Orbit Determination Calculator

Orbital elements from position and velocity vectors.

Perigee altitude (km)

Apogee altitude (km)

Inclination (deg)

Tab to move between fields

Semi-major axis (km)

6,771

Eccentricity

Orbital period (min)

92.41

Velocity at perigee (km/s)7.67

Velocity at apogee (km/s)7.67

Circular velocity (km/s)7.67

Specific energy (km²/s²)-29.43

Mean motion (rev/day)15.58

Inclination (deg)51.6

Semi Minor Axis6,771

Specific Ang Momentum51,951.17

Mean Motion0

Nodal Period (min)92.41

How to Use This Calculator

Enter perigee altitude (km) and apogee altitude (km) for your orbit.
Set orbital inclination (degrees) relative to Earth's equatorial plane.
Review semi-major axis, eccentricity, orbital period (min), and velocities at perigee and apogee.
Use apogee velocity to plan Hohmann transfer burns or phasing maneuvers.
Check period against your ground-repeat requirement to confirm the orbit geometry.

How the result changes with Perigee altitude (km)

Perigee altitude (km)	Semi-major axis (km)	Orbital period (min)
50,090	56,461	2,225.27
175,065	181,436	12,818.73
325,035	331,406	31,644.65
450,010	456,381	51,138.86

Perigee altitude (km): Lowest point of the orbit above Earth's surface. ISS: ~408 km, GEO: 35,786 km.
Apogee altitude (km): Highest point of the orbit. Equal to perigee for a circular orbit. GTO apogee: ~35,786 km.
Inclination (deg): Angle between orbital plane and equator. ISS: 51.6°, polar: 90°, sun-sync: ~98°, equatorial: 0°.

Semi-major axis (km): Half the longest diameter of the orbital ellipse.
Eccentricity: Shape of orbit: 0 = circular, 0-1 = elliptical.
Orbital period (min): Time for one complete orbit from Kepler's third law.
Velocity at perigee (km/s): Fastest point in the orbit (vis-viva equation).
Velocity at apogee (km/s): Slowest point in the orbit.
Circular velocity (km/s): Reference circular orbit velocity at perigee altitude.
Specific energy (km²/s²): Specific orbital energy (negative for bound orbits).
Mean motion (rev/day): Number of orbits completed per day.
Inclination (deg): Orbital inclination as entered.

Identify Input Parameters
Perigee altitude (km) = 400, Apogee altitude (km) = 400, Inclination (deg) = 51.6 = 3 input(s) provided
Calculate Semi-major axis
Semi-major axis = (rPerigee + rApogee) / 2
6771 = 6771
Calculate Eccentricity
Eccentricity = (rApogee - rPerigee) / (rApogee + rPerigee)
0 = 0
Calculate Orbital period
Orbital period = periodSec / 60
92.41 = 92.41
Calculate Velocity at perigee
Velocity at perigee = sqrt(GM_EARTH * (2 / rPerigee - 1 / semiMajorAxis))
7.673 = 7.673
Calculate Velocity at apogee
Velocity at apogee = sqrt(GM_EARTH * (2 / rApogee - 1 / semiMajorAxis))
7.673 = 7.673