Chapter 27: Geodesy and Cartography of Théxar
"Before mapping — measure. Before measuring — understand what exactly you are measuring. Théxar does not tolerate approximation." — From "Guide for Geodesists," Guild of Navigators, +2 800 E.U.
General calculations and planetary maps use a reference sphere of radius 6,112 km. Precise surveying also accounts for terrain and variations in the gravity field.
27.1 Geodetic System
27.1.1 Reference Ellipsoid
The Théxar coordinate system is based on the WGS-Théxar reference surface, approved by the Guild of Navigators in +2 200 E.U.
| Parameter | Value |
|---|---|
| Reference radius | 6,112 km |
| Great-circle circumference | ≈38,403 km |
| Surface area | ≈469.436 million km² |
27.1.2 Geoid
The Théxar geoid is a model of the planet's shape accounting for gravitational anomalies. Geoid deviations from WGS-Théxar:
| Region | Anomaly (sha) | Cause |
|---|---|---|
| Khar-Tor Ridge | +51 sha | Gravitational excess (mountain mass) |
| Thash Trench | −46 sha | Gravitational deficit (deep-sea trench) |
| Raal Plateau | +22 sha | Excess crustal density |
| Shan Desert | −15 sha | Thin crust |
27.2 Coordinate System
27.2.1 Geographic Coordinates
The Xha'Ruun use a spherical coordinate system:
- Latitude (φ): 0° (equator) → +90° (north) / −90° (south)
- Longitude (λ): 0° (prime meridian) → +180° (east) / −180° (west)
- Height (h): above the WGS-Théxar reference surface
27.2.2 Prime Meridian
The prime meridian passes through the center of the Government Quarter square of Khar-Vexar, at coordinates:
- WGS-Théxar: φ = 42°18'24" N, λ = 0°00'00"
- Mark: bronze plate 1.2 sha in diameter at the center of the square
27.2.3 Equator
The Théxar equator crosses the southern tip of the Kharak continent and the northern tip of Rhuval. At the intersection with the 48° E meridian stands the Equator Monument — a 15-sha stele of black basalt.
27.3 Height Systems
| System | Application | Zero Level |
|---|---|---|
| Orthometric (H) | Topography | Mean level of the Thalas Ocean |
| Dynamic | Hydrology | Geoid |
| Normal (H*) | Leveling | Quasigeoid |
| Geopotential | Global | 9.32 × 10⁷ sha²/s² |
The mean ocean level is determined from 12 tidal stations distributed along the coasts of all three continents.
27.4 Cartographic Projections
| Projection | Type | Application | Scale | Continent |
|---|---|---|---|---|
| Conformal (Mercator) | Cylindrical | Navigation | 1:500 000 | All |
| Equal-Area (Lambert) | Conic | Areas, statistics | 1:1 million | Kharak |
| Transverse Mercator | Cylindrical | Topography (UMS) | 1:50 000 | All |
| Conic (Lambert) | Conic | Regional maps | 1:500 000 | Rhuval, Vexar |
| Azimuthal | Azimuthal | Polar regions | 1:2 million | Polar |
| Pseudo-cylindrical | Sinusoidal | Educational | 1:10 million | Planet |
27.4.1 Standard Scales
| Scale | Xha'Ruun Name | Resolution | Example |
|---|---|---|---|
| 1:1 000 | "Palm" | 0.61 sha | Buildings |
| 1:10 000 | "Street" | 6.1 sha | Cities |
| 1:50 000 | "District" | 30 sha | Topography |
| 1:500 000 | "Country" | 305 sha | Regions |
| 1:5 000 000 | "Continent" | 0.51 mo | Physical map |
| 1:50 000 000 | "Planet" | 5.1 mo | Educational |
27.5 Geodetic Network
27.5.1 SGS Points (State Geodetic Survey)
| Class | Quantity | Accuracy | Purpose |
|---|---|---|---|
| 1st class | 4 200 points | ±0.01″ | Scientific |
| 2nd class | 28 000 points | ±0.05″ | State |
| 3rd class | 210 000 points | ±0.2″ | Municipal |
27.5.2 Satellite Geodesy
24 GNSS (Global Navigation Satellite System) satellites in orbits at altitudes of 3 660–4 470 mo provide:
- Positioning accuracy: ±2.3 pa (civilian), ±0.58 pa (military)
- Coverage: 100% of Théxar's surface
- Fix time: <10 s
27.6 History of Cartography
| Period | Event | Significance |
|---|---|---|
| ~−7 000 | First maps on clay tablets | Thar River valley |
| ~−500 | First map of the known world (Kharak) | "Map of the Center" |
| +180 yr | Measurement of Théxar's circumference (Khar-Vexar) | Error <2% |
| +800 yr | Creation of the Unified Cartographic Service | Data consolidation |
| +1 500 yr | First map of the Thalas ocean floor | Bathymetry |
| +2 800 yr | Digital map of the planet (1:50 000) | Full coverage |
| +3 800 yr | WGS-Théxar v3.0 | Current standard |
Chapter Summary
- Théxar’s reference radius is 6,112 km.
- Prime meridian: Khar-Vexar (42°18'24" N).
- 6 main cartographic projections.
- 242 200 SGS points (state geodetic network).
- GNSS: 24 satellites, accuracy ±2.3 pa.