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Double altitudes (another blast from the past...)
From: Jeff Gottfred
Date: 1996 Jan 2, 21:45 -0700
From: Jeff Gottfred
Date: 1996 Jan 2, 21:45 -0700
O.K., Now that we are all off and practicing our lunars (or, like me, waiting for the skys to clear once more) How about I prize open another kettle 'o fish... How about double altitudes for latitude? I have a couple of methods from Cotter here, one of which I can't get to work, and another which seems to be very inaccurate. Here is more info on what I am talking about: O.K., you have a watch, but it is no good for measuring absolute time, just short intervals, hence it is O.K. for lunars, but it does not keep time well enough for the classic Sumner line approach. So, If we have a sun altitude, and a couple of hours later another sun altitude, and we know the time difference between the two obs, then can we compute a latitude directly? In theory, yes. Here is one method. P is the north pole, X is the first obs, Y is the second obs, Z is the Zenith. .,-P ,' / \ ,' / \ Z..../ \ | /`---. \ | / ``. \ | / `-. \ |/ `--. \ Y--------------------- X We know PX, PY and the time difference converted to arc P So, use the law of cosines to compute XY. Now, use the law of cosines to find angle PXY. Now, we measured ZX, and ZY, and computed XY, so, using law of cosines, solve for ZXY. Now, PXZ = PXY - ZXY Now, we know PXZ, PX, and XZ, so using law of cosines, solve for PZ Our latitude is 90 - PZSo, with this, and the same lousy watch we use for lunars, we get a latitude without having to hope for clear skies at LAN... Comments?? Cheers! Jeff! ------------------------------------------------------------------------ This mail list is managed by the majordomo program. To from this list, send the following message to majordomo@ronin.com: navigation For help, send the following message to majordom@ronin.com: help Do NOT send administrative requests to navigation@ronin.com. Thanks. -ben ------------------------------------------------------------------------ From mail Fri Jan 5 00:07 EST 1996 Received: from dg-rtp by wellspring.us.dg.com (5.4R3.10/dg-gens08) id AA23267; Fri, 5 Jan 1996 00:07:19 -0500 Received: from gomoku.ronin.com by dg-rtp.dg.com (5.4R3.10/dg-rtp-v02) id AA00184; Fri, 5 Jan 1996 00:08:41 -0500 Received: from localhost (ben@localhost) by gomoku.ronin.com (8.6.5/8.6.5) id AAA05420 for navigation-outgoing; Fri, 5 Jan 1996 00:01:28 -0500 Received: from linux4nn.gn.iaf.nl (root@linux4nn.iaf.nl [193.67.144.34]) by gomoku.ronin.com (8.6.5/8.6.5) with ESMTP id XAA05312 for ; Thu, 4 Jan 1996 23:43:11 -0500 Received: from uni4nn.iaf.nl (root@uni4nn.iaf.nl [193.67.144.33]) by linux4nn.gn.iaf.nl (8.6.9/8.6.9) with SMTP id VAA03729 for ; Thu, 4 Jan 1996 21:37:24 +0100 Received: from slip11.gn.iaf.nl by uni4nn.iaf.nl with SMTP id AA01769 (5.67b/IDA-1.5 for ); Thu, 4 Jan 1996 21:37:01 +0100 Date: Thu, 4 Jan 1996 21:37:01 +0100 Message-Id: <199601042037.AA01769@uni4nn.iaf.nl> X-Sender: slip0039@uni4nn.iaf.nl X-Mailer: Windows Eudora Version 1.4.4 Mime-Version: 1.0 To: navigation@ronin.com From: J.van.Puffelen@uni4nn.iaf.nl (Jan van Puffelen) Subject: Re: double altitudes (another blast from the past...) Sender: owner-navigation@ronin.com Precedence: bulk Reply-To: navigation@ronin.com Errors-To: owner-majordomo@ronin.com Content-Type: text/plain; charset="us-ascii" Content-Length: 3936 >Jeff Gottfred wrote: >Here is more info on what I am talking about: > >O.K., you have a watch, but it is no good for measuring absolute time, >just short intervals, hence it is O.K. for lunars, but it does not keep >time well enough for the classic Sumner line approach. So, If we have a >sun altitude, and a couple of hours later another sun altitude, and we >know the time difference between the two obs, then can we compute a >latitude directly? > >In theory, yes. Here is one method. > >P is the north pole, X is the first obs, Y is the second obs, Z is the >Zenith. > > .,-P > ,' / \ > ,' / \ > Z..../ \ > | /`---. \ > | / ``. \ > | / `-. \ > |/ `--. \ > Y--------------------- X > > >We know PX, PY and the time difference converted to arc P >So, use the law of cosines to compute XY. > >Now, use the law of cosines to find angle PXY. > >Now, we measured ZX, and ZY, and computed XY, so, using law of cosines, >solve for ZXY. > >Now, PXZ = PXY - ZXY > >Now, we know PXZ, PX, and XZ, so using law of cosines, solve for PZ > >Our latitude is 90 - PZ > >So, with this, and the same lousy watch we use for lunars, we get a >latitude without having to hope for clear skies at LAN... > >Comments?? > This method looks of little practical value at sea: * It depends on the fact that the latitude does not chance between the two observations. This is usually not true at sea. * It also depends on the fact that the longitude does not change between the two observations. After all, if the longitude changes, the LHA changes as well. Again, this is usually not the case at sea. * If the GMT is not known, the sun nor the moon can be used. For these two objects the declination depends on the time. This limits the use of this method to the brightest stars and planets. * However, in order to measure the altitude of stars both the night sky and the horizon must be visible at the same time. This is only the case in the nautical twilight which is of a very limited duration (especially in the tropics). This duration is too short for the two observations of the same star. This makes even star sights unpractical. The only practical application is IMHO on land, with an artificial horizon. But then again, this method is fairly complex as opposed to the simple noon altitude (or meridian passage). A far more simple approach would be to determine true N or S with a magnetic compass and take the highest/lowest altitude of a star or planet during the meridian passage. This will provide the latitude on a very simple and accurate way. Regards, Jan van Puffelen slip0039@uni4nn.iaf.nl 52d 24.5'N 4d 55'E >Cheers! > >Jeff! > > > >------------------------------------------------------------------------ >This mail list is managed by the majordomo program. >To from this list, send the following message >to majordomo@ronin.com: navigation >For help, send the following message to majordom@ronin.com: help >Do NOT send administrative requests to navigation@ronin.com. Thanks. -ben >------------------------------------------------------------------------ > ------------------------------------------------------------------------ This mail list is managed by the majordomo program. To from this list, send the following message to majordomo@ronin.com: navigation For help, send the following message to majordom@ronin.com: help Do NOT send administrative requests to navigation@ronin.com. Thanks. -ben ------------------------------------------------------------------------