# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Position-Finding

**Re: Latitude by Talcott-Horrebow Method**

**From:**Peter Monta

**Date:**2018 Nov 8, 04:15 -0800

Hi Brad,

> Okay, so now I am just a bit confused. The geoditic monuments that Peter mentioned must have their asigned latitude and longitude changed as they move about due to plate tectonics, or so it is stated.

Yes, they are specified by a position, (x,y,z) or equivalently (lat,lon,ellipsoidal_height), and the corresponding velocity components, of order a few cm/year. So to calculate the coordinates, it's just a linear extrapolation: you take the coordinate at the epoch and add the velocity times the delta-time since the epoch. Something like proper motion for stars. The tectonic plates stand out very well because all the stations on a given plate are moving in roughly the same direction and speed.

> But are they also reassigned as a function of pole wander?

To first order, no. ITRF is crust-based, so polar motion has no effect on the crustal coordinates. But this is a complicated question and I'm not sure I understand what the reference-frame people have to say on the matter. There's something called a "pole tide" that results in a subtle bias in the modeling, and it has to do with the secular drift of the polar motion and its effect on the geopotential. But apparently the effect is small (~1 cm). It's described in IERS TN36.

> If not, then how are the two systems aligned. Example of confusion. I take my GPS receiver to a geoditic monument. The GPS ephemeris updated to include pole wander, as per Paul. So the geoditic latitude will NOT match the GPS latitude.

The coordinate systems are the same in both cases, so they should match. The GPS ephemeris will give you the satellite's position in the same ECEF coordinate system as the monuments (WGS84(GPSx) for the broadcast orbits, ITRF(x) if you get the precise orbits from IGS, etc.; but they are the same for all practical purposes). I think Paul meant that the orbital models absorb the polar motion in the sense that they're adjusted to be slightly unphysical, that is, not pure Keplerian, so as to give the result in WGS84. The satellites don't care about earth orientation---they orbit around the center of mass---so something has to give. They're not Keplerian for a number of other reasons too, like tidal perturbations and solar radiation pressure, so the orbit models have the appropriate bells and whistles.

Cheers,

Peter

> Okay, so now I am just a bit confused. The geoditic monuments that Peter mentioned must have their asigned latitude and longitude changed as they move about due to plate tectonics, or so it is stated.

Yes, they are specified by a position, (x,y,z) or equivalently (lat,lon,ellipsoidal_height), and the corresponding velocity components, of order a few cm/year. So to calculate the coordinates, it's just a linear extrapolation: you take the coordinate at the epoch and add the velocity times the delta-time since the epoch. Something like proper motion for stars. The tectonic plates stand out very well because all the stations on a given plate are moving in roughly the same direction and speed.

> But are they also reassigned as a function of pole wander?

To first order, no. ITRF is crust-based, so polar motion has no effect on the crustal coordinates. But this is a complicated question and I'm not sure I understand what the reference-frame people have to say on the matter. There's something called a "pole tide" that results in a subtle bias in the modeling, and it has to do with the secular drift of the polar motion and its effect on the geopotential. But apparently the effect is small (~1 cm). It's described in IERS TN36.

> If not, then how are the two systems aligned. Example of confusion. I take my GPS receiver to a geoditic monument. The GPS ephemeris updated to include pole wander, as per Paul. So the geoditic latitude will NOT match the GPS latitude.

The coordinate systems are the same in both cases, so they should match. The GPS ephemeris will give you the satellite's position in the same ECEF coordinate system as the monuments (WGS84(GPSx) for the broadcast orbits, ITRF(x) if you get the precise orbits from IGS, etc.; but they are the same for all practical purposes). I think Paul meant that the orbital models absorb the polar motion in the sense that they're adjusted to be slightly unphysical, that is, not pure Keplerian, so as to give the result in WGS84. The satellites don't care about earth orientation---they orbit around the center of mass---so something has to give. They're not Keplerian for a number of other reasons too, like tidal perturbations and solar radiation pressure, so the orbit models have the appropriate bells and whistles.

Cheers,

Peter