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Radar ranging and relativity

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  Radar ranging and relativity Richard Hertz <hertz778@gmail.com> - 2023-03-17 09:45 -0700
    Re: Radar ranging and relativity Richard Hertz <hertz778@gmail.com> - 2023-03-17 10:21 -0700
    Re: Radar ranging and relativity "Dono." <eggy20011951@gmail.com> - 2023-03-17 19:03 -0700
      Re: Radar ranging and relativity Richard Hertz <hertz778@gmail.com> - 2023-03-17 19:51 -0700
        Cretin Richard Hertz at work "Dono." <eggy20011951@gmail.com> - 2023-03-17 21:17 -0700
    Re: Radar ranging and relativity "Dono." <eggy20011951@gmail.com> - 2023-03-17 19:48 -0700
      Re: Radar ranging and relativity whodat <whodaat@void.nowgre.com> - 2023-03-17 22:02 -0500
    Re: Radar ranging and relativity Sylvia Else <sylvia@email.invalid> - 2023-03-18 14:01 +1100
      Re: Radar ranging and relativity Richard Hertz <hertz778@gmail.com> - 2023-03-17 20:12 -0700
        Re: Radar ranging and relativity whodat <whodaat@void.nowgre.com> - 2023-03-17 22:29 -0500
          Re: Radar ranging and relativity Richard Hertz <hertz778@gmail.com> - 2023-03-18 05:44 -0700
        Re: Radar ranging and relativity Sylvia Else <sylvia@email.invalid> - 2023-03-18 15:08 +1100
        Re: Radar ranging and relativity Volney <volney@invalid.invalid> - 2023-03-19 00:31 -0400
          Re: Radar ranging and relativity whodat <whodaat@void.nowgre.com> - 2023-03-18 23:49 -0500
          Re: Radar ranging and relativity Maciej Wozniak <maluwozniak@gmail.com> - 2023-03-19 00:20 -0700
    Re: Radar ranging and relativity "mitchr...@gmail.com" <mitchrae3323@gmail.com> - 2023-03-18 12:49 -0700
      Re: Radar ranging and relativity Richard Hertz <hertz778@gmail.com> - 2023-03-18 13:33 -0700
        Re: Radar ranging and relativity "Dono." <eggy20011951@gmail.com> - 2023-03-18 16:14 -0700
    Re: Radar ranging and relativity "Paul B. Andersen" <paul.b.andersen@paulba.no> - 2023-03-21 22:24 +0100

#604432 — Radar ranging and relativity

Why the popularized equation for radar ranging is:

R = 1/2 t c₀

https://www.radartutorial.eu/01.basics/Distance-determination.en.html

which is clearly wrong?

Being t the loop time for the reception of the EM pulse echo, actually

R = 1/2 t (c₀ - v)

being v the radial velocity between the target and the radar antenna,
positive is the target is moving away, and negative if it's coming closer.

CALCULATIONS

For time t = 0, the target is R meters far away, moving with speed v.

An EM pulse is periodically sent (every 1 msec).

To hit the target, the time involved is t₁, so that

c₀t₁ = R + vt₁ (the target is moving)

t₁ = R/(c₀ - v) 

Coming back from the new distance of the target, requires

 c₀t₂  = R + vt₁

R + vt₁ = R + vR/(c₀ - v) =  Rc₀/(c₀ - v), so

c₀t₂  = R + vt₁ = Rc₀/(c₀ - v)

t₂ = R/(c₀ - v) = t₁

t = t₁ + t₂ = 2R/(c₀ - v), hence

R = 1/2 t (c₀ - v) ≠ 1/2 t c₀ (the last expression is being taught in a radar course).

If the target is moving away, it takes MORE time to hit it than chasing it at c₀.

If the target is coming, radially, to the source, it takes LESS TIME to hit it.


Simplification or denial?

How is it about light speed c₀ and motion of bodies?


Read "The farce of physics", by Bryan G. Wallace. It's about the cover-up
of c ± v, when radar ranging the position of Mars by the military in the '60s.

He was "supressed" and "humilliated" as a subversive, ignorant crank.


 

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#604441

On Friday, March 17, 2023 at 1:45:57 PM UTC-3, Richard Hertz wrote:
> Why the popularized equation for radar ranging is: 
> 
> R = 1/2 t c₀ 
> 
> https://www.radartutorial.eu/01.basics/Distance-determination.en.html 
> 
> which is clearly wrong? 
> 
> Being t the loop time for the reception of the EM pulse echo, actually 
> 
> R = 1/2 t (c₀ - v) 
> 
> being v the radial velocity between the target and the radar antenna, 
> positive is the target is moving away, and negative if it's coming closer. 
> 
> CALCULATIONS 
> 
> For time t = 0, the target is R meters far away, moving with speed v. 
> 
> An EM pulse is periodically sent (every 1 msec). 
> 
> To hit the target, the time involved is t₁, so that 
> 
> c₀t₁ = R + vt₁ (the target is moving) 
> 
> t₁ = R/(c₀ - v) 
> 
> Coming back from the new distance of the target, requires 
> 
> c₀t₂ = R + vt₁ 
> 
> R + vt₁ = R + vR/(c₀ - v) = Rc₀/(c₀ - v), so 
> 
> c₀t₂ = R + vt₁ = Rc₀/(c₀ - v) 
> 
> t₂ = R/(c₀ - v) = t₁ 
> 
> t = t₁ + t₂ = 2R/(c₀ - v), hence 
> 
> R = 1/2 t (c₀ - v) ≠ 1/2 t c₀ (the last expression is being taught in a radar course). 
> 
> If the target is moving away, it takes MORE time to hit it than chasing it at c₀. 
> 
> If the target is coming, radially, to the source, it takes LESS TIME to hit it. 
> 
> 
> Simplification or denial? 
> 
> How is it about light speed c₀ and motion of bodies? 
> 
> 
> Read "The farce of physics", by Bryan G. Wallace. It's about the cover-up 
> of c ± v, when radar ranging the position of Mars by the military in the '60s. 
> 
> He was "supressed" and "humilliated" as a subversive, ignorant crank.

I'd enjoy watching how Lorentz transforms and motion relative to X frame of reference are introduced here.

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#604514

On Friday, March 17, 2023 at 9:45:57 AM UTC-7, Richard Hertz wrote:
> Why the popularized equation for radar ranging is: 
> 
> R = 1/2 t c₀ 
> 
> https://www.radartutorial.eu/01.basics/Distance-determination.en.html 
> 
> which is clearly wrong? 


It is not wrong, it is the formula used for target stationary wrt the radar source.

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#604527

On Friday, March 17, 2023 at 11:03:16 PM UTC-3, Dono. wrote:

<snip>

> It is not wrong, it is the formula used for target stationary wrt the radar source.

You are a special kind of retarded, but not a human one.

The radar source is stationary. Is the target which moves, imbecile. Radar 101, since 1936.

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#604537 — Cretin Richard Hertz at work

On Friday, March 17, 2023 at 7:51:55 PM UTC-7, Richard Hertz wrote:
> On Friday, March 17, 2023 at 11:03:16 PM UTC-3, Dono. wrote: 
> 
> <snip>
> > It is not wrong, it is the formula used for target stationary wrt the radar source.
>I am a special kind of retarded

Based on the answers that you received, I have to agree, you are retarded. The special kind, the odious kapo kind

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#604526

On Friday, March 17, 2023 at 9:45:57 AM UTC-7, Richard Hertz wrote:

> Read "The farce of physics", by Bryan G. Wallace.

Best Sunday comics. Better than yours. He was a crank, just like you. At this point, I suggest that you collect your imbecilities in a book. 

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#604529

On 3/17/2023 9:48 PM, Dono. wrote:
> On Friday, March 17, 2023 at 9:45:57 AM UTC-7, Richard Hertz wrote:
> 
>> Read "The farce of physics", by Bryan G. Wallace.
> 
> Best Sunday comics. Better than yours. He was a crank, just like you. At this point, I suggest that you collect your imbecilities in a book.

"What one fool can do, another can."

The only place I found this book available is at GoodReads
for $4.00. He wrote a second book that has no reviews either.

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#604528

On 18-Mar-23 3:45 am, Richard Hertz wrote:
> Why the popularized equation for radar ranging is:
> 
> R = 1/2 t c₀
> 
> https://www.radartutorial.eu/01.basics/Distance-determination.en.html

For a target, moving or otherwise, it gives the distance to the target 
at the point where the radar signal was reflected, which happens after 
half of the total transit time. The velocity of the target is irrelevant.

Sylvia.

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#604531

On Saturday, March 18, 2023 at 12:01:26 AM UTC-3, Sylvia Else wrote:
> On 18-Mar-23 3:45 am, Richard Hertz wrote: 
> > Why the popularized equation for radar ranging is: 
> > 
> > R = 1/2 t c₀ 
> > 
> > https://www.radartutorial.eu/01.basics/Distance-determination.en.html
> For a target, moving or otherwise, it gives the distance to the target 
> at the point where the radar signal was reflected, which happens after 
> half of the total transit time. The velocity of the target is irrelevant. 
> 
> Sylvia.

This is the basic theory for radar ranging, taught to kids in high school.

I wrote the OP in order to show the DISINFORMATION that plagues the web, being in this case from a "serious" site.

Since the 60s, radar ranging is complemented with Doppler measurement, in a single frequency swept pulse, and even
better techniques.

Since the 90s, phased array radars are used along with computes, to acquire targets in a 3D space with resolutions of meters.

Imagine a Patriot system trying to hit a 5,000 Km/hr incoming missile (or 20,000 Km/Hr for ICBM).

The real position is tracked in real time. No turning antennae anymore.

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#604532

On 3/17/2023 10:12 PM, Richard Hertz wrote:
> On Saturday, March 18, 2023 at 12:01:26 AM UTC-3, Sylvia Else wrote:
>> On 18-Mar-23 3:45 am, Richard Hertz wrote:
>>> Why the popularized equation for radar ranging is:
>>>
>>> R = 1/2 t c₀
>>>
>>> https://www.radartutorial.eu/01.basics/Distance-determination.en.html
>> For a target, moving or otherwise, it gives the distance to the target
>> at the point where the radar signal was reflected, which happens after
>> half of the total transit time. The velocity of the target is irrelevant.
>>
>> Sylvia.
> 
> This is the basic theory for radar ranging, taught to kids in high school.
> 
> I wrote the OP in order to show the DISINFORMATION that plagues the web, being in this case from a "serious" site.
> 
> Since the 60s, radar ranging is complemented with Doppler measurement, in a single frequency swept pulse, and even
> better techniques.
> 
> Since the 90s, phased array radars are used along with computes, to acquire targets in a 3D space with resolutions of meters.
> 
> Imagine a Patriot system trying to hit a 5,000 Km/hr incoming missile (or 20,000 Km/Hr for ICBM).
> 
> The real position is tracked in real time. No turning antennae anymore.

I worked R&D on the first airborne phased array radar
(designated a decade downstream for the F-15 and F-16)
at Raytheon in 1967.

Note that most radars today (by sheer numbers) have both
the radar set as well as the target in motion. In 1967
the "computer" used hard wired logic since the programmable
chip had not yet been developed. That earliest model was
slow, cumbersome, and physically heavy.

Banerjee claims to later have worked on modifying some Russian
phased array system for his home country of India but such
knowledge as he expressed indicates he was, once again, making
false claims.

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#604577

On Saturday, March 18, 2023 at 12:29:50 AM UTC-3, whodat wrote:
> On 3/17/2023 10:12 PM, Richard Hertz wrote: 
> > On Saturday, March 18, 2023 at 12:01:26 AM UTC-3, Sylvia Else wrote: 
> >> On 18-Mar-23 3:45 am, Richard Hertz wrote: 
> >>> Why the popularized equation for radar ranging is: 
> >>> 
> >>> R = 1/2 t c₀ 
> >>> 
> >>> https://www.radartutorial.eu/01.basics/Distance-determination.en.html 
> >> For a target, moving or otherwise, it gives the distance to the target 
> >> at the point where the radar signal was reflected, which happens after 
> >> half of the total transit time. The velocity of the target is irrelevant. 
> >> 
> >> Sylvia. 
> > 
> > This is the basic theory for radar ranging, taught to kids in high school. 
> > 
> > I wrote the OP in order to show the DISINFORMATION that plagues the web, being in this case from a "serious" site. 
> > 
> > Since the 60s, radar ranging is complemented with Doppler measurement, in a single frequency swept pulse, and even 
> > better techniques. 
> > 
> > Since the 90s, phased array radars are used along with computes, to acquire targets in a 3D space with resolutions of meters. 
> > 
> > Imagine a Patriot system trying to hit a 5,000 Km/hr incoming missile (or 20,000 Km/Hr for ICBM). 
> > 
> > The real position is tracked in real time. No turning antennae anymore.
> I worked R&D on the first airborne phased array radar 
> (designated a decade downstream for the F-15 and F-16) 
> at Raytheon in 1967. 
> 
> Note that most radars today (by sheer numbers) have both 
> the radar set as well as the target in motion. In 1967 
> the "computer" used hard wired logic since the programmable 
> chip had not yet been developed. That earliest model was 
> slow, cumbersome, and physically heavy. 
> 
> Banerjee claims to later have worked on modifying some Russian 
> phased array system for his home country of India but such 
> knowledge as he expressed indicates he was, once again, making 
> false claims.

What a privilege, whodat.

For anybody trying to grasp the incredible evolution of radar technology since WWII, watching old scify movies
about "invasions" from the outer space is a good visual source.

Many of them, during the '50s, were full of military clips inserted in order to show how USA was "prepared" for attacks
from USSR (disguised as alien attacks), done as B class "cheesy" movies for the gullible audience. One of them is
"The lost missile". Pentagon was very pleased to display, even shortly, the technological capabilities USA & Canada had
by then. 

But this kind of propaganda became less and less usual, as such clips were plenty of information that intelligence services
from USSR (and China) could use. The same happened with technology magazines like the historic "Electronics" in the 70s,
with too much information about R&D, drawings, calculations and military technology.

This movement ended abruptly with the Reagan's Act of Public Information, in 1980, which directly ordered to wash down 
any kind of information on technology and applications.

"Electronics" became then a magazine of "disinformation", and reduced his monthly amount of published information by more
than half. It became just a worthless publicity magazine. This Reagan's Act extended to ANY scientific publication, and has
remained in that way for 43 years.

Claims by scientists about the importance of "cross-fertilization" by publishing true data were dismissed.

Now, you only can access to publications of dubious value, which include books, blogs and access to historical data.

So, to track technology advances since 1982/1983 until these days is a matter of pure speculation. In particular, to understand
if something is TRUE or just DISINFORMATION.

Secrets are kept within corporations from the MIC (of any country), so you'll never know the true stuff (like in radars).

Ukraine's microwar can help to access to some real information, but you have to use Telegram and carefully filter the information,
even when its presented in the form of video. CGI has make almost impossible to know if graphic information is real or not.

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#604536

On 18-Mar-23 2:12 pm, Richard Hertz wrote:
> On Saturday, March 18, 2023 at 12:01:26 AM UTC-3, Sylvia Else wrote:
>> On 18-Mar-23 3:45 am, Richard Hertz wrote:
>>> Why the popularized equation for radar ranging is:
>>>
>>> R = 1/2 t c₀
>>>
>>> https://www.radartutorial.eu/01.basics/Distance-determination.en.html
>> For a target, moving or otherwise, it gives the distance to the target
>> at the point where the radar signal was reflected, which happens after
>> half of the total transit time. The velocity of the target is irrelevant.
>>
>> Sylvia.
> 
> This is the basic theory for radar ranging, taught to kids in high school.
> 
> I wrote the OP in order to show the DISINFORMATION that plagues the web, being in this case from a "serious" site.
> 
> Since the 60s, radar ranging is complemented with Doppler measurement, in a single frequency swept pulse, and even
> better techniques.
> 
> Since the 90s, phased array radars are used along with computes, to acquire targets in a 3D space with resolutions of meters.
> 
> Imagine a Patriot system trying to hit a 5,000 Km/hr incoming missile (or 20,000 Km/Hr for ICBM).
> 
> The real position is tracked in real time. No turning antennae anymore.
> 

That has nothing to do with your earlier claim that the correct equation 
involved the velocity of the target.

Sylvia.

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#604657

On 3/17/2023 11:12 PM, Richard Hertz wrote:
> On Saturday, March 18, 2023 at 12:01:26 AM UTC-3, Sylvia Else wrote:
>> On 18-Mar-23 3:45 am, Richard Hertz wrote:
>>> Why the popularized equation for radar ranging is:
>>>
>>> R = 1/2 t c₀
>>>
>>> https://www.radartutorial.eu/01.basics/Distance-determination.en.html
>> For a target, moving or otherwise, it gives the distance to the target
>> at the point where the radar signal was reflected, which happens after
>> half of the total transit time. The velocity of the target is irrelevant.
>>
>> Sylvia.
> 
> This is the basic theory for radar ranging, taught to kids in high school.
> 
> I wrote the OP in order to show the DISINFORMATION that plagues the web, being in this case from a "serious" site.
> 
> Since the 60s, radar ranging is complemented with Doppler measurement, in a single frequency swept pulse, and even
> better techniques.
> 
> Since the 90s, phased array radars are used along with computes, to acquire targets in a 3D space with resolutions of meters.
> 
The more you post on electronics, the more I think you are not an EE, 
but you know all the buzzwords.

It doesn't matter about all the phased array, Doppler shifted, 
spread-spectrum, jamproof AM/FM discombobulated 4D space color display 
radar that can tell what the pilot of an enemy fighter had for breakfast 
that morning, deep down underneath it all, the radar sends out a signal 
and some of it gets reflected by a target and returned to the sending 
unit with a delay. Part of the information available is the range R=1/2 
ct where t is the delay of a certain portion of the signal returned to 
the radar unit.

The fact there's no longer a turning dish going "ping" and an 
oscilloscope type display with green dots showing the targets is 
irrelevant. (although I see the Russians still use equipment with the 
turning antennas)

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#604658

On 3/18/2023 11:31 PM, Volney wrote:
> On 3/17/2023 11:12 PM, Richard Hertz wrote:
>> On Saturday, March 18, 2023 at 12:01:26 AM UTC-3, Sylvia Else wrote:
>>> On 18-Mar-23 3:45 am, Richard Hertz wrote:
>>>> Why the popularized equation for radar ranging is:
>>>>
>>>> R = 1/2 t c₀
>>>>
>>>> https://www.radartutorial.eu/01.basics/Distance-determination.en.html
>>> For a target, moving or otherwise, it gives the distance to the target
>>> at the point where the radar signal was reflected, which happens after
>>> half of the total transit time. The velocity of the target is 
>>> irrelevant.
>>>
>>> Sylvia.
>>
>> This is the basic theory for radar ranging, taught to kids in high 
>> school.
>>
>> I wrote the OP in order to show the DISINFORMATION that plagues the 
>> web, being in this case from a "serious" site.
>>
>> Since the 60s, radar ranging is complemented with Doppler measurement, 
>> in a single frequency swept pulse, and even
>> better techniques.
>>
>> Since the 90s, phased array radars are used along with computes, to 
>> acquire targets in a 3D space with resolutions of meters.
>>
> The more you post on electronics, the more I think you are not an EE, 
> but you know all the buzzwords.



To the real point, what does any of that matter? Posts are right or they
are wrong/mistaken. There's still an awful lot of "angels dancing on the
head of a pin" style discussion here. Personally I find it useless and
boring. The conditions that created uncle al are unchanged. Too bad.

With very little effort these could be worthwhile newsgroups as they
once were.


> It doesn't matter about all the phased array, Doppler shifted, 
> spread-spectrum, jamproof AM/FM discombobulated 4D space color display 
> radar that can tell what the pilot of an enemy fighter had for breakfast 
> that morning, deep down underneath it all, the radar sends out a signal 
> and some of it gets reflected by a target and returned to the sending 
> unit with a delay. Part of the information available is the range R=1/2 
> ct where t is the delay of a certain portion of the signal returned to 
> the radar unit.
> 
> The fact there's no longer a turning dish going "ping" and an 
> oscilloscope type display with green dots showing the targets is 
> irrelevant. (although I see the Russians still use equipment with the 
> turning antennas)

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#604662

On Sunday, 19 March 2023 at 05:31:09 UTC+1, Volney wrote:
> On 3/17/2023 11:12 PM, Richard Hertz wrote: 
> > On Saturday, March 18, 2023 at 12:01:26 AM UTC-3, Sylvia Else wrote: 
> >> On 18-Mar-23 3:45 am, Richard Hertz wrote: 
> >>> Why the popularized equation for radar ranging is: 
> >>> 
> >>> R = 1/2 t c₀ 
> >>> 
> >>> https://www.radartutorial.eu/01.basics/Distance-determination.en.html 
> >> For a target, moving or otherwise, it gives the distance to the target 
> >> at the point where the radar signal was reflected, which happens after 
> >> half of the total transit time. The velocity of the target is irrelevant. 
> >> 
> >> Sylvia. 
> > 
> > This is the basic theory for radar ranging, taught to kids in high school. 
> > 
> > I wrote the OP in order to show the DISINFORMATION that plagues the web, being in this case from a "serious" site. 
> > 
> > Since the 60s, radar ranging is complemented with Doppler measurement, in a single frequency swept pulse, and even 
> > better techniques. 
> > 
> > Since the 90s, phased array radars are used along with computes, to acquire targets in a 3D space with resolutions of meters. 
> >
> The more you post on electronics, the more I think you are not an EE, 
> but you know all the buzzwords. 
> 
> It doesn't matter about all the phased array, Doppler shifted, 


And do you still believe that  9 192 631 770  ISO idiocy
is some "Newton mode"? You're such an amazing idiot, 
stupid Mike, even considering the standards of your
moronic religion.

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#604616

On Friday, March 17, 2023 at 9:45:57 AM UTC-7, Richard Hertz wrote:
> Why the popularized equation for radar ranging is: 
> 
> R = 1/2 t c₀ 
> 
> https://www.radartutorial.eu/01.basics/Distance-determination.en.html 
> 
> which is clearly wrong? 
> 
> Being t the loop time for the reception of the EM pulse echo, actually 
> 
> R = 1/2 t (c₀ - v) 
> 
> being v the radial velocity between the target and the radar antenna, 
> positive is the target is moving away, and negative if it's coming closer. 
> 
> CALCULATIONS 
> 
> For time t = 0, the target is R meters far away, moving with speed v. 
> 
> An EM pulse is periodically sent (every 1 msec). 
> 
> To hit the target, the time involved is t₁, so that 
> 
> c₀t₁ = R + vt₁ (the target is moving) 
> 
> t₁ = R/(c₀ - v) 
> 
> Coming back from the new distance of the target, requires 
> 
> c₀t₂ = R + vt₁ 
> 
> R + vt₁ = R + vR/(c₀ - v) = Rc₀/(c₀ - v), so 
> 
> c₀t₂ = R + vt₁ = Rc₀/(c₀ - v) 
> 
> t₂ = R/(c₀ - v) = t₁ 
> 
> t = t₁ + t₂ = 2R/(c₀ - v), hence 
> 
> R = 1/2 t (c₀ - v) ≠ 1/2 t c₀ (the last expression is being taught in a radar course). 
> 
> If the target is moving away, it takes MORE time to hit it than chasing it at c₀. 
> 
> If the target is coming, radially, to the source, it takes LESS TIME to hit it. 
> 
> 
> Simplification or denial? 
> 
> How is it about light speed c₀ and motion of bodies? 
> 
> 
> Read "The farce of physics", by Bryan G. Wallace. It's about the cover-up 
> of c ± v, when radar ranging the position of Mars by the military in the '60s. 

Einstein declared as much... that science would fail...
Einstein was more believable than the world
having to win him over QM. He did win the world.

Mitchell Raemsch
> 
> He was "supressed" and "humilliated" as a subversive, ignorant crank.

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#604623

On Saturday, March 18, 2023 at 4:49:18 PM UTC-3, mitchr...@gmail.com wrote:

<snip>

> Einstein declared as much... that science would fail... 
> Einstein was more believable than the world 
> having to win him over QM. He did win the world. 
> 
> Mitchell Raemsch

So, for you Einstein is a deity, a truly believable genius.

But NASA and ESA have been nesting the most deceitful people in the world for decades. Just liars, deceiver cretins.

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#604635

On Saturday, March 18, 2023 at 1:34:01 PM UTC-7, Richard Hertz wrote:
> On Saturday, March 18, 2023 at 4:49:18 PM UTC-3, mitchr...@gmail.com wrote: 
> 
> <snip>
> > Einstein declared as much... that science would fail... 
> > Einstein was more believable than the world 
> > having to win him over QM. He did win the world. 
> > 
> > Mitchell Raemsch
> So, for you Einstein is a deity, a truly believable genius. 
> 
kookfight

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#604922

Den 17.03.2023 17:45, skrev Richard Hertz:
> Why the popularized equation for radar ranging is:
> 
> R = 1/2 t c₀
> 
> https://www.radartutorial.eu/01.basics/Distance-determination.en.html
> 
> which is clearly wrong?

It isn't wrong.
It gives the distance to the target when the pulse hits the target.

> 
> Being t the loop time for the reception of the EM pulse echo, actually
> 
> R = 1/2 t (c₀ - v)

Sure.
It gives the distance to the target when the pulse is detected.

> 
> being v the radial velocity between the target and the radar antenna,
> positive is the target is moving away, and negative if it's coming closer.
> 

Exactly.
And since the radial velocity of the target isn't generally known,
the equation is in most cases useless.

Of course, if it is a Doppler radar, the radial velocity
when the pulse was reflected could be known, and your
equation could be used to find the distance to the target
when the pulse hits the radar.
Weather radars are often Doppler radars where the radial
velocity of the wind (clouds and rain are moving with the wind)
is measured, but this speed is not used in the calculation of
the position.
Other uses of Doppler radars are when the main point is to
measure the speed rather than the position, like the radar gun
used to measure the speed of cars.
Your equation would be pointless in this case.

But let's consider an example:

We have a X-band radar with range 70 km,
and pulse repetition frequency f = 2000 Hz.
Time between pulses  T = 1/f = 0.5 ms

The target is an aeroplane with speed
v = 800 km/h = 222 m/s

Distance moved by plane during T:
d = T*v = 0.5e-3*222 = 0.1 m = 10 cm

The distance moved by plane between the time
the pulse hit the plane, and it hit the radar
can be anything between 0 and 5 cm depending
on the distance to the plane.

So when using the equation R = t⋅c/2 the track of the target
on the screen (ignoring the delay in the electronics) will never
be wrong by more that 5 cm, even when the target is a fast plane.
A computer can obvious calculate the position now, and a short
time in the future. It can also compensate for the known delay in
the electronics.

The error in position is negligible, and is
always less than a pixel on the screen.

Do you now understand why it in most cases is no point
in using your equation to determine the position?

Of course you don't.


> CALCULATIONS

Are trivial.

-- 
Paul

https://paulba.no/

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