1. What is Kepler's Third Law?

Kepler's Third Law relates the orbital period of a planet to the semi-major axis of its orbit around the Sun. It states that the square of the orbital period is proportional to the cube of the semi-major axis.

2. How Does the Calculator Work?

The calculator uses Kepler's Third Law:

Where:

• \( T \) — Orbital period (years)
• \( a \) — Semi-major axis (AU)
• \( G \) — Gravitational constant (6.67430 × 10⁻¹¹ m³/kg·s²)
• \( M_{\odot} \) — Solar mass (1.989 × 10³⁰ kg)
• \( AU \) — Astronomical unit (1.496 × 10¹¹ m)

Explanation: The equation calculates the period in seconds then converts it to years by dividing by the number of seconds in a year (365.25 × 86400).

3. Importance of Orbital Period Calculation

Details: Calculating orbital periods is fundamental in astronomy for understanding planetary motion, exoplanet detection, and spacecraft trajectory planning.

4. Using the Calculator

Tips: Enter the semi-major axis in astronomical units (AU). 1 AU is the Earth-Sun distance (~150 million km). The value must be positive.

5. Frequently Asked Questions (FAQ)

Q1: Does this work for objects orbiting other stars?
A: Yes, but you would need to replace the solar mass with the mass of the star being orbited.

Q2: What if the orbit is highly elliptical?
A: The semi-major axis still determines the period, but the actual distance varies throughout the orbit.

Q3: Why is the Earth's period not exactly 1 year?
A: The calculator uses 365.25 days to account for leap years, but Earth's actual orbital period is about 365.256 days.

Q4: Can this calculate periods of moons?
A: No, this is specifically for objects orbiting the Sun. For moons, you'd need to use the planet's mass instead of the Sun's.

Q5: How accurate is this calculation?
A: Very accurate for simple two-body systems. Real orbits may have small perturbations from other bodies.