Earth Orbit Calculator

A satellite is any object that orbits a larger body. Earth itself is a satellite of the Sun, and the Moon is Earth's only natural satellite. Artificial satellites are spacecraft deliberately launched into orbit — from tiny CubeSats in low Earth orbit to geostationary communication satellites at ~35,786 km altitude.

Orbital speed is found using the formula: v = √(G·Mₑ / (Rₑ + h)), where G is the gravitational constant (6.674 × 10⁻¹¹ N·m²/kg²), Mₑ is Earth's mass (5.972 × 10²⁴ kg), Rₑ is Earth's mean radius (6,371 km), and h is the altitude above the surface. A satellite at 400 km altitude travels at roughly 7.67 km/s.

The orbital period T = 2π × √((Rₑ + h)³ / (G·Mₑ)). This is derived from Kepler's third law. The ISS at ~400 km completes one orbit in roughly 92 minutes, while geostationary satellites at ~35,786 km take exactly 24 hours to match Earth's rotation.

The orbital period depends solely on the orbital altitude (or semi-major axis) and Earth's gravitational parameter. Crucially, a satellite's mass does not affect its period — two satellites at the same altitude, regardless of size or weight, will have the same orbital period. This follows directly from Newton's law of gravitation.

Gravity provides the centripetal force needed for circular orbit. When you set gravitational force equal to centripetal force and solve for velocity, the satellite's mass cancels out completely. Only the orbital radius and Earth's gravitational parameter matter, so mass is irrelevant to orbital speed or period.

Geostationary orbit exists at the unique altitude where a satellite's orbital period equals exactly 24 hours (one Earth sidereal day). This altitude is fixed by Earth's mass and rotation rate — it cannot be moved. A satellite at any other altitude will either orbit faster or slower than Earth's rotation and will not appear stationary from the ground.

Escape velocity is the minimum speed an object needs to break free from Earth's gravity without further propulsion. At Earth's surface it is about 11.19 km/s, and it decreases with altitude following v_esc = √(2·G·Mₑ / (Rₑ + h)). At 400 km altitude (ISS level) escape velocity is roughly 10.85 km/s.

Apogee is the farthest point of an elliptical orbit from Earth's center, and perigee is the closest point. Together they define the shape and size of the orbit. The semi-major axis equals half the sum of apogee and perigee distances from Earth's center, and the eccentricity describes how elliptical the orbit is (0 = circular, approaching 1 = highly elliptical).