrong?
« Reply #10 on: 14/03/2006 21:17:21 »
George - I think DrB has almost got what I mean. I'm not talking about the centre of gravity, although that obviously comes into it.
I wasn't considering the object stretching - but I suppose that would be a by-product. My point was that if the bottom of the sphere & the bottom of the cone were the same distance from the planet, the part of the cone that was higher than the sphere would not be attracted with the same strength as the sphere. I was wondering whether that would cause the sphere to be accelerated more rapidly.

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another_someone

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Re: Was Galileo wrong?
« Reply #11 on: 15/03/2006 02:43:53 »
quote:
Originally posted by DoctorBeaver

George - I think DrB has almost got what I mean. I'm not talking about the centre of gravity, although that obviously comes into it.
I wasn't considering the object stretching - but I suppose that would be a by-product. My point was that if the bottom of the sphere & the bottom of the cone were the same distance from the planet, the part of the cone that was higher than the sphere would not be attracted with the same strength as the sphere. I was wondering whether that would cause the sphere to be accelerated more rapidly.




I think I see what you are getting at, although I think you are still making a mistake, insofar as if the base of the cone is the same distance as the base of the sphere, then would not the centre of gravity of the cone be above the centre of gravity of the sphere?

What is more interesting in your experiment is if the cone was on its side, since that would mean that one side of the cone would be lower that the other, and if one follows your logic, it should cause one side to fall faster than the other side, and thus inducing a spin.

Where this kind of issue might be pertinent is when one gets close to the centre of a black hole, where the gravitational gradient could become very steep.  Certainly, it is this gradient which, AIUI, is the presumed cause of Hawkins radiation.



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Offline DoctorBeaver

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Re: Was Galileo wrong?
« Reply #12 on: 17/03/2006 03:02:43 »
quote:
I think I see what you are getting at, although I think you are still making a mistake, insofar as if the base of the cone is the same distance as the base of the sphere, then would not the centre of gravity of the cone be above the centre of gravity of the sphere?


Of course it would. That's exactly the point I'm getting at. Think of it this way:-

Hold a hammer (h1) so the head is at the bottom. Then get an identical hammer (h2) but with the head fixed halfway up the shaft. Hold them so their bottoms align. The head of h1 will be nearer the ground than the head of h2, but the nearest point of h1 to the ground (the bottom of the head) will be the same height as the nearest point of h2 (the lower end of the shaft).

Gravitational attraction is the inverse square of the distance between the objects, so there must be more gravitational attraction acting on the head of h1 than on the head of h2. Also, as gravitational attraction is also a function of the sum of the masses involved, there must be a stronger force between the ground and the head of h1 than between the ground and the lower end of the shaft of h2.

Now drop them. As the gravitational force acting on h1 is greater than on h2, h1 must accelerate faster. Therefore the first part of h1 to hit the ground will do so before the first part of h2.

It is the very fact that the sum of the masses of the objects involved is a factor in the gravitational attraction between them that makes me have doubts Galileo's theory. Or am I just misunderstanding the effects of gravity?

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Re: Was Galileo wrong?
« Reply #13 on: 17/03/2006 07:06:04 »
quote:
Originally posted by DoctorBeaver

Hold a hammer (h1) so the head is at the bottom. Then get an identical hammer (h2) but with the head fixed halfway up the shaft. Hold them so their bottoms align. The head of h1 will be nearer the ground than the head of h2, but the nearest point of h1 to the ground (the bottom of the head) will be the same height as the nearest point of h2 (the lower end of the shaft).




Totally valid, but does it contradict anything Galileo said?

I don't know for sure exactly how Galileo worded his assertion, but my understanding is that it pertained to the notion that two objects of different mass will fall at the same weight, it does not say anything about shape or mass distribution.

The fact that the same hammer is rotated through 180 degrees does not alter its mass, only its mass distribution.

Furthermore, rotating a hammer through 180 degrees, if it is rotated around its centre of shape, will shift its centre of mass.  A proper comparison would be to rotate the hammer through its centre of mass, which would shift its centre of shape.

In other words, if the a hammer is 12 inches long, but its centre of mass is 3 inches from its head, this means that a rotation around its centre of mass would leave the closest point between the hammer and the Earth beneath either 3 inches or 9 inches beneath the centre of gravity (i.e rotating the hammer will effectively alter its closest point by 6 inches).

Beyond this, you may also be right that there might be a very slight additional shift due to the inverse square law, but that slight difference will be in addition to the very much greater difference that would be true even if gravity was linear in nature that would arise because you are apparently rotating around the centre of shape rather than the centre of mass.



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Offline DocN

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Re: Was Galileo wrong?
« Reply #14 on: 17/03/2006 22:00:25 »
Another neat domonstration I used to do in my physics classes, was to take three clay balls (all the same mass) and drop two of them from the same height (both being the same mass, hit the same time) than take these two clay balls and press them together (one ball now, double the mass) and drop it and the other clay ball--they all hit at the same time.  What difference does it make whether they are separated or stuck together?
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Offline DoctorBeaver

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Re: Was Galileo wrong?
« Reply #15 on: 26/03/2006 22:45:17 »
quote:
I don't know for sure exactly how Galileo worded his assertion, but my understanding is that it pertained to the notion that two objects of different mass will fall at the same weight...


(I assume you meant "rate" not "weight")

But that's exactly what I'm questioning. Gravity is a 2-way force. An object with more mass will cause a stronger gravitational attraction between itself and the earth. A ping-pong ball would not cause so strong an attraction as a ball of the same size made of lead.

A ball will fall faster on Earth than on the moon because the moon's gravity is less. Gravity on Earth is greater because it has more mass.  More mass = stronger gravity. Now scale that down to the size of ping-pong balls. The same holds true - the 1 with more mass will have a stronger gravitational field. That will cause it to accelerate faster. Therefore, in a vacuum, the lead MUST fall faster.

Or, if you prefer, scale it up. Move the Earth and the moon so they're a million miles or so from the sun, make sure they're both stationary, then let them go. They will both be pulled into the sun, but there will be a greater attraction between the sun and the Earth than between the sun and the moon. In this instance there would probably be a noticeable difference in their rate of acceleration towards the sun.



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Offline Ophiolite

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Re: Was Galileo wrong?
« Reply #16 on: 26/03/2006 23:27:07 »
Sorry. You are talking nonsense. The lead ball has more mass, more inertia, than the ping pong ball. It requires more force to accelerate it at the same rate as the ping pong ball. That force is available precisely because it is more massive.

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Offline DoctorBeaver

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Re: Was Galileo wrong?
« Reply #17 on: 27/03/2006 16:44:38 »
quote:
Originally posted by Ophiolite

Sorry. You are talking nonsense. The lead ball has more mass, more inertia, than the ping pong ball. It requires more force to accelerate it at the same rate as the ping pong ball. That force is available precisely because it is more massive.

Observe; collate; conjecture; analyse; hypothesise; test; validate; theorise. Repeat until complete.



Right... at least someone has finally given a reason why my thinking was wrong. So inertia exactly balances out the extra gravitational attraction? That in itself is quite fascinating.

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Re: Was Galileo wrong?
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