Posted on 11/02/2011 3:14:29 PM PDT by SunkenCiv
Explanation: If you drop a hammer and a feather together, which reaches the ground first? On the Earth, it's the hammer, but is the reason only because of air resistance? Scientists even before Galileo have pondered and tested this simple experiment and felt that without air resistance, all objects would fall the same way. Galileo tested this principle himself and noted that two heavy balls of different masses reached the ground simultaneously, although many historians are skeptical that he did this experiment from Italy's Leaning Tower of Pisa as folklore suggests. A good place free of air resistance to test this equivalence principle is Earth's Moon, and so in 1971, Apollo 15 astronaut David Scott dropped both a hammer and a feather together toward the surface of the Moon. Sure enough, just as scientists including Galileo and Einstein would have predicted, they reached the lunar surface at the same time. The demonstrated equivalence principle states that the acceleration an object feels due to gravity does not depend on its mass, density, composition, color, shape, or anything else. The equivalence principle is so important to modern physics that its depth and reach are still being debated and tested even today.
(Excerpt) Read more at 129.164.179.22 ...

We never went to the Moon.
/xfiles music
So let me get this straight.... If you dropped Obama and Biden’s brain at the same time....
Oh never mind.
Yes, you got it, they'd both float
That would be like dropping Santa Claus and the Tooth Fairy at the same time.
It’s a good idea, because the only way I could get anything out of that show would be to listen and not watch. ;’)
;’)
When she was written out, the show passed its peak. Still like it though.
The hammer will fall slightly faster, as every mass has it’s own gravity. The hammers greater mass has greater gravitational pull on moon.
You'd be stoned stupider than Ozzy.
That's true, but the "greater gravitational pull" is balanced by that fact that there's a greater mass to be accelerated.
“Brain’’? Obama and Biden!?! What makes you think either of those two have a brain?
Also true.
You could move a supermassive black hole with a feather if you could anchor the feather somehow and had a few billion years to do it in.
Forgive my advanced ignorance, but doesn’t the mass have to rotate to induce the gravity field? Or have I drowned in a sea of scifi hog swill.
Regards
A variation on that concept has been suggested as a means of altering the trajectories of asteroids that appear to be on earthcolliding trajectories.
Negative on the rotation.
That’s why it’s called science “fiction”.
Thank you.
The clue was in the name I suppose!
Regards.
Negative. All mass has the same reaction to gravitational forces, inertia and force are linear. 1000 lb takes more to get moving than 100 lb, but there IS more to get it moving.
At the hammer and feather scale it is so minute to be almost ridiculous, but think of it this way. If you could stop the Earth and Moon from rotating and place a feather the same distance from Earth as the Moon, I guarantee that we will collide with the Moon first.
Gravity is probably the best know yet least understood force in nature.
We think of people on the space station as being weightless but that’s really just an effect of the free fall they’re in. I think I read that the gravitational pull at that distance from the earth’s surface is less than 1% less than it is at sea level.
To avoid any complications due to different compositions, instead of a feather use a small iron ball of the same mass, and the USS Missouri, also generally made of iron.
Suspend them each one mile above the surface of the moon.
Each is composed of a collection of iron atoms.
The gravitational attraction between each atom of iron and the moon is the same, thus each atom of iron (assuming all of the same isotope) will accelerate towards the moon at the same rate.
Therefore, since the featherweight piece of iron and the Missouri are both merely composed of many atoms of iron, though in different numbers, accelerating at the same rate, “in formation”, they will both hit the moon at the same time.
This holds for any distance from the moon.
The gravitational attraction between two objects is proportional to the product of the masses of the two objects divided by the square of the distance between the two objects.
Assume, to avoid having to do triple integrals, all mass of the earth is concentrated at a very dense point at the center of the earth, surrounded by a massless, 4000mileradius shell that we stand on.
We are thus separated from the mass of the earth by 4000 miles, which, squared, has a magnitude of 16000000.
The orbit of the ISS has an average altitude of about 225 miles.
It, then, is about 4225 miles from the mass of the earth; 4225 squared is about 17850000.
Therefore, the gravitational pull of the earth at the altitude of the space station is 16000000/17850000 relative to that on earth, or roughly 90%.
Even if you assume the far half of the earth doesn’t exist because the “1 over rsquared” term makes it less important and use a radius of 2000 miles rather than 4000, that still puts the earth’s gravitational attraction on the ISS equal to about 80% of that on the surface of the earth.
LOL I’ll take your word for it. I love the science but really suck at the math.
Let's try math, instead of handwaving. We wish to determine the acceleration due to gravity acting upon an object as a function of its proximity to some other object. The two objects are (let us say) a hammer, and the moon. The each have mass M_{h} and M_{m}. According to Newton, a force acting on a mass M causes acceleration.
F=m*a
The gravitational force between two massive objects can be computed
F_{g} = G*(M_{1}*M_{2})/ R^{2}
where "R" is the distance between them. So, the gravitational acceleration of a hammer falling on the moon may be calculated:
F_{g} = G*(M_{m}*M_{h})/ R^{2} = M_{h}*a
Note that M_{h} cancels out of this equation. Acceleration of an object (a hammer) due to the gravitational attraction of another object (the moon) is not a function of the first object's (the hammer) mass.
I’m impressed.
I knew what the equations were, but lacked the ambition to actually “typeset” them in HTML.
“Typesetting” them is the only way I know of to make them readable. My knowledge of HTML is really quite limited.
I guess < sub > and < super > handles most of it.
That, and ambition.
Really, so Jupiter and Earth have the same pull on the sun in your world.
You only did half of the equation.
If gravity is as you say, why do object accelerate faster in a fall on Earth than they do on the moon.
As in your example, the Earth and the Moon are just groupings of individual atoms right?
Again, you are only doing half of the equation.
Indeed, it is impossible to find zero gravity anywhere matter exists, but it is possible to find points and conditions of balanced gravity, which have the same obervable result.
Lately I’ve been wondering about the concept of true motionlessness. I wonder if its even possible in expanding space where all things are moving at incredible speeds.
Objects accelerate faster in a fall on Earth than they do on the Moon because Earth is bigger than the Moon. Work the equations for yourself. Substitute the mass of Earth, Jupiter, another hammer, whatever you like. You can solve for the acceleration towards any of these.
Gravitational acceleration towards any object X is a function of the mass of that object and the distance from that object, as I showed upthread.
Don't wave your hands, do the math.
Do two magnets with their N S poles facing each other create a greater attractive force than a single magnet? If the force is greater doesn't that equate to greater acceleration?
If a hammer were orbiting the Earth, it would not measurably effect the tides, but the moon does. Hmmm. Why is that? Because the large object exerts greater force. Hmmm. Going back into your acceleration formulas.
As I said, you forgot that the equation has to be made for both objects, not just one, and then the result combined.
Math is great, but garbage = garbage out. Acceleration of gravity formulas must use the mass of both objects. With small objects we don't do this because it doesn't matter (measurably), but with large objects we absolutely combine the masses.
The attraction between the Earth and Moon is determined using the combined mass of both, not the mass of the Earth. This is easily understood if you think of what would happen if you pushed the Earth and Moon into one ball. That ball would have a greater gravitational attraction than the Earth right? Sure, so the same applies before they are combined.
All measurements of movement are relative to an arbitrarily chosen position.
What you are clearly doing is treating one of the masses as a parent mass, and ignoring the other.
According to your equation, if we swapped the moon and hammer as M1 and M2, the gravitational force would immediately drop off to near nothing.
Indeed, do the math.
It's like taking two identical rubber bands and stretching one to twice its unstretched length. That will produce a certain amount of tension. If you then stretch both that same amount, you'll get twice the force.
Same thing for interatomic attractions.
Hey, why is it always just pretty girls? Of course, at my age, I’d just as soon have pictures of pretty dogs. :)
Another big lie! Biden doesn’t have a brain....
Oh my goodness. I think I’m better at handwaving! :)
If you go back and read what AB posted, he said exactly that:
The gravitational force between two massive objects can be computedThat's the force BETWEEN any two objects  that same force acts equally on each of the two objects.F_{g} = G*(M_{1}*M_{2})/ R2
The gravitational force would be unchanged.
Have you never heard of the "Commutative property of multiplication"?
Apparently not.
Let me introduce you to it: "Two numbers can be multiplied in either order."
This means that a room that is 10' x 15' has the same floor area as a room that is 15' x 10'.
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