What is the compass heading from San Diego to Avalon Catalina?

To find the compass heading from San Diego to Avalon Catalina, we can use the Great Circle distance formula to calculate the angle between the two locations. Let's assume the coordinates of San Diego are (32.7157° N, 117.1611° W) and the coordinates of Avalon Catalina are (33.3406° N, 118.3590° W).

1. Calculate the difference in latitude (Δφ) and difference in longitude (Δλ):

Δφ = φ2 - φ1 = 33.3406° - 32.7157° = 0.6249°

Δλ = λ2 - λ1 = 118.3590° - 117.1611° = 1.1979°

2. Convert the latitude and longitude differences to radians:

Δφ (in radians) = 0.6249° * (π/180) = 0.0109 radians

Δλ (in radians) = 1.1979° * (π/180) = 0.0209 radians

3. Use the Great Circle distance formula to calculate the compass heading (θ):

θ = atan2(sin(Δλ) * cos(φ2), cos(φ1) * sin(φ2) - sin(φ1) * cos(φ2) * cos(Δλ))

θ = atan2(sin(0.0209) * cos(33.3406°), cos(32.7157°) * sin(33.3406°) - sin(32.7157°) * cos(33.3406°) * cos(0.0209))

θ = 0.1885 radians

4. Convert the compass heading from radians to degrees:

θ (in degrees) = 0.1885 radians * (180/π) = 10.78°

Therefore, the compass heading from San Diego to Avalon Catalina is approximately 10.78°.