Terminal velocity as defined is translation along \(c_1\),Terminal Velocity = \(c_1\)
Not \(c_2\) which is circular speed, changing direction all the time. Nor it is \(c\) the instantaneous resultant of \(c_1\) and \(c_2\)
\(c^2=c^2_1+ c^2_2\)
Light speed will be \(c_1\). But terminal velocity as a limiting velocity, as a consequent of space density/viscosity then it should be \(c\). That is,
\(c^2\propto drag force\)
Terminal Velocity = \(c\) and
\(c>c_1\)
But \(c_1\) is the measured value, as such light speed is less than \(c\). By symmetry,
\(c_1=c_2\)
because moving in one direction is the same as moving in another in uniform space.
\(c^2=2c^2_1\)
\(c=\sqrt{2}c_1=\sqrt{2}.light speed\)
The actual terminal velocity of space is \(\sqrt{2}.light speed\). This is the velocity by which electrons orbit around the nucleus. This is also the velocity that prevents the atom from collapsing.
\(\cfrac{m_e.2c^2}{r_o}=\cfrac{q^2}{4\pi \varepsilon_o r^2_o}\) and
\(r_o=\cfrac{q^2}{8\pi \varepsilon_o{m_ec^2}}<r_{n}\)
where \(r_{n}\) is the radius of the positive nucleus.
In these expressions, \(c^2\) has been replaced with \(2c^2\) and in the case for \(c\), to be replaced by \(\sqrt{2}c\). The speed limit for charge particles in general is \(\sqrt{2}c\).
