Question

Assuming that the polar flattening of the Earth \( f = 3.353 \times 10^{-3} \), the difference between the geodetic and geocentric latitudes is maximum at

• A. the poles
• B. 60° geocentric latitude
• C. 45° geocentric latitude
• D. 30° geocentric latitude

Hint:

Remember: The geodetic and geocentric latitudes are equal at the equator and poles. The maximum difference occurs at 45°, because the sine function peaks at that angle.

Answer 1

The Correct Option is C

Step 1: Understanding the difference.
- The geocentric latitude is the angle between the equatorial plane and a line from the Earth's center.
- The geodetic latitude is the angle between the equatorial plane and the normal to the reference ellipsoid.
Because Earth is an oblate spheroid (\(f > 0\)), these two latitudes are not identical except at the equator and poles. Step 2: Expression for the difference.
The difference between geodetic (\(\phi\)) and geocentric (\(\theta\)) latitude is given approximately by: \[ \phi - \theta \approx f \sin(2\phi) \] where \(f\) is the flattening. Step 3: Maximization condition.
The maximum difference occurs when \(\sin(2\phi)\) is maximum.
\(\sin(2\phi)\) attains its maximum value \(= 1\) at \[ 2\phi = 90^\circ \quad \Rightarrow \quad \phi = 45^\circ \] Step 4: Conclusion.
Thus, the difference between geodetic and geocentric latitudes is maximum at \(45^\circ\) latitude. \[ \boxed{\text{Option (C) 45° geocentric latitude}} \]