Calculate Satellite Position From Tle

Calculate precise satellite positions using Two-Line Element (TLE) data with this orbital mechanics calculator. Enter your TLE parameters and get real-time position coordinates in Earth-Centered Inertial (ECI) or Earth-Centered Earth-Fixed (ECEF) frames.

How to Use This Calculator

To calculate a satellite's position from TLE data:

Enter the first line of the TLE (Line 1) in the designated field
Enter the second line of the TLE (Line 2) in the corresponding field
Select the time for which you want the position calculation
Choose the coordinate frame (ECI or ECEF)
Click "Calculate" to get the satellite's position

TLE data is typically provided by NORAD and includes orbital elements that describe a satellite's position and velocity.

Formula Used

The satellite position is calculated using the SGP4 algorithm, which is the standard for propagating TLE data. The algorithm converts the TLE elements into position and velocity vectors in the Earth-Centered Inertial (ECI) frame, which can then be transformed to Earth-Centered Earth-Fixed (ECEF) coordinates if needed.

// SGP4 Algorithm Pseudocode function sgp4(tle, time) { // Parse TLE elements const elements = parseTLE(tle); // Initialize orbital parameters const [a, e, i, Ω, ω, M] = elements; // Calculate mean anomaly at epoch const M0 = M; // Calculate mean motion const n = calculateMeanMotion(a); // Calculate time since epoch const Δt = time - epoch; // Calculate mean anomaly const M = M0 + n * Δt; // Solve Kepler's equation const E = solveKeplersEquation(M, e); // Calculate true anomaly const ν = calculateTrueAnomaly(E, e); // Calculate position in orbital plane const [r, v] = calculatePositionVelocity(a, e, ν); // Rotate to ECI frame const positionECI = rotateToECI(r, i, Ω, ω); // Convert to ECEF if needed const positionECEF = convertECItoECEF(positionECI, time); return positionECEF; }

Worked Example

Let's calculate the position of a satellite with the following TLE data:

Line 1: 1 25544U 98067A 21001.50000000 .00001677 00000-0 38782-4 0 9993 Line 2: 2 25544 51.6432 103.3786 0007240 39.7646 65.0