1. What is the Planet Year Length Equation?

The Planet Year Length equation calculates the orbital period of a planet around its star using Kepler's Third Law of Planetary Motion. It provides the length of a planet's year in Earth years based on the semi-major axis of its orbit and the mass of its star.

2. How Does the Calculator Work?

The calculator uses the following equation:

Where:

• \( a \) — Semi-major axis of the planet's orbit (in AU)
• \( G \) — Gravitational constant (6.67430 × 10⁻¹¹ m³/kg/s²)
• \( m_{star} \) — Mass of the star (in kg)
• 31536000 — Number of seconds in an Earth year

Explanation: The equation derives from Kepler's Third Law, relating the orbital period of a planet to the size of its orbit and the mass of the star it orbits.

3. Importance of Year Length Calculation

Details: Calculating a planet's year length is fundamental in astronomy for understanding planetary systems, habitability potential, and comparing exoplanets to Earth.

4. Using the Calculator

Tips: Enter the semi-major axis in astronomical units (AU) and the star's mass in kilograms. Both values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the semi-major axis?
A: The semi-major axis is half the longest diameter of an elliptical orbit, representing the average distance between the planet and its star.

Q2: How do I find a star's mass?
A: Star masses are often measured in solar masses (1 M☉ = 1.989 × 10³⁰ kg). Multiply by this value for stars with known solar masses.

Q3: Why is the result in Earth years?
A: Earth years provide a familiar reference frame. The calculation divides by 31,536,000 seconds (1 Earth year) to convert from seconds.

Q4: Does this work for circular orbits?
A: Yes, for circular orbits the semi-major axis is simply the orbital radius.

Q5: What about the planet's mass?
A: The planet's mass is negligible compared to the star's mass in most cases, so it's not included in this simplified calculation.