More Transverse Combinations 1

Copyright Carl Janssen 2025

More Transverse Combinations 1

Abbreviations used for Variable names were defined in previous articles, I may rewrite or copy and paste them later when I have time

The difference between time of reception and time of emission is the same regardless of the chosen time of reception or emission for the middle signal but a particular time is chosen because I think choosing that time will make some aspects of doing the calculations easier.  Other times could be chosen but should give the same end results for the period of reception as a function of the period of emission when the constant velocities of the source and receiver and the constant Y value distance are held the same

Direction between source and receiver is perpendicular to direction of movement of source and or receiver when

1 When Signal is received at receiver

A Source and Receiver are both moving

B Source is stationary and receiver is moving

C Source is moving and receiver is stationary

Chosen Middle time of Reception is 0.  At a time of 0 source is located at ( 0, Y) and receiver is located at ( 0, 0 )

Xe = Ve * T

Ye = Y

Xr = Vr * T

Yr = 0

MTr = 0

( MXr - MXe ) ^ 2 + ( MYr - MYe ) ^ 2 = c ^ 2 * ( MTr - MTe ) ^ 2

( Vr * MTr - Ve * MTe ) ^ 2 + Y ^ 2 = c ^ 2 * ( MTr - MTe ) ^ 2

( Vr * 0 - Ve * MTe ) ^ 2 + Y ^ 2 = c ^ 2 * ( 0 - MTe ) ^ 2

Y ^2 + Ve ^ 2 * MTe ^ 2 = c ^ 2 * MTe ^ 2

( c ^ 2 - Ve ^ 2 ) * MTe ^ 2 = Y ^ 2

MTe = Y ^ 2 / ( c ^ 2 - Ve ^ 2 )

( RXr - RXe ) ^ 2 + Y ^ 2 = c ^ 2 * ( RTr - RTe ) ^ 2

RXr = Vr * RTr

RXe = Ve * RTe

RTe = MTe + Pe

Plug in and solve for RTr using quadratic equation choose only one out of plus or minus based on what is appropriate criteria for this was discussed in a previous article

Do likewise to calculate LTr only using LTe = MTe - Pe

Once RTr and LTR are calculated

Symmetric Period multiplier

SPm = ( RTr - LTr ) / ( 2 * Pe )

RPm = ( RTr - MTr ) / Pe

LPM = ( MTr - LTr ) / Pe

Compare SPm, RPm and LPm with functions of Lorentz Factors Gamma and Alpha and get percent error for various combinations of Vr, Ve, Pe and Y.  Might use absolute value of Vr - Ve in place of V when comparing with V that is plugged into Lorentz Factor to solve for Lorentz Factor

2 When Signal is emitted at source

A Source and Receiver are both moving

B Source is stationary and receiver is moving

C Source is moving and receiver is stationary

Chosen Middle time of Emission is 0.  At a time of 0 source is located at ( 0, Y) and receiver is located at ( 0, 0 )

Xe = Ve * T

Ye = Y

Xr = Vr * T

Yr = 0

( MXr - MXe ) ^ 2 + ( MYr - MYe ) ^ 2 = c ^ 2 * ( MTr - MTe ) ^ 2

( Vr * MTr - Ve * MTe ) ^ 2 + Y ^ 2 = c ^ 2 * ( MTr - MTe ) ^ 2

( Vr * MTr - Ve * 0 ) ^ 2 + Y ^ 2 = c ^ 2 * ( MTr - 0 ) ^ 2

follow a similar method to that above to get RTr and LTr and then period multipliers and then comparing period multipliers with Lorentz factors

Finish later

A lot of information from previous articles needs to be copied and pasted into this article or rewritten explaining the same concept as in previous articles with different words after calculations are done but calculations should be done first