I can understand that it's hard to come to terms with the fact that just perhaps, the gravitational constant may NOT be an actual
constant created by nature but one that was artificially introduced to make a particular equation work and produce the "right" sort of
answers.
Tauristicus, I have great respect for your contributions here on ATS, but I am disappointed at your attitude on this thread. I concede that my
disappointment has no effect on the validity of your claims, nor my or any other criticisms of your OP, But.....
There is no need to imply that any disagreement to your thoughts is merely based in some kind of fear at being unable to come to any terms regarding
being "wrong".
Originally posted by tauristercus
However, looking at my alternative equation of
there is no hidden or disguised gravitational constant there at all ... and in fact there's no need for it whatsoever as the equation (when
multiplied by the mass of the orbiting body) automatically produces results that are already in units of force and therefore doesn't need to be
"massaged" as does Newton's.
You use centripetal acceleration in your reasoning and your equation, do you not?
This is an effect of centripetal force, driven by gravity, including the gravitational constant.
So Yes, there is. It is the constants you mention in your OP, when you substitute 6 into 5. That being Velocity and Radius, both are driven by Gravity
and contain the value G expressed in your equation.
The velocity(which we know is variable) and elliptical orbits that Kepler noted, show the Force acting to generate these two constants, and include
the G constant. These two constants of velocity and radius are not independent of the system driving it, but consequences of it and expression of
these forces.
Mathematically speaking, the numbers match because you are merely describing the forces as the constants of Centripetal acceleration in masses.
A great way to settle this, I guess, is if you would provide ATS with a formula for calculating optimum altitude for Geostationary orbits in
satellites, without using the gravitational constant or even the geocentric gravitational constant.
My equation ONLY uses an integer (4), pi, a distance (r) and the value of K uses only a distance and a time. There is no way to
derive a gravitational constant or even to hide one using only distance and time.
Like you say, you only need use the interger, pi and K which is its velocity(orbit time) and its
radius......BUT you don't know the radius,
because you actually need to include certain forces(including the G constant), in order to derive an altitude. An altitude which will then become your
radius, that your formula is actually dependent on. This presents somewhat of a paradox.
Once again, I offer my apologies well in advance, if I have misunderstood your posts.