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
23rd May 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 .....
rpenner
23rd May 2007 - 03:29 PM
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
23rd May 2007 - 05:31 PM
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.
Comments or discussion welcome.
Pan
23rd May 2007 - 07:00 PM
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
23rd May 2007 - 08:33 PM
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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