1. What is the Orbital Period to Distance Calculation?

This calculation determines the semi-major axis (average distance) of an orbiting body based on its orbital period and the mass of the central body. It's derived from Kepler's Third Law of Planetary Motion.

2. How Does the Calculator Work?

The calculator uses the following equation:

Where:

• \( a \) — Semi-major axis (distance) in meters
• \( T \) — Orbital period in seconds
• \( G \) — Gravitational constant (6.67430 × 10⁻¹¹ m³/kg·s²)
• \( M \) — Mass of the central body in kilograms

Explanation: This equation relates the cube of the orbital distance to the square of the orbital period, with the gravitational constant providing the proportionality factor.

3. Importance of Orbital Calculations

Details: These calculations are fundamental in astronomy and space exploration, used for determining satellite orbits, planetary motions, and spacecraft trajectories.

4. Using the Calculator

Tips: Enter the orbital period in seconds and the mass of the central body in kilograms. For Earth, mass is approximately 5.972 × 10²⁴ kg.

5. Frequently Asked Questions (FAQ)

Q1: What units should I use for input?
A: The calculator expects the period in seconds and mass in kilograms. Convert other units accordingly.

Q2: Does this work for circular orbits?
A: Yes, for circular orbits the semi-major axis equals the orbital radius.

Q3: Can I use this for binary star systems?
A: For binary systems, you need to use the reduced mass of the system.

Q4: What's the difference between semi-major axis and distance?
A: Semi-major axis is the average distance for elliptical orbits. For circular orbits, they're equal.

Q5: How accurate is this calculation?
A: It's highly accurate for two-body systems without significant perturbations.