1. What is the Lunar Orbital Period Equation?

The Lunar Orbital Period equation calculates the time it takes for an object to complete one orbit around the Moon based on its semi-major axis. This is derived from Kepler's Third Law of Planetary Motion.

2. How Does the Calculator Work?

The calculator uses the orbital period equation:

Where:

• \( T \) — Orbital period in seconds
• \( a \) — Semi-major axis in meters
• \( G \) — Gravitational constant (6.67430 × 10⁻¹¹ m³/kg·s²)
• \( M_{moon} \) — Mass of the Moon (7.342 × 10²² kg)

Explanation: The equation shows that the orbital period depends on the cube of the semi-major axis and the mass of the Moon.

3. Importance of Orbital Period Calculation

Details: Calculating orbital periods is essential for mission planning around the Moon, satellite deployment, and understanding lunar orbital mechanics.

4. Using the Calculator

Tips: Enter the semi-major axis in meters (distance from the Moon's center to the orbiting object). The value must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is semi-major axis?
A: For circular orbits, it's simply the radius. For elliptical orbits, it's half the longest diameter.

Q2: Does this work for orbits around other bodies?
A: Yes, but you would need to substitute the appropriate mass value for the central body.

Q3: What are typical values for lunar orbits?
A: Low lunar orbits might be 1,800 km (1,800,000 m) above the surface, which is about 2,440 km (2,440,000 m) from the Moon's center.

Q4: Why is the Moon's mass important?
A: The gravitational force depends on the mass of both objects, but since the satellite's mass is negligible compared to the Moon's, only the Moon's mass appears in the equation.

Q5: How does this relate to Kepler's Third Law?
A: This is a direct application of Kepler's Third Law, which states that the square of the orbital period is proportional to the cube of the semi-major axis.