I Why does Kepler's Third Law exist?

[sophiecentaur]

is the specific relationship between orbital relationships defined by science [then as defined by Kepler, not forgetting ever Newton, or is it just the way it is?

Everything in our lives is "the way it is". Science attempts to apply models to help us predict what will happen or explain what has happened in terms of those models. That's all. You will appreciate that most of those models involve Maths and Maths is a lot more reliable than arm waving.
Hopefully you will get more familiar and competent with Maths or your personal picture of Science will be limited to stuff that Science Journalists provide.

 

[Martyn Arthur]

erm... reference "the gravitational force is proportional to mass, as is acceleration, according to Newton's laws of gravity and motion respectively. The motion of bodies under the force of gravity, whether parabolic projectile motion or elliptical orbits, is therefore independent of the mass of the body."
Given the standard equation F = G(m1m2)/R^2 how can the mass of a body under the force of gravity be irrelevant?
An increase in the mass of a body orbiting the sun would change the relationship.

 

[sophiecentaur]

erm... reference "the gravitational force is proportional to mass, as is acceleration, according to Newton's laws of gravity and motion respectively. The motion of bodies under the force of gravity, whether parabolic projectile motion or elliptical orbits, is therefore independent of the mass of the body."
Given the standard equation F = G(m1m2)/R^2 how can the mass of a body under the force of gravity be irrelevant?
An increase in the mass of a body orbiting the sun would change the relationship.

You would normally read, along with this statement that it only applies for small bodies on much larger ones - as with artillery shells and the Earth or the Earth orbiting the Sun. It's valid for so many situations that people can be a bit sloppy about using the caveat.
Your version of the Force equation is more like the correct one. It's only correct when the bodies can be considered to be point masses.

 

[Martyn Arthur]

That's fair thanks, now reading well ahead into my course I read that the K3 relationship is defined as a consequence of the gravitational effect on orbiting bodies, which seems to tie in with my understanding that K3 demonstrates a factual situation, a relationship that is a consequence of the gravitational consequence of the masses of bodies orbiting, here the sun.
Please I just want to understand, is it the case that K3 demonstrates that the orbital periods of bodies orbiting the sun are a direct consequence of the relationship between the masses of those bodies and the mass of the sun.
Hence there is a rule that would extend to all bodies with an orbital relationship.
Hence if the mutual gravitational force is too weak the orbiting body exits the orbit, if too great it crashes into the central object, else it occupies an orbital period commensurate with the model prescribed by K3.

 

[sophiecentaur]

Sorry but you are demonstrating that , without the Maths as a model, one can drop into a black hole at any minute.
If you gave the Sun twice the mass, K3 would still apply - just with reduced orbital radii. The ‘equation’ is the only way to communicate something like this. You keep demonstrate this. Wait till you have the Maths and it will all be clear.

 

[Martyn Arthur]

Guys, I thought this forum was for anyone seeking to understand.
If you were giving an introductory talk to a class of 14-year-olds in a school how would you explain things, or having regard to a couple (just a couple of earlier comments) is this below this forum?
My undergraduate stating second-year course says the relationship is essentially due to the effect of gravitational forces why do you find it so impossible to quantify the core figures, or indeed are they not known?

 

[sophiecentaur]

What “core figures’” are unidentified? We know G and the mass of the Sun. Afaik, you can build a pretty good solar system. Taking each planet on its own and its orbit radius (assuming circular).
You need to improve that for elliptical orbits and further by including planetary interactions.
Or do you want a model that starts with primeval disc of gas and dust and yields the present structure? There are too many variables for that. Also, all exoplanet systems are different. So they where do you want to go with this? The answer is not 42. ;-)

 

[Doc Al]

Enough already. This thread is done.