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Orbital Elements Lab

Five elements fix the orbit in space. The sixth puts the satellite on it. Hover or drag a slider to light up what it controls.

ECI frame · X → ♈ vernal equinox · Z → north pole

Real orbits

Period–

Revs per day–

Speed now–

Perigee alt.–

Apogee alt.–

Altitude now–

Node drift Ω̇ (J2)–

Apsis drift ω̇ (J2)–

Mean anomaly M–

Size and shape

aSemi-major axis km

Half the long diameter of the ellipse. It alone sets the period and the orbital energy.

eEccentricity

0 is a circle; toward 1 the ellipse stretches out. Earth sits at a focus, offset from the center by ae.

Orientation of the plane

iInclination °

Tilt of the orbital plane against the equator, hinged on the line of nodes. Also the angle between Z and the orbit normal h.

ΩRight ascension of the ascending node °

Swings the tilted plane around the polar axis. Measured east along the equator from ♈ to where the satellite crosses heading north.

Orientation within the plane

ωArgument of periapsis °

Spins the ellipse inside its own plane. Measured from the ascending node to periapsis, in the direction of motion.

Position on the orbit

νTrue anomaly °

Where the satellite is right now: the angle from periapsis to the satellite, seen from Earth's center. Press Play to let time move it.

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Labels Equatorial plane Orbital plane Angle guides

Earth-centered inertial frame: X points to the vernal equinox ♈, Z to the north pole. Earth's daily spin isn't drawn because the elements don't depend on it. Motion is pure two-body Kepler; the drift rates add only Earth's J2 oblateness. Earth and orbits are to scale.