How To Calculator Orbital Period

Orbital Period Equation:

\[ T = 2\pi \sqrt{\frac{r^3}{G M}} \]

Orbital Period (T):

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1. What is Orbital Period?

The orbital period is the time a given astronomical object takes to complete one orbit around another object. This calculator computes the period for a circular orbit using Kepler's third law.

2. How Does the Calculator Work?

The calculator uses the orbital period equation:

\[ T = 2\pi \sqrt{\frac{r^3}{G M}} \]

Where:

\( T \) — Orbital period (seconds)
\( r \) — Orbital radius (meters)
\( G \) — Gravitational constant (6.67430 × 10⁻¹¹ m³/kg·s²)
\( M \) — Mass of central body (kg)

Explanation: The equation shows that the period squared is proportional to the orbital radius cubed (Kepler's third law).

3. Importance of Orbital Period Calculation

Details: Calculating orbital periods is essential for satellite deployment, space mission planning, and understanding celestial mechanics.

4. Using the Calculator

Tips: Enter the orbital radius in meters and the central mass in kilograms. Both values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: Does this work for elliptical orbits?
A: This calculator is for circular orbits. For elliptical orbits, use the semi-major axis instead of radius.

Q2: What units should I use?
A: Use meters for distance and kilograms for mass to get results in seconds.

Q3: Can I calculate for multiple objects?
A: The equation works for any two-body system where one mass is much larger than the other.

Q4: How accurate is this calculation?
A: It's theoretically exact for ideal two-body systems without external perturbations.

Q5: What's the gravitational constant value?
A: G = 6.67430 × 10⁻¹¹ m³/kg·s² (2018 CODATA recommended value).