Earth Orbit Calculator

Find how fast a satellite must travel and how long its orbit takes.

How the Math Works

The Earth Orbit Calculator uses two fundamental physics equations to determine orbital characteristics. The orbital speed formula v = √(GM/r) calculates how fast an object must travel to maintain a stable orbit at a specific altitude, where G is the gravitational constant, M is Earth's mass, and r is the distance from Earth's center. The period formula T = 2π·√(r³/GM) determines how long it takes to complete one orbit. Both formulas derive from Newton's law of gravitation and the requirement for centripetal force in circular motion, showing how gravity provides the necessary inward force to keep satellites in orbit.

Practical Applications

To use this calculator, simply enter your desired altitude above Earth's surface in kilometers or miles. The calculator automatically converts this to the orbital radius by adding Earth's average radius (approximately 6,371 km). For example, at 400 km altitude, the orbital radius is about 6,771 km, resulting in an orbital speed of roughly 7.67 km/s and a period of approximately 92 minutes. This helps aerospace engineers design satellite missions, determine fuel requirements, and plan orbital maneuvers for spacecraft deployment.

Day-to-Day Use

While most people don't calculate orbital mechanics daily, this knowledge underpins many modern technologies we use constantly. Your GPS device relies on satellites in precise orbits calculated using these very formulas. Every weather forecast you check depends on satellite data from orbits determined by these calculations. Understanding orbital speeds and periods also helps explain why the International Space Station orbits Earth every 90 minutes, giving astronauts a unique perspective on our planet, and why different satellites serve different purposes based on their orbital characteristics.

Worked example

400 km (ISS altitude) → about 7672 m/s, 92.6 min period.

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