1. What is the Equatorial Longitude Calculation?

The equatorial longitude calculation determines the angular distance east or west of the prime meridian at the equator from given x and y coordinates. It's fundamental in geographic and astronomical coordinate systems.

2. How Does the Calculator Work?

The calculator uses the atan2 function:

Where:

• \( y \) — Y coordinate in arbitrary units
• \( x \) — X coordinate in arbitrary units
• The result is converted from radians to degrees

Explanation: The atan2 function computes the principal value of the arc tangent of y/x, using the signs of both arguments to determine the quadrant of the return value.

3. Importance of Longitude Calculation

Details: Accurate longitude calculation is essential for navigation, mapping, satellite positioning, and various scientific applications involving coordinate systems.

4. Using the Calculator

Tips: Enter both x and y coordinates in the same units. The calculator handles all quadrants correctly, returning values between -180° and +180°.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between atan and atan2?
A: atan2 uses both x and y coordinates to determine the correct quadrant, while atan only uses the ratio y/x and returns values between -π/2 and π/2.

Q2: What coordinate system is this for?
A: This calculation works for any Cartesian coordinate system projected onto the equatorial plane.

Q3: How is this related to geographic longitude?
A: When applied to Earth coordinates, this gives longitude at the equator. For other latitudes, additional spherical trigonometry is needed.

Q4: What's the range of possible outputs?
A: The result ranges from -180° to +180°, with positive values east of the prime meridian and negative values west.

Q5: Can I use negative coordinates?
A: Yes, the calculator handles all combinations of positive and negative x and y values correctly.