An Invalidation of Newtonian Mechanics

An Invalidation of Newtonian Mechanics is Presented Below.

Newtonian Orbital Mechanics requires that to calculate the circular orbit of a planet, the centrifugal and centripetal forces must balance. A logical analysis is performed applying the Newtonian equations used to determine a circular orbit. The analysis will show that Newtonian physics of orbits is logically invalid.

 1) gravity force, F= GmM/r², which is described in terms of m as 

1b) m= Fr²/(GM)

Let m= f(r,F,G,M)

m is dependent upon r,F,G and M.

Which is stated as If m, then r and F and G and M. (True)

If 1b is true, then all of it's members are true.

Then in accord with the logical law of conjunctions -

If m then r (True)
If m then F (True)
If m then G (True)
If m then M (True)

2b) r = mv²/F

Let r = f(m,v,F)

r is dependent upon m, v, and F.

Then logically - If r then m and v and F. (True)

Then in accord with the logical law of conjunctions -

If r then m (True)
If r then v, (True)

which may be reversed as

If v then r (True)
If r then F (True)

And because r is common, then

If m then v (True)
If v then m (True)

3) v = (GM/r)^1/2

v= f(G,M,r)

v is dependent upon G, M, and r.

Therefore,

Then if v then G and M and r (True)

Then in accord with the logical law of conjunctions -

If v then G (True)
If v then M (True)
If v then r (True)

But from 2b) above –

If v then m. (True)

But 3) excludes m which infers

If v then not m, for m is excluded from formula 3)

And according to the law of conjunction the above statement is reversible -

If not m then v. (True)

Then syllogistically 

If m then r. (True)
If r then v. (True)
Therefore not m then v. (True)

All lines are true, but the syllogism is invalid. Hence, Newtonian mechanics is logically invalid.

JM