Geodetic Coordinates¶

This tutorial is about the satkit.itrfcoord data type — how to describe a specific point on or near the Earth's surface and convert between geodetic and Cartesian representations of that point.

For the abstract definition of the ITRF reference frame, and for rotating vectors between ITRF and other frames (GCRF, TEME, ...), see the Coordinate Frames tutorial.

All points here live in the International Terrestrial Reference Frame (ITRF) — the Earth-fixed, Earth-rotating frame used in geodesy and satellite operations. satkit.itrfcoord represents a position in this frame and provides conversions between:

• Geodetic coordinates: latitude, longitude, and altitude above the WGS-84 ellipsoid (ellipsoid-normal, not geocentric latitude)
• Cartesian coordinates: a 3-element (x, y, z) vector in meters with origin at Earth's center of mass
• Local tangent planes: East-North-Up (ENU) and North-East-Down (NED) for range/bearing-style computations near a reference point
• Geodesic distances: great-circle-equivalent distances along the WGS-84 ellipsoid between two itrfcoord values

This tutorial demonstrates constructing coordinates from geodetic parameters, converting to and from Cartesian vectors, and computing distances between locations.

In [1]:

import satkit as sk

# Specify a coordinate via Geodetic latitude & longitude (if altitude is left out, default is 0
boston = sk.itrfcoord(latitude_deg=42.14, longitude_deg=-71.15)

# Denver, CO is at a higher altitude; altitude is specified in meters
denver = sk.itrfcoord(latitude_deg=32.7392, longitude_deg=-104.99, altitude=1600)
print(f'Denver = {denver}')

# Get the Cartesian vector for Denver
print(f'Denver vector coordinate is {denver.vector}')

# Create a duplicate of the Denver coordinate, using vector as input
denver2 = sk.itrfcoord(denver.vector)
print(f'Denver created from Cartesian is {denver2}')

import satkit as sk # Specify a coordinate via Geodetic latitude & longitude (if altitude is left out, default is 0 boston = sk.itrfcoord(latitude_deg=42.14, longitude_deg=-71.15) # Denver, CO is at a higher altitude; altitude is specified in meters denver = sk.itrfcoord(latitude_deg=32.7392, longitude_deg=-104.99, altitude=1600) print(f'Denver = {denver}') # Get the Cartesian vector for Denver print(f'Denver vector coordinate is {denver.vector}') # Create a duplicate of the Denver coordinate, using vector as input denver2 = sk.itrfcoord(denver.vector) print(f'Denver created from Cartesian is {denver2}')

Denver = ITRFCoord(lat:  32.7392 deg, lon: -104.9900 deg, hae:  1.60 km)
Denver vector coordinate is [-1389345.60167272 -5188730.62268842  3430531.07678629]
Denver created from Cartesian is ITRFCoord(lat:  32.7392 deg, lon: -104.9900 deg, hae:  1.60 km)

Creating Coordinates¶

Coordinates can be created from geodetic parameters (latitude, longitude, altitude) or from a Cartesian position vector. The altitude defaults to 0 (on the ellipsoid surface) if not specified.

Geodesic Distance¶

The geodesic_distance method computes the shortest path between two points along the surface of the WGS-84 ellipsoid, returning the distance in meters along with the initial and final headings of the path.

In [2]:

import satkit as sk

newyork = sk.itrfcoord(latitude_deg=40.7128, longitude_deg=-74.0060)
destinations = [
    {'name': 'London', 'latitude_deg': 51.5072, 'longitude_deg': -0.1276},
    {'name': 'Paris', 'latitude_deg': 48.8566, 'longitude_deg': 2.3522},
    {'name': 'Toronto', 'latitude_deg': 43.6532, 'longitude_deg': -79.3832},
    {'name': 'Tokyo', 'latitude_deg': 35.6763, 'longitude_deg': 139.65},
    {'name': 'Sau Paulo', 'latitude_deg': -23.5558, 'longitude_deg': -46.6396}
]
for dest in destinations:
    destcoord = sk.itrfcoord(latitude_deg=dest['latitude_deg'], longitude_deg=dest['longitude_deg'])
    # Distance, start, and end heading along great circle to destination coordinate
    dist, _heading_start, _heading_end = newyork.geodesic_distance(destcoord)
    print(f'New York to {dest['name']} distance is {dist/1e3:.0f} km')

import satkit as sk newyork = sk.itrfcoord(latitude_deg=40.7128, longitude_deg=-74.0060) destinations = [ {'name': 'London', 'latitude_deg': 51.5072, 'longitude_deg': -0.1276}, {'name': 'Paris', 'latitude_deg': 48.8566, 'longitude_deg': 2.3522}, {'name': 'Toronto', 'latitude_deg': 43.6532, 'longitude_deg': -79.3832}, {'name': 'Tokyo', 'latitude_deg': 35.6763, 'longitude_deg': 139.65}, {'name': 'Sau Paulo', 'latitude_deg': -23.5558, 'longitude_deg': -46.6396} ] for dest in destinations: destcoord = sk.itrfcoord(latitude_deg=dest['latitude_deg'], longitude_deg=dest['longitude_deg']) # Distance, start, and end heading along great circle to destination coordinate dist, _heading_start, _heading_end = newyork.geodesic_distance(destcoord) print(f'New York to {dest['name']} distance is {dist/1e3:.0f} km')

New York to London distance is 5585 km
New York to Paris distance is 5853 km
New York to Toronto distance is 551 km
New York to Tokyo distance is 10876 km
New York to Sau Paulo distance is 7658 km