Earth Orbit Calculator
Calculate Earth satellite orbital velocity, period, and energy for any altitude from LEO to GEO. Free orbital mechanics calculator using Kepler's third law.
Minimum 100 km (above atmosphere). ISS: 400 km, GPS: 20,200 km, GEO: 35,786 km.
Mass is only needed to compute total orbital energy. Velocity and period are mass-independent.
About This Calculator
The Earth Orbit Calculator computes key orbital parameters for satellites in circular orbits around Earth using Newton's law of universal gravitation and Kepler's third law of planetary motion. Enter the altitude above Earth's surface and optionally the satellite mass to get instantaneous results for orbital velocity, orbital period, angular velocity, and total mechanical energy.
Orbital velocity is derived from the balance between centripetal force and gravity: v = sqrt(GM/r). The orbital period follows from Kepler's third law: T = 2π√(r³/GM). Both quantities are independent of the satellite's mass — a 1 kg CubeSat and a 450-ton ISS module orbit at the same speed at the same altitude. Total energy E = -GMm/(2r) does depend on mass and is always negative for bound orbits.
Understanding Earth Orbits
Earth's mass M = 5.972×10²⁴ kg and radius R = 6,371 km define the gravitational field. The standard gravitational parameter μ = GM = 3.986×10⁵ km³/s² is used in all orbital mechanics. At 400 km (ISS altitude), orbital velocity is 7.67 km/s and period is 92.7 minutes. At 35,786 km (geostationary), velocity drops to 3.07 km/s and period equals one sidereal day (23h 56m). The Velocity vs Altitude chart shows the smooth decrease in required speed as altitude increases — a consequence of the inverse square root relationship v ∝ 1/√r.
ISRO's PSLV and GSLV rockets, NASA's Crew Dragon resupply missions, and ESA's Galileo constellation all rely on the same Keplerian mechanics computed by this calculator. Whether you are a physics student studying orbital mechanics, an engineering student designing a CubeSat mission, or a space enthusiast exploring satellite dynamics, this free online tool provides accurate, instant results backed by validated astrophysical constants.
Regional Relevance
India: ISRO's GSAT series at GEO (35,786 km), Cartosat at LEO (600-700 km), and IRNSS/NavIC at GEO and inclined orbits all depend on precise orbital calculations.
United States: NASA's ISS operations at ~400 km, Starlink constellations at ~550 km, and GPS satellites at 20,200 km use these same formulas for mission planning.
United Kingdom: UK Space Agency's OneWeb satellites at 1,200 km LEO, Inmarsat GEO fleet, and Surrey Satellite Technology missions rely on Keplerian orbital mechanics for deployment and station-keeping.
Frequently Asked Questions
How is Earth orbital velocity calculated?
Orbital velocity is calculated using the formula v = sqrt(GM/r), where G = 6.674×10⁻¹¹ N·m²/kg² is the gravitational constant, M = 5.972×10²⁴ kg is Earth's mass, and r is the distance from Earth's center (Earth radius + altitude). For a circular low Earth orbit at 400 km altitude (ISS), the orbital velocity is approximately 7.67 km/s.
What is Earth's orbital period at different altitudes?
Orbital period is calculated using Kepler's third law: T = 2π√(r³/GM). At 200 km altitude, the period is about 88 minutes. At ISS altitude (400 km), it is approximately 92.7 minutes. At GPS altitude (20,200 km), it is about 12 hours. At geostationary orbit (35,786 km), the period equals 24 hours, matching Earth's rotation.
What is geostationary orbit and how is it calculated?
A geostationary orbit (GEO) is a circular orbit at 35,786 km above Earth's equator where the satellite's orbital period matches Earth's rotation period (23h 56m 4s). At this altitude, the satellite appears stationary from the ground. The orbital velocity at GEO is about 3.07 km/s. Communication satellites like INSAT and GSAT series operate in geostationary orbit.
Does satellite mass affect orbital velocity or period?
No, orbital velocity and period are independent of the satellite's mass. This is because in the equation mv²/r = GMm/r², the satellite mass m cancels out on both sides. However, total orbital energy E = -GMm/(2r) does depend on mass. A heavier satellite has more negative total energy, meaning it is more deeply bound in orbit.
How do ISRO, NASA, and UK Space Agency use these calculations?
ISRO's PSLV and GSLV rockets deliver satellites to specific orbits by calculating precise injection velocities. NASA's ISS resupply missions use orbital period to plan rendezvous burns. UK-built OneWeb and Inmarsat satellites use these same Keplerian mechanics for constellation planning. The formulas v = sqrt(GM/r) and T = 2π√(r³/GM) are universal across all space agencies.
What is the minimum altitude for a stable Earth orbit?
The practical minimum altitude for a stable Earth orbit is about 160-200 km. Below this, atmospheric drag causes rapid orbital decay, and the satellite will re-enter within hours to days. The Kármán line at 100 km is the internationally recognized boundary of space, but orbits below 200 km are not sustainable without continuous propulsion.
What is total orbital energy and why is it negative?
Total orbital energy E = KE + PE = ½mv² - GMm/r = -GMm/(2r) for a circular orbit. It is always negative for bound orbits, indicating the satellite cannot escape Earth's gravity. A negative total energy means the satellite is gravitationally bound. Zero total energy corresponds to escape velocity, and positive energy means the object is on an escape trajectory.