Marecki on 14/10/2007 at 03:18

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Yes, that was my point - I take it you haven't followed my exchange with RocketMan too closely, otherwise I feel you would have figured out I was "picking on him" (well, not really ;) ) for not having clarified he was talking about motion in vacuum.

RocketMan on 14/10/2007 at 20:16

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The helicopter thing just baffles me....I don't know who said it shouldn't be possible but from my education, I understand it to work the same way fixed wing aircraft work, except the airfoil is rotating and the angle of attack changes with radius due to the changing Reynold's number. Not much mystery there.

I've heard about the bumble bee thing....I think it was in that movie "flight of the phoenix" but my aero prof said that since insects are all flying in the laminar fluid regime, they are able to flap their wings at a special frequency causing them to shed vortices behind them that actually boosts the propulsion that they get for a given expenditure of energy. I forget the dude's name that discovered it but this special frequency exists a lot of places in nature, including birds and allows them to fly very efficiently given their mass and cross section.

To get a visual idea of what I'm saying, recall that when you swim in a pool, you do not kick furiously because it gets you nowhere fast. You also don't kick sluggishly because that doesn't move enough water to do anything. There's a particular learned frequency that most people zero in on when they learn to swim as it gets them the most bang for the buck. This also has to do with vortex shedding.

RocketMan on 15/10/2007 at 20:03

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can't picture the spoon thing unfortunately...

With regards to the big bang, the universe may expand but the rate of change of expansion can still be decreasing. In other words gravity is always acting between matter, slowing down the matter as it receeds and expands but until the universe stops expanding, the gravity can only reduce the rate of expansion, not the direction of expansion itself. Its like when you throw a ball up in the air. The ball goes up until it reaches its apogee so the velocity vector is always up (until then) but gravity is slowing the ascent the whole time.

With the universe, the problem is that as the universe expands, the distance between particles within it also increases and since gravitational force is a function of 1/r^2, the larger the distance the quadratically weaker the gravity. So, is the universe slowing faster than the weakening of gravity. That is, does the rate of change of expansion not decrease quickly enough (due to the weakening of gravity) to bring the velocity vector of receeding particles to 0 (and then - ) Hope that's clear.

RocketMan on 15/10/2007 at 23:51

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No, you are correct about that.....but its sort of a relativity scenario. If 2 objects see the space between them increase, whether this is due to motion of an object resulting from a force or whether it is due to the expansion of space itself, the scenarios are equivalent in that there is relative motion between the 2 objects. This makes the metric "velocity" meaningful, regardless of what is causing it. All inertial frames of reference are equivalent anyway via Einstein so even if you gave one of 2 objects a kick, after that kick its in an inertial frame of reference so its relative velocity can be thought of the same way as that carried by an object that was not kicked, but is being separated from its partner by expanding space.

*Zaccheus* on 16/10/2007 at 17:08

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dvrabel, I use a simple iterative process based on A = M / D*D where A is acceleration, M is mass, and D is distance. There's currently no numerical error correction in my code, I was quite surprised that 64bit floating point numbers are accurate enough to get a good approximation.

RocketMan, I still don't understand the comparison with a ball being thrown in the air: Such a ball is accelerated once (when you throw/kick it), and then gravity constantly accelerates the ball towards the earth, so the ball first slows down and then reverses direction.

However, if all objects continue to be moved apart by the expansion of the universe, then we are not talking about an initial 'kick' but an ongoing moving apart of matter which gravity is fighting against. As matter moves apart, gravity should be increasingly loosing that battle, not starting to be winning it.