1. What is Kepler's Third Law?

Kepler's Third Law states that the square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit. For our solar system, when using astronomical units (AU) and Earth years, the simplified form is T² = a³.

2. How Does the Calculator Work?

The calculator uses Kepler's Third Law equation:

Where:

• \( T \) — Orbital period in Earth years
• \( a \) — Semi-major axis in astronomical units (AU)

Explanation: This relationship shows that planets farther from the Sun have longer orbital periods. For example, at 1 AU (Earth's distance), the period is 1 year.

3. Importance of Orbital Period Calculation

Details: Understanding orbital periods is fundamental in astronomy for predicting planetary positions, planning space missions, and studying exoplanetary systems.

4. Using the Calculator

Tips: Enter the semi-major axis in AU (1 AU = Earth-Sun distance). The value must be positive. For example, Mars is at about 1.52 AU.

5. Frequently Asked Questions (FAQ)

Q1: Why does this only work for our solar system?
A: The simplified form T² = a³ assumes the central mass is 1 solar mass. For other systems, the full form including masses is needed.

Q2: What's the difference between AU and light years?
A: 1 AU is about 93 million miles (Earth-Sun distance), while 1 light year is about 63,241 AU - used for interstellar distances.

Q3: How accurate is this for elliptical orbits?
A: The semi-major axis accounts for ellipticity - the formula works for all closed orbits (circles are special cases of ellipses).

Q4: Can I use this for moons?
A: No, this is for planets orbiting the Sun. Moon orbits would require using Earth's mass instead of the Sun's.

Q5: What about relativistic effects?
A: For most solar system objects, Newtonian physics suffices. Near very massive objects or at high speeds, general relativity adjustments are needed.