Time Period Of Elliptical Orbit Given Semi-Major Axis Calculator

Formula Used:

\[ T_e = \frac{2 \pi a_e^2 \sqrt{1 - e_e^2}}{h_e} \]

Time Period of Elliptic Orbit (T_e):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Time Period of Elliptical Orbit?

The Time Period of Elliptical Orbit is the amount of time a given astronomical object takes to complete one full orbit around another object in an elliptical path. It is a fundamental parameter in orbital mechanics and celestial dynamics.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ T_e = \frac{2 \pi a_e^2 \sqrt{1 - e_e^2}}{h_e} \]

Where:

\( T_e \) — Time Period of Elliptic Orbit (s)
\( a_e \) — Semi Major Axis of Elliptic Orbit (m)
\( e_e \) — Eccentricity of Elliptical Orbit
\( h_e \) — Angular Momentum of Elliptic Orbit (m²/s)
\( \pi \) — Archimedes' constant (≈3.14159)

Explanation: This formula calculates the orbital period based on the semi-major axis, eccentricity, and angular momentum of the elliptical orbit.

3. Importance of Time Period Calculation

Details: Calculating the orbital period is crucial for understanding celestial mechanics, predicting orbital positions, planning space missions, and studying gravitational interactions between celestial bodies.

4. Using the Calculator

Tips: Enter semi-major axis in meters, eccentricity (0 ≤ e < 1), and angular momentum in m²/s. All values must be positive, and eccentricity must be between 0 and 1.

5. Frequently Asked Questions (FAQ)

Q1: What is the relationship between semi-major axis and orbital period?
A: According to Kepler's third law, the square of the orbital period is proportional to the cube of the semi-major axis for elliptical orbits.

Q2: How does eccentricity affect the orbital period?
A: For a given semi-major axis, the orbital period remains constant regardless of eccentricity, as described by Kepler's third law.

Q3: What are typical values for these parameters?
A: Values vary greatly depending on the celestial body. For Earth's orbit around the Sun: a ≈ 149.6 million km, e ≈ 0.0167, T ≈ 365.25 days.

Q4: Can this formula be used for circular orbits?
A: Yes, for circular orbits (e = 0), the formula simplifies to \( T_e = \frac{2 \pi a_e^2}{h_e} \).

Q5: What are the limitations of this formula?
A: This formula assumes a two-body system and doesn't account for perturbations from other bodies, relativistic effects, or non-spherical gravitational fields.