Earth Orbit Calculator

The physics of orbiting bodies relies on balancing gravitational force with centripetal acceleration. Using Earth's gravitational parameter (derived from the gravitational constant G and Earth's mass M), we compute orbital parameters based on the orbital radius r, which equals Earth's mean radius (6,371 km) plus the satellite's height above the surface.

The orbital speed (v) is calculated using the formula: v = sqrt((G * M) / r), where G * M is approximately 3.986 x 10^14 m^3/s^2. The orbital period (T)—the time it takes to complete one full revolution—is derived from Kepler's Third Law: T = sqrt((4 * pi^2 * r^3) / (G * M)).

Let us calculate the orbital speed and period for a satellite placed at a height of 500 kilometers above Earth. First, find the total orbital radius (r) by adding Earth's radius: r = 6,371 km + 500 km = 6,871 km, or 6,871,000 meters.

Next, substitute r into the orbital speed formula: v = sqrt((3.986 x 10^14) / 6,871,000) which yields approximately 7,613 meters per second, or about 26,400 kilometers per hour. For the orbital period, apply Kepler's equation: T = sqrt((4 * pi^2 * (6,871,000)^3) / (3.986 x 10^14)), resulting in roughly 5,676 seconds, which is about 94.6 minutes per orbit.

Always ensure your units are consistent; convert kilometers to meters when working with standard gravitational constants. Keep in mind that these calculations assume a perfectly circular orbit; elliptical orbits require semi-major axis measurements and more complex eccentricity variables. Furthermore, this tool assumes a spherical Earth model, which is sufficient for general estimations but varies slightly from Earth's actual oblate spheroid shape.