On 21/02/2016 08:52, Peter Riedt wrote:
On Sunday, February 21, 2016 at 4:26:41 PM UTC+8, Poutnik wrote:
Dne 21/02/2016 v 03:23 Peter Riedt napsal(a):



Kepler's third law (from the early 1600s) gave us the relative
sizes of the orbits. T^2 ~ a^3

Isaac Newton's version of Kepler's third law
T^2 == (2π)^2 a^3 / G(M+m)

where (2π)^2/G is just a constant of proportionality.

The fundamental point it that Newton proved that the solar system
movements were the result of an inverse square law. It is arguable that
Hooke guessed this mentioned it to Newton who had the mathematical
techniques to prove it. But either way they added a lot to
understanding. Kepler's laws were empirical derived from observations
Newtons was derived theoretically from a set of starting axioms.

Orbits of earth and solar system satellites today are described by
their Keplerian Elements.
https://en.wikipedia.org/wiki/Orbital_elements

Science not only grasped the significance of Kepler's third law,
but make use of it 24/7.

The point is, Kepler laws are laws just by name,
being empirical rules as consequence of the Newton gravity law.

Not the otherwise.

Newton copied his law from Kepler, not the other way.

No.

Newton explained it in terms that we use in classical mechanics as
conservation of energy and conservation of angular momentum.

There are analogous conserved quantities in GR too.

It should be no surprise that each successive improvementof a theory
contains all previous models as a limiting subset of the new model.

--
Regards,
Martin Brown