By Musa Daji Abdullshi
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Extra resources for Electrodynamics for a Particle Accelerated to the Speed of Light with Constant Mass
1) with O as the fixed centre of revolution. For q > 0 < 1 and α < 1, the orbit is an unclosed (aperiodic) ellipse whose major axis (line joining the points of farthest of the particles) rotates about an axis through the centre, perpendicular to the orbital plane. A particle completes a cycle of 2π/α radians while the major axis goes through 2π/α – 2π radians. The exponential decay factor, exp(–qψ), is due to energy radiation. As a result of radiation of energy, after a great number of revolutions in the angle ψ, (A/n) exp(–qψ), the transient, decreases to zero and the radius increases to the steady state nL2/mχ, as long as q is greater than 26 zero.
2. Two equal and oppositely charged particles at P and S having electronic charges –e and +e and the same mass nm (n being an integer and m is the electronic mass) revolving anticlockwise in angle ψ, under mutual attraction, in an orbit of radius r, round the centre of revolution at O. 20) vp = vs = − The two particles, of equal mass, move with the same angular velocity, in a plane orbit, but with relative linear velocity in the radial direction. 26) 1+ = 2 −r 2 nmr c dt dt dt where κ = e2/16πεo.
53) fn λn 2 This ratio is related to the splitting, spread or “fine structure” of a spectral line due to frequency of radiation from the hydrogen atom. The radiation is not of precise frequencies, but has a spread around the frequency of revolution of a particle in the nth stable orbit. 7 Conclusion The orbit of revolution of a neutral body, round a gravitational force of attraction, is a closed ellipse, without radiation of energy. Such a periodic motion may continue ad infinitum. On the other hand, a charged particle revolves in an unclosed (aperiodic) elliptic orbit, with emission of radiation at the frequency of revolution, before settling into a stable circular orbit.