Latitude Given Coriolis Frequency Calculator

Formula Used:

\[ \lambda_e = \sin^{-1}\left(\frac{f}{2 \cdot \Omega_E}\right) \]

Earth Station Latitude (λe):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Earth Station Latitude Calculation?

The Earth Station Latitude calculation determines the geographic latitude of an earth station based on the Coriolis frequency and the angular speed of the Earth. This is derived from the relationship between the Coriolis parameter and latitude.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \lambda_e = \sin^{-1}\left(\frac{f}{2 \cdot \Omega_E}\right) \]

Where:

\( \lambda_e \) — Earth Station latitude (radians)
\( f \) — Coriolis Frequency (Hz)
\( \Omega_E \) — Angular Speed of the Earth (rad/s)

Explanation: The formula calculates the inverse sine of the ratio between Coriolis frequency and twice the angular speed of the Earth to determine the latitude.

3. Importance of Earth Station Latitude Calculation

Details: Accurate latitude calculation is crucial for earth station positioning, satellite communication systems, and understanding geophysical phenomena related to Earth's rotation.

4. Using the Calculator

Tips: Enter Coriolis frequency in Hz and angular speed of the Earth in rad/s. The default value for Earth's angular speed is approximately 7.2921159 × 10⁻⁵ rad/s. Ensure f/(2*ΩE) is between -1 and 1 for valid results.

5. Frequently Asked Questions (FAQ)

Q1: What is Coriolis frequency?
A: Coriolis frequency, also called the Coriolis parameter, is equal to twice the rotation rate of the Earth multiplied by the sine of the latitude.

Q2: What is the standard angular speed of the Earth?
A: The Earth rotates at approximately 7.2921159 × 10⁻⁵ radians per second, which is about 15 degrees per hour.

Q3: Why is the result in degrees?
A: While the mathematical calculation produces radians, the result is converted to degrees for easier interpretation, as geographic coordinates are typically expressed in degrees.

Q4: What are the valid input ranges?
A: Coriolis frequency must be non-negative, angular speed must be positive, and the ratio f/(2*ΩE) must be between -1 and 1 for a valid result.

Q5: Can this calculation be used for any celestial body?
A: The formula is specific to Earth as it uses Earth's angular speed. For other celestial bodies, their respective angular speeds would need to be used.