in order for the horizon effect to keep parallel in both systems, then Light must follow a circular path for very obvious reasons.
They aren't obvious to me, so why don't you explain yourself?
the path of a circle is governed by x(t)=rcost y(t)=rsint. If light travels at c,
then c=sqrt(x'(t)2+y'(t)2), or in other words, light is going in the path of a cir circle at uniform speed.
lol no
You've used the derivatives of x(t) and y(t) in that equation, so you've said nothing about the original functions themselves. Also, protip: c cos t and c sin t aren't the only two expressions whose squares add to c2. I'll leave it as an exercise for you to come up with at least one very simple alternative.
Yet unfortunately for bendy light, if it produces this effect it should also produce other effects such as shifting of star positions proportional to altitude, which does not happen.
Bendy light now disproved 9001 times.
You haven't yet explained why this should be the case, so your proof has null value.
*sigh*
http://www.theflatearthsociety.org/forum/index.php?topic=22317.0remember the curvature vs. bendy light thing?
well the solution is that light bends in a circle:

This ensures that all data fits with the idea that light bends upward on the flat earth.
Lol,yes
the original equation was to show the path.
the derivatives where there to show constant speed.
Which Parsifail,
x(t)=rcos(t) and y(t)=rsin(t), are dummy equations, there to show you the path,
c
2=x'(t)
2+y'(t)
2 is there to show CONSTANT speed.
protip:lrn2higschool mathematicals.
now with information of the path
and info of the vel,
we obtain
x(t)=rcos(tc/r)
y(t)=rsin(tc/r)
x'(t)=-c*sin(tc/r) magnetude of velocity =c
y'(t)=c*cos(tc/r)
x''(t)=-c
2/r *cos(tc/r) magnetude of acceleration=c
2/r
y''(t)=-c
2/r *sin(tc/r)
now dot x'(t),y'(t) with x''(t),y''(t):
-c*sin(tc/r)* -c
2/r *cos(tc/r) + c*cos(tc/r))*-c
2/r *sin(tc/r)=0
to find that acceleration is perpendicular to velocity, meaning that it is along the radius of the circle.
and since f
x,f
y=m*x"(t),y"(t)
the force to make light bend in a circle is centripetal, explain that plz