posted on Oct, 8 2010 @ 01:07 AM
There really is a secret about astronomy
and it is hidden in Kepler by Newton,
so well done on the OP, but it's not
as nefarious as it seems, and it
just means you are past the
'intro to astronomy' phase
where you learn words
and ready to do so
actual work.
First let me do some damage control on
the intent of the OP. Cause I don't want to be dismissive.
But here is the one line punch line in advance, then I'll speak
to what I like about the post.
Flippant one line post: "Great, instead of solving the 3 body problem,
you have reduced the standard two body model into a one body model."
Yeah, heh, so ... what I dig about the OP.
Yes!!!!! the gravitational constant can be tinkered with.
I could increase it by 50% and decrease the mass of the planets by the same,
and get the exact same results. The earth, Venus, mars, everything could be much much
lighter than we have been lead to believe. Of course that's why science likes to test things with
empirical evidence. Like the fact that a 1kg stone on earth weights ... 1kg. I suppose we could call a half kilo the new 1kg and then yes... we
would have to adjust the gravitational constant.
The nice thing is that the entire classical gravity formula can be tuned in with a finer and finer
gravitational constant as our technology to get precise weights increases.
This could be one reason the formula is still alive.
Also, Kepler. ZOMG well done. Yes yes, he is the key.
Newton is Kepler in a really well made suit from London.
But everything is extracted from Keplers equal time equal area law.
I mean everything. Gravity, relativity, space time, even quantum mechanics.
See Keplers law allowed us to measure objects by just looking at them.
The precise implications of the application of this finding
are just starting to be realized. Newton did well
explaining this in a more technical way for engineers
so they could start applying it right away.
Einstein's special theory of relativity
is nothing more than a philosophical way
of explaining the parameters of Keplers laws,
and their implications for the universe.
In a nut shell what he said was that
energy defines geometry. I feel
he learned this by living in
Keplers world.
Alright so the bad part.
Kepler defined the orbit.
Newton figured out how to weigh the planets and moons from this definition.
And Einstein figured out how to weigh light.
But the persistent remaining problem is called the 3 body problem.
With the standard Newton equation we can figure out the orbit of earth around the sun, or even the moon around the earth. But we can't do all three
concurrently. Each one has to be figured separately and then results combined. There is a formula to do 3 bodies concurrently but it is very complex
and hardly worth it. Especially when one considers there are upwards of a hundred planet sized objects in the solar system. All acting on each other
simultaneously. Perturbations can become a recursive set of never ending adjustments, so much so that the closer one gets the longer it takes to
calculate so that eventually it will take longer to calculate their positions than it takes the planets to actually move.
Reducing this to a one body problem isn't actually useful for more than inventing a beginners set of tools. In the one body math presented above all
the objects are assumed to orbit the sun. Well, what if the sun has the mass of a spec of dust... with the one body math, we get the same orbit. A
whole new set would have to generated for each object that has a moon.
I am excited to see someone capable of lending their intellect to solving the three body problem. And I think a completely radical approach coming
from zero assumptions (like the OP) is right thing to do. Perhaps a set of single body formulas for each planet, and one for the Sun, and then there
is a way to run all those concurrently, and then do a pass making adjustments for perturbations, will give more precise results than the current
models.
/Salute
David Grouchy