19. IMAGE AND
SOURCE AND THE 44TH BIT
Let’s see the topic “Image and
Source” here by going back to the
example in the 44th Bit and using real values. Let’s find where Image
Objects of planes are relative to the transmitter’s reference system at
the moment Source Objects of the planes reach the meeting line.
We will make use of Alice Equations for the calculation.
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Now
that we examined the event for an observer at the Signal Station (and
this observer can be a radar, as well), this time the signal
transmitter is the planes. The signal station is now in the position of
the signal receiver. In the equation above, let’s find the values of
numerator and denominator respectively:
The distance the OUTGOING
signal covers relative to the transmitter:
We know that the locations of Source Objects of planes are at the
meeting line. The distance between the meeting line and the Signal
Station gives us “the distance the OUTGOING signal covers relative to
the transmitter”.
Speed of the OUTGOING signal
relative to the transmitter:
We already calculated the signal speeds in the part “Byte Shift”. If
the signal goes from the Signal Station to the plane at the top at c+v
speed, the speed of the signal going to the signal station from the
plane is (c+v), as well. Similarly, the speed of the signal going to
the station for the plane at the bottom is (c-v). We already calculated
the signal speed. So, there is nothing unknown in the topic “speed of
the OUTGOING signal relative to the transmitter”.
Speed of the INCOMING signal
relative to the receiver: There is
no need to calculate it as it is always c.
The distance the INCOMING
signal covers relative to the receiver:
This is a value that we need to find. The coordinate value of the
emitted signal at relative to the receiver’s reference system gives the
distance at which it will see the image object. When we calculate this
value for both the planes, we find the locations of planes’ Image
Objects.
We see the
necessary calculation in the table below.
The values that
are found were placed beforehand while preparing the figure above.
| Description | Calculation Method | Value | Unit |
|---|---|---|---|
| Outgoing Signal Speeds According to the Transmitter | |||
| From the upper plane to the signal transmitter | c+v | 299793308 | m/s |
| From the lower plane to the signal transmitter | c-v | 299791608 | m/s |
| Incoming Signal Speeds According to the Receiver | |||
| Constant for all receivers | c | 299792458 | m/s |
| Outgoing Signal Path According to the Transmitter | |||
| Distance between the aircraft at the meeting line and the Transmitter Station | d0 | 500.000 | m |
| Incoming Signal Path According to the Receiver | |||
| Position of the image object of the upper plane | d1 = d0.c/(c+v) | 4999985824 | m |
| Position of the image object of the lower plane | d2 = d0.c/(c-v) | 500001,4177 | m |
Now,
let’s find which value for the distance of the Signal Station from them
the chief pilots in the cockpit will see when they look at the radar
screen.
Now that we know the locations
of the planes, the Signal Station, and
Image Objects of the planes, we can make use of the parallelogram
method. But we have a tiny problem. As the movements take place on the
X axis, how can we form the parallelogram? There is an easy way. Let’s
form the parallelograms first and then carry the Objects to the X axis.
After seeing the locations of objects on the X axis, we can show where
image objects of the Signal Station relative to the planes by making
use of the values in the table. We see these processes in the figure
below.
We get a good
result from here. The location of
the image object of an object can be at different locations relative to
different reference systems.