That pretty much sums it up. Fednis48 doesn't know much about gravitational physics. Not even Newtons model. Not even the consequences of Newtons First Law Of Motion. Pretty much nothing. I think you've ferreted out another crank. His attempt to talk down to you is pathetic nonsense.
I'm inclined to link him to the Sock Puppet Army of Zealots (SPAZ) attackers, but that's inferred by a a dozen or so things he posted. It was strange that RJBerry summoned hum like a genie from a lamp, then he came in quick to denounce the science, by putting up some rather moronic math which vaguely reminded me of some of the cranks you & I have taken to task before. And he was quick to heap lavish praises on the hearsay evidence that tashja kept offering in the other thread. I think it was Declan Lunny who posted the remark that grabbed me--that the good professor had referred to Sgt A* as a "massive star", as if tashja (or whoever fabricated the email) was assuming that Sagittarius A-star is actually a star!
The SPAZ attackers are keenly interested in sowing seeds of doubt and dissention among the purveyors of science, as a scheme to shore up creationism; as if to say 'Look we can't rely on radioactive dating since there is this other theory we call
the coordinate speed of light and then there is serious doubt about the Big Bang since it's tied to the Big Crunch which is tied to black holes --
and now we see reason to even doubt the existence of black holes. . . ' (etc.)
I know you know all of this but I'm mentioning it again for the other readers who may be undecided or unaware about the extent of SPAZmodics.
I haven't been keeping up with the posts here in general -- just responding to replies I get -- so I'm not aware of the consensus of the good readers here who have been immunized against SPAZms of their own by working to develop their skills. So I hope I'm not repeating anything already posted when I post the following analysis but it might interest you.
RJBeery said:
Additionally, me making an error in the analysis is inconsequential to the underlying point of the OP...unless you can make the fall times equal for objects of varying masses; that's a feat which would be quite impressive indeed!
Let me begin by noting that the Earth is not exactly inertial, since the centripetal accelerations due to diurnal rotation and annual orbits contribute a little. But it's around 0.3 % the magnitude of acceleration due to gravity, so no one usually cares. We ignore it as negligible, and we usually treat the Earth as an inertial reference frame for all applications like this.
This thread purports to present an issue in gravity, but it's actually an issue in Galilean relativity. Let me establish what that means:
1. The Earth-centered observer sees
$$\\ F\quad =\quad \frac { G{ m }_{ ⊕ }{ m }_{ 0 } }{ { \left\| r \right\| }^{ 2 } } (-\hat { r } )\quad =\quad { m }_{ 0 }g\quad ,\quad g\quad =\quad \frac { G{ m }_{ ⊕ } }{ { \left\| r \right\| }^{ 2 } } (-\hat { r } )\\ \\ h\quad =\quad \frac { 1 }{ 2 } \left\| g \right\| { t }_{ 0 }^{ 2 }\quad ,\quad \quad { t }_{ 0 }\quad =\quad \left| \sqrt { \frac { 2h }{ \left\| g \right\| } } \right| \\ $$
And all is good and well. In a nutshell, this is not simply a problem in mechanics, but in vector mechanics. Those vectors are not portable across a change of reference frame without the required forward and inverse transformations.
2. A faerie riding on the falling object sees exactly the same thing, in reverse. As far as she knows, the Earth is falling on her, and the impact is also at $${ t }_{ 0 }$$.
3. At the OP you pick a third arbitrary reference frame. You liked this idea because you noticed that from this POV you can detect motion in both the Earth and the object. Without asking for help from the skilled readers, you quickly concluded the following: both objects are in motion, therefore the impact will be sooner than Newton says, therefore Galileo must be wrong. And of course by this you really mean Newton must be wrong.
4. A flurry of objections were raised. At some point I suggested that you need to choose a reference frame. You chose the center of mass. What does that mean? It means we want to know the radial coordinate -- on the radial extending from the center of the Earth out to the object as it falls -- satisfying the following:
$$
{ r }_{ c.m. }\quad =\quad \frac { \sum _{ i=1 }^{ N }{ { r }_{ i }{ m }_{ i } } }{ { m }_{ \oplus }+{ m }_{ 0 } } $$
where N = number of particles in the earth + object system, and $${ m }_{ i }$$ is the mass of the ith particle, including all the particles in the falling object. This is no simple task for you to figure out. And BTW it's very near the center of the Earth -- dead on the c.m. of the Earth when the falling object lands.
5. After the formula is in place which describes the origin of the coordinate system as a function of time, you need to construct the transformation that maps values in your system to values in Galileo's frame. Galileo's
r maps to RJ-space according to the transformation
r' = T[
r(t)]. This is going to be messy, and it requires experience in calculus which as far as I can tell is not your forte.
6. Once you define T[∙], you will discover [or you will have to be led to that trough to drink -- whether you do is highly dubious] -- that T[∙] ≠
I. Once that dawns on you -- if that is achievable in the near future -- you would have to admit that you were mistaken. You didn't understand that you needed to compute the time of impact using
r' = T[
r] and
g' = T[
g]. Once you do this, you will get the exact same results as Galileo did, and as the faerie did. But I doubt that you can pull that off, and I doubt you will want to attempt it since it will prove you wrong.
But this is your chance to come clean if you're not actually part of the SPAZ attack, or harboring some unrelated reason for attacking science.
] need to realise that forums such as this are the only outlet these people have.....