calculate_orbital_period
Calculate orbital period for circular orbits using Kepler's Third Law. Input orbital radius and central body mass to get period, velocity, and time conversions.
Instructions
Calculate orbital period: T = 2π√(r³/GM).
Kepler's Third Law for circular orbits. Period depends on orbital
radius and central body mass.
Args:
orbital_radius: Orbital radius in meters (from center of central body)
central_mass: Mass of central body in kg
gravitational_constant: G in m³/(kg⋅s²) (default 6.674e-11)
Returns:
Dict containing:
- period: Orbital period in seconds
- orbital_velocity: v in m/s
- period_hours: Period in hours (for convenience)
- period_days: Period in days (for convenience)
Tips for LLMs:
- Higher orbit → longer period
- More massive central body → shorter period
- Earth: M = 5.972e24 kg, R = 6.371e6 m
- Moon orbit: r ≈ 384,400 km, T ≈ 27.3 days
- ISS orbit: r ≈ 6,771 km (altitude 400 km), T ≈ 90 minutes
Example - ISS orbit:
result = await calculate_orbital_period(
orbital_radius=6.771e6, # meters
central_mass=5.972e24 # Earth mass (kg)
)
# T ≈ 5,558 seconds ≈ 92.6 minutesInput Schema
TableJSON Schema
| Name | Required | Description | Default |
|---|---|---|---|
| orbital_radius | Yes | ||
| central_mass | Yes | ||
| gravitational_constant | No |