RJBeery
Taking air resistance out of the equation do objects with different mass truly fall at the same speed? What I'm asking is, is their rate of fall theoretically identical or just "so close as to call it identical"?

I know the gravitational force is different since it depends on mass of the Earth and mass of the dropped objects. What I'm wondering is if the extra "pull" needed to overcome the inertia of the more massive of the dropped objects is EXACTLY what is provided by its greater gravitational attraction...

?
Nick
YOU COULD DROP THE MASS OF THE WHOLE UNIVERSE AND IT WOULD FALL JUST THE SAME WAY.

MITCH RAEMSCH -- LIGHT FALL --
QUOTE (RJBeery+May 18 2007, 11:29 PM)
Taking air resistance out of the equation do objects with different mass truly fall at the same speed? What I'm asking is, is their rate of fall theoretically identical or just "so close as to call it identical"?

I know the gravitational force is different since it depends on mass of the Earth and mass of the dropped objects. What I'm wondering is if the extra "pull" needed to overcome the inertia of the more massive of the dropped objects is EXACTLY what is provided by its greater gravitational attraction...

Yes, they fall at the identical rate of 9.8 meters per second per second. Everything falls in a gravitational field at the same rate. Objects with higher masses need a stronger gravitational pull to cause them to fall at the same rate as smaller objects, so although the force is greater with larger objects, everything falls at the same rate - so the answer is yes.

For a more exact explanation: according to General Relativity, gravity is caused by the curvature of spacetime. Since all matter moves through spacetime at the same rate, as objects move closer to more massive objects, their geodesic becomes more and more curved, resulting in acceleration through space, but their total rate through spacetime remains the same. All objects, no matter what their mass, will move at the same speed through spacetime in the same conditions (without friction, air resistance, etc.).
Zephir
QUOTE (RJBeery+May 19 2007, 07:29 AM)
is their rate of fall theoretically identical or just "so close as to call it identical"?

By AWT the flat objects with lower density will be attracted more, then the compact dense ones, because the high gravitational field curvature is the source of weak repulsive force (a kind of "surface tension" effect).
Pan
Within some ridiculous amount, like 1 part in a billion, they are the same.

Edit:
Meaning that so far as we can tell, they are exactly the same.
Guest
Check out the following (sorry for the spaces) science .nasa .gov /headlines/y2007/ 18may_equivalenceprinciple.htm

This article has a graph showing how the precision of measurement has increased over the many years of experimentation. The article states in part: Galileo's experiments were only accurate to about 1%, leaving room for doubt, and skeptical physicists have been "testing EP" ever since. The best modern limits, based on, e.g., laser ranging of the Moon to measure how fast it falls around Earth, show that EP holds within a few parts in a trillion (1012). This is fantastically accurate, yet the possibility remains that the equivalence principle could fail at some more subtle level."

science .nasa. gov /headlines/y2007 /images/equivalenceprinciple/ limits_med.jpg

Perhaps a member would like to post the image?
N O M
rpenner
Originally at http://relativity.livingreviews.org/Articl...06-3/fig_1.html , part of The Confrontation between General Relativity and Experiment by Clifford M. Will
Singularity
Hypothetical situation;

So if we drop Moon (by stopping its revolution) form its orbital height and on the opposite side of earth we drop a umm, a Coin. (opposite side so that Coin dont fall on Moon )

What will reach the earth first ?
rpenner
Singularity, the Moon and Earth collide first, which is caused by the Earth falling towards the Moon and away from the coin (assuming they start equal distances as measured center-to-center).

If the Moon and the coin are on the same side of Earth this is no problem and the coin and the moon fall together, but the moon still hits first because of it's greater finite radius.

If the Moon were compressed to the same radius as a baseball (which is super-dense but not as dense as a lunar Black Hole) and the compressed baseball and a regulation baseball were dropped side-by-side, then they would hit the Earth at the same time. (same radius, same side so no relative motion of the Earth)

Whew.
Singularity

What if we compress Jupiter to size of baseball and drop them together on earth ?
Nick
QUOTE (Singularity+May 22 2007, 05:31 AM)
What if we compress Jupiter to size of baseball and drop them together on earth ?

THAT IS MY POINT. YOU COULD DROP THE MASS OF THE WHOLE UNIVERSE AND IT WOULD FALL JUST THE SAME WAY.

GRAVITY WILL MOVE AN APPARENTLY INFINITE MASS THE SAME WAY. THIS INVESTS IN IT A KIND OF POWER. THE POWER TO MOVE ANY AMOUNT OF MASS.

MITCH RAEMSCH -- LIGHT FELL --
bm1957
This is a much more interesting question than anyone has given it credit for!!!

It comes down to whether there is any difference between inertial mass and gravitational mass, a question which has by no way been answered.

It appears that they are the same (by experiment) but there is as yet no theory or even any accepted guess as to why they should be. It's a bit of a mystery!
N O M
QUOTE (rpenner+May 22 2007, 05:03 PM)
If the Moon and the coin are on the same side of Earth this is no problem and the coin and the moon fall together, but the moon still hits first because of it's greater finite radius.

The coin would also be falling toward the moon at 1/6 G.
Ron
Hi All,
BM1957,
Your quote:"It comes down to whether there is any difference between inertial mass and gravitational mass, a question which has by no way been answered.
It appears that they are the same (by experiment) but there is as yet no theory or even any accepted guess as to why they should be. It's a bit of a mystery!"

Is actually just a way of stating the Equivalence Principle as proposed by Einstein. Grant it, there are alot of people still trying to prove it wrong, but no one has yet been able to, leaving us with mountains of results pointing towards it's accuracy.
Peace,
Ron
bm1957
QUOTE (Ron+May 22 2007, 10:55 AM)
Hi All,
BM1957,
Your quote:"It comes down to whether there is any difference between inertial mass and gravitational mass, a question which has by no way been answered.
It appears that they are the same (by experiment) but there is as yet no theory or even any accepted guess as to why they should be. It's a bit of a mystery!"

Is actually just a way of stating the Equivalence Principle as proposed by Einstein. Grant it, there are alot of people still trying to prove it wrong, but no one has yet been able to, leaving us with mountains of results pointing towards it's accuracy.
Peace,
Ron

Absolutely.

Just did some quick reading because I'm not familiar enough with the equivalence principle to talk about it - looks like the error margin between the two experimentally is currently less than one in a trillion.

Still no process for why though. Something along the lines of:

"It's because the particles which account for mass are the only particles which gravity can interact with"

is what I mean. (Obviously I just made that up and it is VERY simplistic, hopefully demonstrates the point though)
Ron
Hi BM1957,
Yeah, why is a tough one. Physicists are just recently (last decade or so) trying to work on the whys. The Higgs field is one of great interest. It's proposed to be the field that gives elementary particles their inertia. I'm not the most fluent in this subject, but basically the Standard model predicts this field (and it's associated Higgs boson) which is somewhere between 100 and 500 proton masses. The LHC might clear this up in the next year or so by either finding the Higgs or not.
Peace,
Ron
rpenner
QUOTE (N O M+May 22 2007, 09:15 AM)
The coin would also be falling toward the moon at 1/6 G.

Thus, I said "Side-by-Side" so that the accelerations are perpendicular to each other. For example, the baseball could literally be in orbit around the lunar-baseball, and assuming this orbit was in the plane normal to the radius connecting Earth and Moon, they would fall at the same rate.
Pan
QUOTE (Singularity+May 22 2007, 05:31 AM)
What if we compress Jupiter to size of baseball and drop them together on earth ?

Well, at some point the problem is no longer that simple, even though the equivalence between inertial mass and gravitational mass (the reason objects of different masses drop at the same rate) would hold.

If you discount the three body problem (the effect of the baseball and Jupiter ball on each other as well as the Earth), and make the earth a similar ball, and all of them fixed and rigid, then I think the math would work out and the ball and Jupiter ball would drop at the same rate.

Otherwise, with the mass of jupiter compared to the earth, distances (1/r^2) become a non-trivial component of the problem.

Cheers.
Singularity
First drop the baseball from certain height x.

Then drop compressed Jupiter of the same size from height x.

Will they both take same time to reach earth ?

Wont Jupiter pull earth more than baseball and hence .....
rpenner
You are abusing coordinate systems. It is not valid to attach your coordinate system to the surface of the Earth when you rig the experiment such that the Earth is guaranteed to be influenced measurably by the experiment. (Technically, the Jupiter-baseball is guaranteed to rip the planet apart.)
Montec
Hello all

I would like to inject a point of observation into this discussion.

In a mass spectrometer we have two or more molecules/atoms ionized to the same level injected with the same velocity into a uniform dialectic field. The inertia/momentum of the molecule/atom resists the force applied by the dialectic field. The more inertia a sample has the further it can travel before being detected by the walls of the apparatus.

If we apply the same thinking to gravity we would expect that the inertia of an object would resist the applied gravitational field as a function of mass. If two objects were dropped at the same time then the object with less mass would accelerate first. However, this does not appear to be the case.

This brings up my point of observation. Gravity directly affects the momentum/inertia of an object. Mass has little to do with it.

Pan
QUOTE (Singularity+May 23 2007, 12:14 PM)
First drop the baseball from certain height x.

Then drop compressed Jupiter of the same size from height x.

Will they both take same time to reach earth ?

Wont Jupiter pull earth more than baseball and hence  .....

Jupiter ball would pull the Earth ball more (and visa versa), but it is also moving accelerating a jupiter mass.

Montec, again, the difference is that the field of force in the gravitational system is dependent on the mass, the same (apparently) mass that is providing the inertia. Thus the force on a heavier object is greater than the force on a lighter object.

F = (G*M*m)/r^2

However, acceleration

a = F/m

By equivalence, the little m's (the m of gravity in the first eq, and the m of inertia in the second) are exactly the same (or experimentally the same to at least 1 part in a trillion)

Thus F and m change in exact proportion, and a remains the same.

For the mass spec, the force is dependent of charge, which can vary rather independently of mass (not actually, but for the purposes of the tool, it does.)
Montec
Hello Pan, et al.

I agree that there must be more force being applied the more massive object. But let us say that the mass of an object is caused by a "widget". Each "widget" has the same inertia and reacts the same to gravity. Therefore, if more "widgets" can be collected in a smaller volume then that volume will have more inertia as well as having more gravitational force being applied to it. The gravitational force per "widget" is the same under the same gravitational field strength. Now this hypothetical "widget" may or may not be associated with the , as yet to be found, higgs particle/field. In any case the energy/momentum affecting the "widget"comes from the gravity field generated by the masses involved. So density does not play a part in gravity other than to allow more "widgets" per unit volume.

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