Orbital Velocity Calculator
Calculate orbital velocity, orbital period, and escape velocity for satellites and spacecraft around celestial bodies including Earth, Sun, Moon, Mars, Jupiter, and Saturn.
About This Calculator
Orbital velocity is the minimum speed an object needs to maintain a stable circular orbit around a celestial body. Governed by Newton's law of universal gravitation, the formula v = sqrt(GM/r) shows that velocity depends only on the central body's mass and the orbital radius -- the satellite's own mass is irrelevant. Our calculator supports six celestial bodies (Earth, Sun, Moon, Mars, Jupiter, Saturn) with accurate mass and radius data from NASA and JPL.
For each calculation, you get three key results: orbital velocity (km/s), orbital period (hours), and escape velocity (km/s). The Velocity vs Radius chart shows how velocity decreases as orbital radius increases, illustrating the inverse square root relationship. The Body Comparison chart lets you compare surface orbital velocities across all six bodies at a glance.
Understanding Orbital Mechanics
The formula v = sqrt(GM/r) comes from equating centripetal force (mv^2/r) with gravitational force (GMm/r^2), where m cancels out. G = 6.674 x 10⁻¹¹ m^3 kg⁻¹ s⁻^2 is the universal gravitational constant. For Earth (mass 5.972 x 10^2^4 kg) at sea level (radius 6371 km), orbital velocity is approximately 7.9 km/s. At the ISS altitude (~408 km above surface), it drops to about 7.7 km/s. Geostationary satellites at 35,786 km altitude orbit at just 3.1 km/s, matching Earth's rotation for fixed-ground coverage -- this principle powers global communications, weather monitoring, and navigation systems worldwide.
India's ISRO uses these exact calculations for the PSLV and GSLV launch vehicles. NASA's Artemis program and ESA's Ariane rockets all depend on the same Newtonian mechanics. The escape velocity result (vₑ = sqrt2 x v_orbital) tells you the speed needed to break free from a body's gravity -- essential for interplanetary missions like Chandrayaan, Mangalyaan (India), the Mars rovers (US), and the James Webb Space Telescope (US/ESA/CSA).
Frequently Asked Questions
What is orbital velocity and how is it calculated?
Orbital velocity is the minimum speed required for an object to stay in a stable orbit around a celestial body. It is calculated using the formula v = sqrt(GM/r), where G is the gravitational constant (6.674 x 10⁻¹¹ m^3 kg⁻¹ s⁻^2), M is the mass of the central body, and r is the orbital radius from the body's center. The calculator uses this formula with pre-loaded masses for Earth, Sun, Moon, Mars, Jupiter, and Saturn.
How is orbital velocity different from escape velocity?
Orbital velocity (v = sqrt(GM/r)) is the speed needed to orbit a body in a circular path, while escape velocity (vₑ = sqrt(2GM/r)) is the speed needed to break free from its gravitational pull entirely. Escape velocity is exactly sqrt2 times the orbital velocity at the same radius. For Earth at sea level, orbital velocity is about 7.9 km/s while escape velocity is about 11.2 km/s.
What is the orbital velocity of Earth around the Sun?
Earth orbits the Sun at an average velocity of approximately 29.8 km/s (107,000 km/h). This is calculated using the Sun's mass (1.989 x 10^3^0 kg) and Earth's average orbital radius (1 astronomical unit ≈ 149.6 million km). You can verify this by selecting the Sun as the central body and entering Earth's orbital radius in our calculator.
How does orbital velocity change with altitude?
Orbital velocity decreases as orbital radius increases. At Earth's surface (6371 km from center), orbital velocity is about 7.9 km/s. At the International Space Station altitude of ~400 km above surface (6771 km from center), it drops to about 7.7 km/s. At geostationary orbit (42,164 km from center), it is only about 3.1 km/s. The Velocity vs Radius chart in our calculator visualizes this inverse relationship.
What is the orbital velocity of the International Space Station?
The International Space Station orbits Earth at an altitude of approximately 408 km above the surface, corresponding to an orbital radius of about 6779 km from Earth's center. At this altitude, its orbital velocity is roughly 7.66 km/s (27,600 km/h), completing one orbit around Earth every 92 minutes. Select Earth with radius 6779 km in this calculator to verify.
Can this calculator help with Indian space missions (ISRO)?
Yes. ISRO missions like Chandrayaan and Mangalyaan rely on precise orbital velocity calculations. Earth's orbital velocity (~7.9 km/s at surface) is the baseline for launch, and escape velocity (~11.2 km/s) must be exceeded for interplanetary missions. Students and researchers in India can use this calculator for academic projects and mission analysis using Earth, Moon, and Mars as central bodies.
Does this calculator support US and UK space agency missions?
Absolutely. NASA (US) and ESA/UK Space Agency missions depend on the same Newtonian mechanics. Whether calculating LEO insertion for a US satellite (~7.8 km/s for a 200 km orbit), a UK-built CubeSat deployment from ISS, or a Jupiter orbiter trajectory, the formula v = sqrt(GM/r) applies universally. Simply select the relevant celestial body (Jupiter for JUNO, Earth for LEO, Sun for heliocentric orbits) and enter the orbital radius.
What determines the orbital period of a satellite?
The orbital period T is given by Kepler's third law: T = 2pisqrt(r^3/GM). It depends only on the orbital radius and the mass of the central body, not on the satellite's mass. Low Earth orbits take about 90 minutes, geostationary orbits take 24 hours, and the Moon takes 27.3 days to orbit Earth. Our calculator computes the orbital period in hours from the velocity and radius.