Path: news.ccsf.jp!tomockey.ddo.jp!border1.nntp.dca.giganews.com!nntp.giganews.com!postnews.google.com!p13g2000yqc.googlegroups.com!not-for-mail From: Dave Newsgroups: alt.math,japan.sci.math,sci.math,sci.physics,sci.physics.relativity Subject: Re: GPS question Date: Mon, 23 Feb 2009 15:31:06 -0800 (PST) Organization: http://groups.google.com Lines: 111 Message-ID: <67327451-af56-47e0-a8c5-3a96131f6d03@p13g2000yqc.googlegroups.com> References: <1faf92f1-847e-41c9-b6eb-09556cdeb0bc@t3g2000yqa.googlegroups.com> <9f09958d-1b9d-4951-8623-d76c3eb4e8de@w34g2000yqm.googlegroups.com> NNTP-Posting-Host: 76.251.38.87 Mime-Version: 1.0 Content-Type: text/plain; charset=windows-1252 Content-Transfer-Encoding: quoted-printable X-Trace: posting.google.com 1235431867 14132 127.0.0.1 (23 Feb 2009 23:31:07 GMT) X-Complaints-To: groups-abuse@google.com NNTP-Posting-Date: Mon, 23 Feb 2009 23:31:07 +0000 (UTC) Complaints-To: groups-abuse@google.com Injection-Info: p13g2000yqc.googlegroups.com; posting-host=76.251.38.87; posting-account=O9zR9AkAAACmp918j6u5m5plppeILcze User-Agent: G2/1.0 X-HTTP-UserAgent: Mozilla/4.0 (compatible; MSIE 7.0; Windows NT 5.1; Ads Filter 1.2.0.72; GTB5; .NET CLR 1.0.3705; .NET CLR 1.1.4322; Media Center PC 4.0; .NET CLR 2.0.50727; .NET CLR 3.0.04506.648; .NET CLR 3.5.21022; .NET CLR 3.0.4506.2152; .NET CLR 3.5.30729),gzip(gfe),gzip(gfe) Xref: news.ccsf.jp japan.sci.math:196 On Feb 23, 4:54=A0pm, torso wrote: > On Feb 23, 11:40 pm, Dono wrote: > > > > > > > On Feb 23, 12:33 pm, Cephalobus_alie...@comcast.net wrote: > > > > On Feb 23, 12:49 pm, koobee.wub...@gmail.com wrote: > > > > > On Feb 20, 4:33 am, "Jon" wrote: > > > > > > Supposing three satellites transmit signals with time stamps that= are picked > > > > > up by a receiver. =A0If the clocks on the satellites are closely = synchronized, > > > > > then > > > > > > |AD|=3D|AB|+t_AB > > > > > |BD|=3D|BC|+t_BC > > > > > |CD|=3D|CA|+t_CA > > > > > > Where > > > > > A,B,C=3Dposition vectors of three satellites > > > > > AB,BC,CA=3Ddistances between satellites > > > > > t_AB,t_BC,t_CA=3Dtime differences between signals at D. > > > > > D=3Dposition vector of receiver. > > > > > > Once |AD|,|BD|,|CD| are found, the coordinates of D can be derive= d. > > > > > > Is this how it is done? > > > > > > summarized at > > > > > >http://mypeoplepc.com/members/jon8338/math/id8.html > > > > > You need four satellites where each satellite should know its time = and > > > > position. =A0Time can just be a counter with all the satellites > > > > synchronized to within a count of each other. =A0Each satellite the= n > > > > 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= four > > > > unknowns are your time (relative to the counter in each satellite) = and > > > > 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. > > > > Currently, only Block IIR satellites are capable of autonomous > > > position monitoring and synchronization independent of the ground > > > control segment. This capability allows Block IIR satellites to > > > mutually correct their clocks and ephemerides information for a > > > period of up to several months should the ground segment be > > > knocked out by, say, nuclear war. For optimum performance under > > > non-wartime conditions, "ground truth" comparisons are still > > > performed on a daily basis to correct the satellites for drift. > > > > GPS satellites before the Block IIR series are incapable of such > > > mutual correction, and require monitoring and daily corrections > > > by the Ground Segment. > > > > Satellite control requires that the Space Segment and Ground > > > Segment clocks be synchronized. The only practical way of > > > synchronizing the world-wide network of ground stations is to > > > use the network of GPS satellites to disseminate time. The only > > > way to use the networks of GPS satellites to disseminate time is > > > if the satellite clocks are adjusted via the GR correction so > > > that they beat in time with Earth clocks. > > > > Jerry- Hide quoted text - > > > > - Show quoted text - > > > Jerry > > > According to Dave's post (see above), the satellites in relative > > motion (at about 6.7km/s) so the Kobee-Wublee idiot needs to > > understand that, even with Block IIR, the relativistic corrections are > > still needed. > > i thought they were geostationary You thought wrong. They orbit at about 20,200 km altitude, and have an orbital period of 12 hours. Dave