Earth Orbit Calculator

An Earth orbit is a continuous free fall in which a spacecraft moves sideways quickly enough that Earth's curved surface falls away beneath it. For an ideal circular orbit, altitude determines orbital radius, speed, and period. This calculator adds the entered altitude to a mean Earth radius of 6,371 kilometers and applies the standard gravitational parameter for Earth, 3.986004418 × 10^14 cubic meters per second squared. Circular orbital velocity is the square root of Earth's gravitational parameter divided by orbital radius. A lower orbit requires a higher speed because gravity is stronger closer to Earth. Orbital period follows Kepler's third law: two pi multiplied by the square root of radius cubed divided by the gravitational parameter. Period increases rapidly with altitude, from roughly ninety minutes in low Earth orbit to nearly one sidereal day near geosynchronous altitude. Local escape velocity is the minimum ideal instantaneous speed needed to depart from the current radius without further propulsion, ignoring the atmosphere and other bodies. It equals the circular speed multiplied by the square root of two. A satellite already in circular orbit would need a velocity change to reach escape speed; the displayed number is the total local speed, not the required engine delta-v. Gravitational force depends on satellite mass as well as radius. The calculator multiplies satellite mass by Earth's gravitational parameter and divides by radius squared. Mass does not affect orbital speed or period in this two-body approximation because inertial and gravitational mass cancel, but doubling satellite mass doubles the gravitational force. The corresponding acceleration remains the same. Real missions require more detailed models. Earth is oblate, its atmosphere creates drag in low orbit, the Moon and Sun perturb trajectories, and spacecraft often travel on elliptical rather than circular paths. Altitude also varies over uneven terrain, whereas this calculator references a mean spherical radius. Use these outputs for education, preliminary estimates, and consistency checks. Mission design and operational navigation require validated ephemerides, perturbation models, coordinate systems, and safety margins.