Free Earth Orbit Calculator

Earth Orbit Calculator: Orbital Speed and Period for Satellites

The Earth Orbit Calculator is a versatile tool designed to compute the orbital speed and orbital period of any satellite around Earth, given its altitude above mean sea level. Acting as both an orbital speed calculator and an orbital period calculator, it applies the universal laws of gravitation and circular motion to provide accurate orbital parameters. Whether you are analyzing the International Space Station (ISS), a weather satellite, or a theoretical payload, this satellite orbit calculator delivers rapid, reliable results.

Background: Satellites and Their Orbits

A satellite is any object—natural or artificial—that orbits a larger celestial body. Earth itself is a satellite of the Sun, and the Moon is Earth's natural satellite. Most man‑made satellites are placed into specific orbits depending on their purpose: Low Earth Orbit (LEO), Medium Earth Orbit (MEO), or Geostationary Orbit (GEO). The first artificial satellite, Sputnik 1, was launched in 1957 into an elliptical LEO at 939 km altitude. Since then, thousands of satellites have been deployed for communication, Earth observation, navigation, and scientific exploration.

For circular orbits—a good approximation for many Earth satellites—the orbital speed and period depend exclusively on the radial distance from Earth’s center. The Earth Orbit Calculator simplifies computation by assuming circular motion, yielding accurate results for typical altitudes.

Key Formulas

The calculator applies Newton’s law of gravitation and the centripetal force equation. The input variables are:

• $G$ — gravitational constant ($6.67430 \times 10^{-11}\ \text{m}^3\ \text{kg}^{-1}\ \text{s}^{-2}$)
• $M$ — Earth’s mass ($5.972 \times 10^{24}\ \text{kg}$)
• $R$ — Earth’s mean radius ($6,371\ \text{km}$)
• $h$ — satellite altitude above Earth’s surface ($\text{km}$)

The orbital speed $v$ is derived from the condition that gravitational attraction equals the required centripetal force:

$$v = \sqrt{\dfrac{G M}{R + h}}$$

The orbital period $T$ follows from the relationship between speed and circumference, or from Newton’s form of Kepler’s third law:

$$T^2 = \dfrac{4\pi^2}{G M} (R + h)^3$$

With these equations, only the altitude $h$ is needed to obtain both parameters instantly.

How to Use the Calculator

1. Choose whether you want the orbital speed, orbital period, or both using this satellite speed calculator.
2. Input the satellite’s altitude in kilometers.
3. The tool returns the speed in km/s and the period in hours (or other selectable units).

This eliminates manual computation and is particularly helpful when comparing multiple altitudes.

Example: International Space Station (ISS)

The ISS circles Earth at approximately 400 km average altitude. Substituting $h = 400\ \text{km}$:

• Orbital speed: $v \approx 7.672\ \text{km/s}$
• Orbital period: $T \approx 1.54\ \text{hours}$ (92.6 minutes)

These values match real ISS telemetry and demonstrate how fast the station moves to maintain orbit.

Effects of Altitude

Higher orbits produce lower speeds and longer periods. For instance, a satellite in geostationary orbit at 35,786 km altitude has a period of exactly 24 hours, appearing stationary from Earth. This calculator helps explore such relationships easily.

Extending the Tool

Although configured for Earth, the same formulas apply to any central body. By replacing $M$ and $R$ with values for another planet or moon, you can compute orbital parameters around that body. Therefore, the Earth Orbit Calculator also serves as a foundational learning tool for orbital mechanics.