Time Since Periapsis In Elliptic Orbit Given Eccentric Anomaly And Time Period Calculator

Formula Used:

\[ t_e = (E - e_e \times \sin(E)) \times \frac{T_e}{2\pi} \]

Eccentric Anomaly (E):

radians

Eccentricity of Elliptical Orbit (e_e):

unitless

Time Period of Elliptic Orbit (T_e):

seconds

Time since Periapsis (t_e):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Time Since Periapsis in Elliptical Orbit?

Time since periapsis in elliptical orbit is a measure of the duration that has passed since an object in orbit passed through its closest point to the central body, known as periapsis. It's a fundamental parameter in orbital mechanics that helps determine the current position of an object along its elliptical path.

2. How Does the Calculator Work?

The calculator uses the Kepler's equation:

\[ t_e = (E - e_e \times \sin(E)) \times \frac{T_e}{2\pi} \]

Where:

\( t_e \) — Time since periapsis (seconds)
\( E \) — Eccentric anomaly (radians)
\( e_e \) — Eccentricity of elliptical orbit (unitless)
\( T_e \) — Time period of elliptic orbit (seconds)
\( \sin \) — Sine trigonometric function
\( \pi \) — Mathematical constant Pi

Explanation: This formula relates the eccentric anomaly to the time elapsed since periapsis passage, accounting for the orbital eccentricity and period.

3. Importance of Time Since Periapsis Calculation

Details: Calculating time since periapsis is crucial for determining the current position of satellites, spacecraft, and celestial bodies in elliptical orbits. It's essential for orbital prediction, mission planning, and navigation in space missions.

4. Using the Calculator

Tips: Enter eccentric anomaly in radians, eccentricity (0-1), and orbital period in seconds. Ensure all values are valid (eccentric anomaly ≥ 0, eccentricity between 0-1, time period > 0).

5. Frequently Asked Questions (FAQ)

Q1: What is eccentric anomaly?
A: Eccentric anomaly is an angular parameter that defines the position of a body moving along a Kepler orbit. It's related to the true anomaly through the eccentricity of the orbit.

Q2: How does eccentricity affect the time calculation?
A: Higher eccentricity values result in more elliptical orbits, which affects the time spent at different parts of the orbit and thus the time since periapsis calculation.

Q3: What are typical values for orbital period?
A: Orbital periods vary greatly - from minutes for low Earth orbits to years for interplanetary missions. For Earth satellites, periods range from about 90 minutes to 24 hours.

Q4: Can this calculator be used for hyperbolic orbits?
A: No, this specific formula is designed for elliptical orbits. Hyperbolic orbits require different equations that account for their open trajectory.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for ideal two-body Keplerian orbits. In real-world applications, perturbations from other bodies and non-spherical gravity fields may require additional corrections.