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From: Eric Gisse <jowr.pi@gmail.com>
Newsgroups: alt.math,japan.sci.math,sci.math,sci.physics,sci.physics.relativity
Subject: Re: GPS question
Date: Mon, 23 Feb 2009 12:26:17 -0800 (PST)
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On Feb 23, 11:22=A0am, koobee.wub...@gmail.com wrote:
> On Feb 23, 12:01 pm, Eric Gisse wrote:
>
>
>
> > On Feb 23, 9:49 am, koobee.wub...@gmail.com wrote:
> > > You need four satellites where each satellite should know its time an=
d
> > > position. =A0Time can just be a counter with all the satellites
> > > synchronized to within a count of each other. =A0Each satellite then
> > > just broadcast its time and position information as almanac signal to
> > > whoever wants to receive it.
>
> > > Since the distance is traveled by light with a known speed, you can
> > > then easily form a set of four equations with four unknowns. =A0The f=
our
> > > unknowns are your time (relative to the counter in each satellite) an=
d
> > > position.
>
> > > ** =A0c^2 (t1 =96 t)^2 =3D (x1 =96 x)^2 + (y1 =96 y)^2 + (z1 =96 z)^2
> > > ** =A0c^2 (t2 =96 t)^2 =3D (x2 =96 x)^2 + (y2 =96 y)^2 + (z2 =96 z)^2
> > > ** =A0c^2 (t3 =96 t)^2 =3D (x3 =96 x)^2 + (y3 =96 y)^2 + (z3 =96 z)^2
> > > ** =A0c^2 (t4 =96 t)^2 =3D (x4 =96 x)^2 + (y4 =96 y)^2 + (z4 =96 z)^2
>
> > > Where
>
> > > ** =A0(t1, x1, y1, z1) =3D Time and position of satellite 1
> > > ** =A0(t2, x2, y2, z2) =3D Time and position of satellite 2
> > > ** =A0(t3, x3, y3, z3) =3D Time and position of satellite 3
> > > ** =A0(t4, x4, y4, z4) =3D Time and position of satellite 4
> > > ** =A0(t, x, y, z) =3D Time and position of the receiver
>
> > > Notice that relativistic effect is never needed.
>
> > ...even tnough t1-4 are wrong by roughly 50,000ns/day?
>
> So, the college drop-out sleeps until 11AM Alaska time today.

No, it was earlier than that. Why do you care?

>
> In the meantime, if t1 is off by 50usec a day relative to the ground,
> as long as t2, t3, and t4 are all off by the same amount, it does not
> matter. =A0There is still no need for any relativistic correction.
> <shrug>

Really?

Show us how an arbitrary scaling in time does not change the position.
It is just algebra and it would prove everyone here wrong, so it would
be a worthwhile exercise for you.