1. What is the Orbital Period Equation?

The orbital period equation calculates the time a planet or satellite takes to complete one full orbit around a central mass. This is derived from Kepler's Third Law of Planetary Motion and Newton's Law of Universal Gravitation.

2. How Does the Calculator Work?

The calculator uses the orbital period equation:

Where:

• \( T \) — Orbital period (seconds)
• \( r \) — Orbit radius (meters)
• \( G \) — Gravitational constant (6.6743 × 10⁻¹¹ m³/kg s²)
• \( M \) — Mass of central body (kg)

Explanation: The equation shows that orbital period increases with orbit radius and decreases with central mass.

3. Importance of Orbital Period Calculation

Details: Calculating orbital periods is essential for satellite deployment, space mission planning, and understanding planetary motion in astronomy.

4. Using the Calculator

Tips: Enter orbit radius in meters, central mass in kilograms, and gravitational constant. The default G value is 6.6743×10⁻¹¹ m³/kg s².

5. Frequently Asked Questions (FAQ)

Q1: Does this work for elliptical orbits?
A: This equation 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, kilograms for mass, and the standard gravitational constant for consistent results.

Q3: Can I calculate for Earth's orbit around the Sun?
A: Yes, use Sun's mass (1.989 × 10³⁰ kg) and Earth's average orbital radius (1.496 × 10¹¹ m).

Q4: Why is G so small?
A: The gravitational constant is a fundamental physical constant with a small value, reflecting the relative weakness of gravity compared to other forces.

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