Posted on 06/23/2003 9:25:12 AM PDT by RightWhale
I am not a 1st year engineering student, but will I do?
Distance of the Earth to the center of the galaxy: about 30,000 light years
Total distance traveled for one rotation = Pi x D = 188,400 light years
Speed of light = 299,792,458 meters per second
There are 86400 seconds in one day with approximately 365.25 days per year giving us approximately 31,557,600 seconds/year.
So the distance of one light year is around 9.46 x 1015meters.
This gives us a total distance travel for one rotation of 1.78 x 1021meters.
Rotational period of the galaxy: 2.25 x 108 years.
This gives us about 8 x 1012meters traveled per year.
8 x 1012 divided by 365.24 = approximately 2.2 x 1010 meters/day or 912,600 kilometers per hour.
This then is approximately 565,837 miles per hour or 157 miles per second.
Times 8.3 minutes = 78,186 miles (for some reason I had it in my head that the Sun traveled 270,000 miles in the time that it took Light to reach Earth from the Sun, bizarre).
So the question is whether the Earth rotates in an orbital plane around where the Sun was 8.3 minutes ago, which will always be 78,186 miles away from its current position (if your math is valid), or whether the Earth orbit is centered more closely to the actual position of the Sun at the present time.
And that answer will tell us the speed of Gravity.
Remember it takes one year for the earth to orbit the sun once. Visualize it as a combined system (earth/sun) orbiting about a common point of mass moving as a whole relative to the center of the galaxy. Don't forget the galaxy is also moving linearly as a "whole" as well.
That is just too cool! :-)
A poor analogy, but should give you an idea, is you dropping a ball on a moving train. The ball falls strait down (relative to you) because it is moving horizontally at the same velocity the train is.
It takes Light 8.3 minutes to reach the Earth. If Gravity travels as slow as Light, then it takes 8.3 minutes for Gravity to reach the Earth.
The Gravity wave is going to pull the Earth towards the center of where the Sun was when the Gravity wave left the Sun.
If that was 8.3 minutes ago, then the Earth will be orbiting, at any given moment, around a center point that is 78 thousand miles away from where the Sun is at the present if Gravity really is as slow as Light (because that's how far the Sun will have traveled in those 8.3 minutes). Gravity and the Earth aren't predicting the *future*, after all, but rather reacting to current and past events.
And yes, the Earth is *also* traveling those same 78,000 miles in those 8.3 minutes, but the angle of the plane of the Earth's orbit is still going to be centered on where the Sun was when Gravity left it.
And this angle will be different (perhaps only slightly, perhaps by a large amount, depending upon the speed of Graivty) the further a planet resides from the Sun.
Or perhaps there is no significant delay. Hmmm, rather than having nature "conspire", perhaps Newton was basically correct that Gravity (who knows, possibly even the electromagentic field effect, too) propagated at near instantaneous speeds, say, the Speed of Light squared.
Where to start. Hmmmm.....Here is a really good explanation:
http://zebu.uoregon.edu/~imamura/talks/gravity_waves/gw_intro.html
Nope! Go read both links I provided.
ROFL! Oh yea!
Come on, let's simply examine observable phenomena. The Earth orbits the Sun of either 8.3 minutes ago or the Sun of right now (or something in between).
Where ever that point resides, from the Sun of 8.3 minutes up to the Sun of this very moment, will let us calculate the speed of Gravity (unless Gravity can somehow be slow *AND* predict where the Sun will be in 8.3 minutes).
Consider two bodies -- call them A and B -- held in orbit by either electrical or gravitational attraction. As long as the force on A points directly towards B and vice versa, a stable orbit is possible. If the force on A points instead towards the retarded (propagation-time-delayed) position of B, on the other hand, the effect is to add a new component of force in the direction of A's motion, causing instability of the orbit. This instability, in turn, leads to a change in the mechanical angular momentum of the A-B system. But total angular momentum is conserved, so this change can only occur if some of the angular momentum of the A-B system is carried away by electromagnetic or gravitational radiation.
Now, in electrodynamics, a charge moving at a constant velocity does not radiate. (Technically, the lowest order radiation is dipole radiation, which depends on the acceleration.) So to the extent that that A's motion can be approximated as motion at a constant velocity, A cannot lose angular momentum. For the theory to be consistent, there must therefore be compensating terms that partially cancel the instability of the orbit caused by retardation. This is exactly what happens; a calculation shows that the force on A points not towards B's retarded position, but towards B's "linearly extrapolated" retarded position. Similarly, in general relativity, a mass moving at a constant acceleration does not radiate (the lowest order radiation is quadrupole), so for consistency, an even more complete cancellation of the effect of retardation must occur. This is exactly what one finds when one solves the equations of motion in general relativity.
The first part in BOLD precisely agrees with what I've been saying all along on this thread, and the second bolded part does not disagree with what I've been saying, as it is an unknown at this point.
In other words, up to this point your source *agrees* with me.
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