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After so many questions about Twins Paradox and Universe Frame of Reference, I'd like to know about Lorentz and Doppler. First.

Here V is ##\sqrt{0.75}## ≈ 86.60%. If we put V in Lorentz Transformation formula as speed, we'll have Gamma = 2.

Okay here's the question.

Two probes A and B.

Clocks are synchorized.

Distance is 100 Ly.

Each year they're sending digital signal, containing their respective time.

A will send A0, A1, A2, A3 for each respective year.

B also send B0, B1, B2,... each year.

Signal from B is always late for 100 years

So each year A will receive:

Code (Text):Signal A Time Interval

B0 100.00

B1 101.00 1.00 year

B2 102.00 1.00 year

..

..

B98 198.00

B99 199.00 1.00 year

B100 200.00 1.00 year

Is this true?

When B clock (and A clock) shows 100 year, B ignites its rocket RIGHT AFTER B sents B100. Catapulted at 86% c then the rocket stops, leaving B moves steadily at 86% c to the 'west', heading toward A

B will reach A at 115.4701 years.

Because ##\gamma = 2##, then B will reach A according to B clock for 57.7350 years.

When B arrive, A clock will read 115.4701

Is this true?

How will BPICK UPsignal from A?

From where B stays and A1 there's 1 ly

B travels at V_{b}

V_{b}.t + ct = 1 ly, if V_{b}is relative to c, then c = 1

V_{b}.t + t = 1

##t = \frac{1}{1+V_b}/\gamma##

t = 0.27

Is this true?

Code (Text):Signal B Time Interval

A0 100.00

A1 100.27 0.27

A2 100.54 0.27

..

..

A212 156.81 0.27

A213 157.07 0.27

A214 157.34 0.27

A215 157.61 0.27 B meets A

How will A receive signal from B?

B is still sending signal.

Signal B101 is not sent 100 lys from A because B is moving.

Signal B101 is sent at V_{b}.t distance

Signal B101should besent at (100-0.86) ly from A. Because ##\gamma = 2##, so B101 is sent at 98.27 ly from A.Is this true?

B01 will be picked by A after 102 years, not 101 years, because 1 year for B is 2 years for A

So B101 will be received by A when T_{a}is 102 + 98.27 = 200.27.Is this true?

Code (Text):Signal A Time Interval

B0 100.00 when A received B0, A still doesn't know that B has

already traveled.

B1 101.00 1.00 year A still doesn't know that B has moved

B2 102.00 1.00

..

..

B98 198.00

B99 199.00 1.00 Still doesn't know

B100 200.00 1.00 Stil doesn't know

B101 200.27 0.27 Suddenly A begins receiving signals at 0.27

years interval

B102 200.54 0.27 Is this true?

B103 200.80 0.27

..

..

B155 214.74 0.27

B156 215.01 0.27

B157 215.27 0.27 B meets A

Is the table above is true?

The difference with A scenario is that the instance B ignites its rocket, the time interval for signal receiving is 0.27. Whlie A has to wait for 200 years to have 0.27 interval.

Is this true?

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# Lorentz and Doppler and signal pick up

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