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🌍 Earth Orbit Calculator

Calculate orbital period, velocity, and altitude for Earth orbits

For circular orbits, this equals the distance from Earth's center. Earth radius: ~6,371 km

Example: 6871 km = 6,871,000 m (500 km altitude)

How to Use This Calculator

1

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. For example, a 500 km altitude orbit has a semi-major axis of 6,871,000 m (6,371 km Earth radius + 500 km altitude).

2

Calculate Orbital Parameters

Click "Calculate" to get the orbital period, velocity, and altitude. The calculator uses Kepler's laws and Newtonian gravity to compute these values.

3

Interpret Results

Review the orbital period (how long one orbit takes), orbital velocity (how fast the satellite moves), and altitude above Earth's surface. These values are essential for satellite mission planning.

Formula

Orbital Period: T = 2π√(a³/GM)

Kepler's Third Law

Orbital Velocity: v = √(GM/a)

Circular Orbit Velocity

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:

For a satellite in low Earth orbit 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 = √((6.67430×10⁻¹¹ × 5.972×10²⁴) / 6,871,000)

v ≈ 7.61 km/s

Common Earth Orbits:

  • Low Earth Orbit (LEO): 160-2,000 km altitude, ~90-120 min period, ~7.8 km/s
  • Medium Earth Orbit (MEO): 2,000-35,786 km altitude, 2-24 hours period
  • Geostationary Orbit: 35,786 km altitude, 24 hours period, ~3.07 km/s
  • Polar Orbit: ~700-800 km altitude, ~98 min period

About the Earth Orbit Calculator

The Earth Orbit Calculator determines orbital parameters for satellites and spacecraft orbiting Earth. It uses Kepler's laws and Newtonian gravitational mechanics to calculate orbital period, velocity, and altitude. This calculator is essential for satellite mission planning, space station operations, and understanding orbital mechanics.

When to Use This Calculator

  • Satellite Design: Determine orbital parameters for new satellites
  • Mission Planning: Calculate required orbital periods and velocities
  • Educational Purposes: Learn about orbital mechanics and Kepler's laws
  • Space Station Operations: Understand International Space Station orbit characteristics
  • Astronomy: Calculate orbital parameters for Earth-orbiting telescopes

Why Use Our Calculator?

  • ✅ Kepler's Laws: Accurate implementation of orbital mechanics
  • ✅ Multiple Parameters: Calculate period, velocity, and altitude simultaneously
  • ✅ Educational Tool: Understand the relationship between orbital parameters
  • ✅ Real-World Applications: Values match actual satellite orbits
  • ✅ Free to Use: No registration required
  • ✅ Mobile Friendly: Works on all devices

Understanding Orbital Parameters

Three key parameters describe an orbit:

  • Orbital Period: The time it takes for one complete orbit. Lower orbits have shorter periods (LEO: ~90 minutes), while geostationary orbit matches Earth's rotation (24 hours).
  • Orbital Velocity: The speed at which the satellite travels. Lower orbits require higher velocities (LEO: ~7.8 km/s), while higher orbits are slower (geostationary: ~3.07 km/s).
  • Altitude: The height above Earth's surface. This affects orbital period, velocity, and atmospheric drag. Most satellites orbit between 160 km and 36,000 km altitude.

Kepler's Laws

This calculator is based on Kepler's laws of planetary motion, discovered by Johannes Kepler in the early 17th century:

  • First Law: Orbits are elliptical with the central body at one focus
  • Second Law: A line connecting the satellite to Earth sweeps equal areas in equal times
  • Third Law: The square of the orbital period is proportional to the cube of the semi-major axis (T² ∝ a³)

Types of Earth Orbits

  • Low Earth Orbit (LEO): 160-2,000 km altitude. Used by ISS, Hubble, most satellites. Fast orbital periods (~90-120 min).
  • Medium Earth Orbit (MEO): 2,000-35,786 km altitude. Used by GPS satellites. Periods range from 2-24 hours.
  • Geostationary Orbit (GEO): Exactly 35,786 km altitude. 24-hour period matches Earth's rotation. Used by communications satellites.
  • Polar Orbit: Passes over Earth's poles. Used for Earth observation and weather satellites.

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 require more frequent station-keeping due to atmospheric drag
  • Geostationary orbit is special: satellites appear stationary relative to Earth's surface
  • For elliptical orbits, the semi-major axis is the average of perigee and apogee distances

Frequently Asked Questions

What is the semi-major axis?

The semi-major axis (a) is half the longest diameter of an elliptical orbit. For circular orbits, it equals the distance from Earth's center to the satellite. It's the key parameter that determines orbital period according to Kepler's third law.

How does altitude affect orbital period?

Higher altitude means longer orbital period. This relationship follows Kepler's third law: T² ∝ a³. A satellite at 500 km takes ~94 minutes, while one at 35,786 km (geostationary) takes exactly 24 hours.

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 geostationary orbit?

Geostationary orbit is at exactly 35,786 km altitude where the orbital period matches Earth's 24-hour rotation. Satellites in this orbit appear stationary relative to Earth's surface, making them ideal for communications and weather monitoring.

Can this calculator be used for elliptical orbits?

Yes, but you need to use the semi-major axis, which is the average of the perigee (closest) and apogee (farthest) distances. The calculated period and average velocity apply to elliptical orbits, though the actual velocity varies throughout the orbit.

What altitude is the International Space Station?

The ISS orbits at approximately 400-420 km altitude, with an orbital period of about 92-93 minutes. It travels at roughly 7.66 km/s, completing about 15.5 orbits per day.