# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

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Re: Time of meridian passage accuracy
From: Andrés Ruiz
Date: 2009 Oct 8, 08:16 +0200

Antoine is right in saying: “Only the presence of higher order terms (in t**4 and maybe t**6) prevented Andres to do the perfect pick of the exact Culmination time.”

I have simulated two theoretical cases with very high speed, and the curve obtained for the altitude near meridian transit is like this:

R=180º

V=3000 kt

R=135º

V=3000 kt

In this case the least squares fit gives for Hmax:

yLS = a0+a1*x+a2*x2+a3*x3+...+anxn

a0 = -51168.479530

a1 = 4885.116188

a2 = 118.025783

a3 = -20.281600

a4 = 0.107351

a5 = 0.025145

a6 = -0.000455

 x y yLS y - yLS ErrorRel_y ErrorRel_yLS 17.508889 53.34053 53.178178 0.162352 0.30437 0.305299

And the solution is:

 R V UT1 B L GHA Dec LHA H Z UT1 tTransit-tMax 135 3000 Transit: 17.0775 21.4216279 -76.4695651 76.471408 -23.434998 0.00184292 45.1433741 180.002397 17:04:39 135 3000 Hmax: 17.5088889 6.16972746 -60.8005176 82.9400037 -23.4348594 22.1394861 53.3405304 215.389641 17:30:32 0:25:53

Andrés Ruiz

Asunto: [NavList 10061] Re: Time of meridian passage accuracy

...

I am quite surprised by these results because for culminations close to zenit (say above 85d) the effect of a high N/S speed component and/or change in declination significantly skews the heights vs times curve. Given the almost perfect symmetry of this Altitude curve, the algorithm used by Andres - apparently a second degree best fit as seems to be indicated on his site - was very powerful to pick up almost the exact the Culmination time. Only the presence of higher order terms (in t**4 and maybe t**6) prevented Andres to do the perfect pick of the exact Culmination time.

...

Antoine M. "Kermit" Couette

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