Introduction:
In this tutorial, we’ll explore how to calculate the azimuth, elevation, and slant range between two points on the Earth’s surface using Python. The concepts of azimuth and elevation are essential in various fields such as navigation, astronomy, and satellite communication. The slant range, on the other hand, is the direct distance between two points on the Earth’s surface.
In various fields such as geodesy, aviation, and satellite communication, it is crucial to calculate parameters like azimuth (bearing), elevation angle, and slant range between two geographic points. These calculations help in tasks such as navigation, antenna pointing, and understanding line-of-sight obstructions. In this tutorial, we will explore how to compute these values using Python and basic trigonometry, specifically using the Haversine formula for distance calculations.
Background:
Azimuth is the horizontal angle measured clockwise from the north, indicating the direction of a target point relative to the observer. Elevation is the vertical angle above the local horizon, describing the target point’s height relative to the observer. The slant range is the 3D distance between the observer and the target point.
Requirements:
- Python 3.x
- Basic understanding of Python programming
- Familiarity with coordinate systems (latitude, longitude)
The Python Code:
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import math # Constants EARTH_RADIUS = 6371000 # in meters def calculate_distance(lat1, lon1, lat2, lon2): # Convert decimal degrees to radians lat1_rad = math.radians(lat1) lon1_rad = math.radians(lon1) lat2_rad = math.radians(lat2) lon2_rad = math.radians(lon2) # Haversine formula dlat = lat2_rad - lat1_rad dlon = lon2_rad - lon1_rad a = math.sin(dlat/2) * math.sin(dlat/2) + math.cos(lat1_rad) * \ math.cos(lat2_rad) * math.sin(dlon/2) * math.sin(dlon/2) c = 2 * math.atan2(math.sqrt(a), math.sqrt(1-a)) distance = EARTH_RADIUS * c return distance def calculate_bearing(lat1, lon1, lat2, lon2): # Convert decimal degrees to radians lat1_rad = math.radians(lat1) lon1_rad = math.radians(lon1) lat2_rad = math.radians(lat2) lon2_rad = math.radians(lon2) dlon = lon2_rad - lon1_rad y = math.sin(dlon) * math.cos(lat2_rad) x = math.cos(lat1_rad) * math.sin(lat2_rad) - \ math.sin(lat1_rad) * math.cos(lat2_rad) * math.cos(dlon) bearing_rad = math.atan2(y, x) bearing_deg = math.degrees(bearing_rad) # Normalize to [0, 360) degrees bearing_deg = (bearing_deg + 360) % 360 return bearing_deg def calculate_elevation(lat1, lon1, elev1, lat2, lon2, elev2): distance = calculate_distance(lat1, lon1, lat2, lon2) elevation_rad = math.atan2(elev2 - elev1, distance) elevation_deg = math.degrees(elevation_rad) return elevation_deg def calculate_slant_range(lat1, lon1, elev1, lat2, lon2, elev2): distance = calculate_distance(lat1, lon1, lat2, lon2) slant_range = math.sqrt(distance**2 + (elev2 - elev1)**2) return slant_range if __name__ == "__main__": # Input location 1 lat1 = -34.0973 lon1 = 150.7796 elev1 = 210 # Input location 2 lat2 = -25.1765 lon2 = 148.4382 elev2 = 810000 # Calculate values distance_down_range = calculate_distance(lat1, lon1, lat2, lon2) bearing = calculate_bearing(lat1, lon1, lat2, lon2) elevation = calculate_elevation(lat1, lon1, elev1, lat2, lon2, elev2) slant_range = calculate_slant_range(lat1, lon1, elev1, lat2, lon2, elev2) # Output results print(f"\nFrom Location 1 to Location 2:") print(f"Bearing Degrees (True North): {bearing:.4f}") print(f"Elevation in Degrees: {elevation:.4f}") print(f"Down Range in Meters: {int(distance_down_range)}") print(f"Slant Range in Meters: {int(slant_range)}") |
Step-by-step explanation:
- Import the math library, which is used for trigonometric and other mathematical functions.
- Define a constant EARTH_RADIUS in meters.
- Write a function calculate_distance() to calculate the distance between two points on Earth using the Haversine formula.
- Write a function calculate_bearing() to calculate the bearing (azimuth) between two points on Earth.
- Write a function calculate_elevation() to calculate the elevation angle between two points on Earth.
- Write a function calculate_slant_range() to calculate the slant range (3D distance) between two points on Earth.
- In the main program, define the input locations (latitude, longitude, and elevation) for the two points.
- Call the functions to calculate the azimuth, elevation, and slant range between the two points.
- Print the results.
With this code, you can easily calculate the azimuth, elevation, and slant range between any two points on Earth’s surface.
I hope this tutorial will create a good foundation for you. If you want tutorials on another GIS topic or you have any queries, please send an mail at contact@spatial-dev.guru.