🛰️ Orbital Period Calculator
Calculate orbital period, velocity, and frequency for Earth orbits
Distance from Earth's center. For circular orbits, this equals the orbital radius.
Example: 6,871,000 m = 500 km altitude (6,371 km Earth radius + 500 km)
How to Use This Calculator
Enter Semi-Major Axis
Input the semi-major axis of the orbit in meters. For circular orbits, this is the distance from Earth's center to the satellite. Remember to add Earth's radius (6,371 km) to the altitude.
Calculate Orbital Parameters
Click "Calculate" to get the orbital period, velocity, and frequency. The calculator uses Kepler's laws and Newtonian gravity to compute these values accurately.
Interpret Results
Review the orbital period (time for one complete orbit), orbital velocity (speed of the satellite), and frequency (how many orbits per day). These are essential for satellite mission planning.
Formula
Orbital Period: T = 2π√(a³/GM)
Kepler's Third Law
Orbital Velocity: v = √(GM/a)
Where:
- T = Orbital period (seconds)
- v = Orbital velocity (m/s)
- a = Semi-major axis (meters)
- G = Gravitational constant = 6.67430 × 10⁻¹¹ m³kg⁻¹s⁻²
- M = Earth mass = 5.972 × 10²⁴ kg
- π = Pi (3.14159...)
Example Calculation: Low Earth Orbit
For a satellite at 500 km altitude:
- Earth radius: R = 6,371,000 m
- Altitude: h = 500,000 m
- Semi-major axis: a = R + h = 6,871,000 m
Orbital Period:
T = 2π√(a³/GM)
T = 2π√((6,871,000)³ / (6.67430×10⁻¹¹ × 5.972×10²⁴))
T ≈ 5,675 seconds ≈ 94.6 minutes
Orbital Velocity:
v = √(GM/a)
v ≈ 7.61 km/s
Orbits per Day:
Frequency = 86,400 / 5,675 ≈ 15.2 orbits/day
Common Earth Orbits:
- LEO (500 km): Period ~94.6 min, Velocity ~7.61 km/s, ~15.2 orbits/day
- ISS (400 km): Period ~92.6 min, Velocity ~7.66 km/s, ~15.5 orbits/day
- GPS (20,200 km): Period ~12 hours, Velocity ~3.87 km/s, ~2 orbits/day
- Geostationary (35,786 km): Period 24 hours, Velocity ~3.07 km/s, 1 orbit/day
About the Orbital Period Calculator
The Orbital Period Calculator determines the time it takes for a satellite or spacecraft to complete one full orbit around Earth. It uses Kepler's Third Law and Newtonian gravitational mechanics to calculate not only the orbital period, but also the orbital velocity and frequency (orbits per day). This calculator is essential for satellite mission planning, space station operations, and understanding orbital mechanics.
When to Use This Calculator
- Satellite Design: Determine orbital periods for different altitudes
- Mission Planning: Calculate how many orbits per day a satellite will complete
- Ground Station Scheduling: Plan communication windows based on orbital period
- Educational Purposes: Learn about orbital mechanics and Kepler's laws
- Space Station Operations: Understand ISS orbital characteristics
Why Use Our Calculator?
- ✅ Complete Analysis: Calculates period, velocity, and frequency simultaneously
- ✅ Kepler's Laws: Accurate implementation of orbital mechanics
- ✅ Educational Tool: Understand the relationship between altitude and period
- ✅ Real-World Values: Matches actual satellite orbits
- ✅ Free to Use: No registration required
- ✅ Mobile Friendly: Works on all devices
Understanding Orbital Period
The orbital period is the time for one complete orbit:
- Dependence on Altitude: Higher orbits have longer periods. The relationship follows Kepler's Third Law: T² ∝ a³
- Low Earth Orbit: Periods range from ~90-120 minutes (1.5-2 hours)
- Medium Earth Orbit: Periods range from 2-24 hours
- Geostationary Orbit: Exactly 24 hours, matching Earth's rotation
- Orbital Frequency: How many orbits per day = 86,400 seconds / period
Orbital Velocity
Orbital velocity is the speed needed to maintain a circular orbit:
- Inverse Relationship: Higher orbits have lower velocities (v = √(GM/a))
- Low Earth Orbit: ~7.8 km/s (very fast!)
- Geostationary Orbit: ~3.07 km/s (slower, but still 11,000 km/h)
- Escape Velocity: For comparison, Earth's escape velocity is ~11.2 km/s
Real-World Applications
- International Space Station: ~92.6 minute period, 15.5 orbits/day at 400 km altitude
- GPS Satellites: ~12 hour period, 2 orbits/day at 20,200 km altitude
- Geostationary Satellites: Exactly 24 hour period, appears stationary from Earth
- Hubble Space Telescope: ~96 minute period, ~15 orbits/day at 547 km altitude
- Polar Orbiting Satellites: ~98 minute period, used for Earth observation
Tips for Using This Calculator
- For circular orbits, the semi-major axis equals the distance from Earth's center
- Remember to add Earth's radius (6,371 km) when calculating from altitude
- Lower orbits have shorter periods but require higher velocities
- Geostationary orbit is special because its period matches Earth's rotation
- For elliptical orbits, use the semi-major axis (average of perigee and apogee)
Frequently Asked Questions
What is orbital period?
Orbital period is the time it takes for a satellite or spacecraft to complete one full orbit around Earth (or any celestial body). For low Earth orbit, this is typically 90-120 minutes, while geostationary satellites take exactly 24 hours.
How does altitude affect orbital period?
Higher altitude means longer orbital period. This follows Kepler's Third Law: T² ∝ a³. If you double the semi-major axis (distance from Earth's center), the period increases by 2√2 ≈ 2.83 times. For example, 500 km altitude has ~94.6 minute period, while 35,786 km (geostationary) has 24 hour period.
Why do lower orbits have higher velocities?
Lower orbits require higher velocities to overcome Earth's stronger gravitational pull. The relationship is v = √(GM/a), so as distance (a) decreases, velocity must increase to maintain orbit. This is why LEO satellites move at ~7.8 km/s while geostationary satellites move at ~3.07 km/s.
What is the difference between orbital period and orbital frequency?
Orbital period is the time for one complete orbit (e.g., 94.6 minutes). Orbital frequency is how many orbits occur per day (e.g., 15.2 orbits/day). They're inversely related: frequency = 86,400 seconds / period.
How many orbits does the ISS complete per day?
The International Space Station orbits at ~400 km altitude with a period of ~92.6 minutes, completing approximately 15.5 orbits per day. This means astronauts on the ISS see 15-16 sunrises and sunsets per day!
Why is geostationary orbit at exactly 35,786 km?
Geostationary orbit requires a 24-hour period to match Earth's rotation. Using Kepler's Third Law with T = 24 hours, we solve for the semi-major axis and get 42,164 km from Earth's center, which is 35,786 km above the surface (42,164 - 6,378 km Earth radius).