1. What is Sidereal Period?

The sidereal period is the time it takes for a planet to complete one full orbit around the Sun relative to the fixed stars. It's a fundamental orbital parameter in astronomy.

2. How Does the Calculator Work?

The calculator uses Kepler's third law formula:

Where:

• \( P \) — Sidereal period (seconds)
• \( a \) — Semi-major axis of orbit (meters)
• \( G \) — Gravitational constant (6.67430 × 10⁻¹¹ m³/kg·s²)
• \( M_{sun} \) — Mass of the Sun (1.9885 × 10³⁰ kg)

Explanation: The equation shows that the square of the orbital period is proportional to the cube of the semi-major axis of its orbit.

3. Importance of Sidereal Period

Details: Knowing a planet's sidereal period is essential for understanding its orbital dynamics, predicting its position, and planning space missions.

4. Using the Calculator

Tips: Enter the semi-major axis in meters. Default values are provided for gravitational constant and solar mass. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between sidereal and synodic period?
A: Sidereal period is relative to distant stars, while synodic period is relative to Earth's position (e.g., time between conjunctions).

Q2: How to convert the result to Earth years?
A: Divide the result in seconds by 31,557,600 (seconds in a sidereal year).

Q3: Why does this formula work for all planets?
A: Kepler's third law is universal for any two-body system, with the period depending only on the semi-major axis and the masses.

Q4: Can this be used for moons orbiting planets?
A: Yes, by replacing the solar mass with the planet's mass in the calculation.

Q5: What if I know the period and want to find the semi-major axis?
A: The formula can be rearranged to solve for a: \( a = \sqrt[3]{\frac{P^2 G M}{4 \pi^2}} \)