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import math
def distance_to_sun(latitude, longitude, sun_radius_degrees=0, sun_angle_degrees=0, sun_height_km=5000):
"""
Calculate the distance from a point on the polar plane to the sun hovering above the plane.
Parameters:
latitude (float): Latitude of the point in the polar coordinate system (in degrees, +90 at origin).
longitude (float): Longitude in degrees of the point in the polar coordinate system.
sun_radius_degrees (float): Radius of the sun's position in the polar coordinate system (in degrees, +90 at origin).
sun_angle_degrees (float): Angle in degrees of the sun's position in the polar coordinate system.
sun_height_km (float): Height above the plane in kilometers (default is 5000 km).
Returns:
float: Distance from the point on the polar plane to the sun in kilometers.
"""
# Convert radius degrees to km
def radius_degrees_to_km(radius_degrees):
if radius_degrees >= 0:
return 10000 - (radius_degrees / 90) * 10000
else:
return 10000 + (abs(radius_degrees) / 90) * 10000
latitude_km = radius_degrees_to_km(latitude)
sun_radius_km = radius_degrees_to_km(sun_radius_degrees)
# Convert polar coordinates to Cartesian coordinates
longitude_radians = math.radians(longitude)
point_x = latitude_km * math.cos(longitude_radians)
point_y = latitude_km * math.sin(longitude_radians)
point_z = 0 # All points on the plane have z = 0
# Convert sun polar coordinates to Cartesian coordinates
sun_angle_radians = math.radians(sun_angle_degrees)
sun_x = sun_radius_km * math.cos(sun_angle_radians)
sun_y = sun_radius_km * math.sin(sun_angle_radians)
sun_z = sun_height_km
# Calculate the distance between the point and the sun
distance = math.sqrt((point_x - sun_x)**2 + (point_y - sun_y)**2 + (point_z - sun_z)**2)
return distance
# Example Usage
sun_latitude_degrees = -22.9 # sun's latitude in degrees
sun_longitude_degrees = -160.90 # sun's longitude in degrees
sun_height_km = 5812.8426 # Height above the plane in km
observer_latitude = -53.16 # Latitude of the observer point in degrees
observer_longitude = -70.90 # Longitude of the observer point in degrees
distance = distance_to_sun(observer_latitude, observer_longitude, sun_latitude_degrees, sun_longitude_degrees, sun_height_km)
print(f"Distance from the point on the polar plane to the sun: {distance:.2f} km")
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