What are the six orbital elements?

Six numbers — size, shape, tilt, two orientation angles and position along the orbit — are enough to pin down an orbit and where the satellite is on it.

An orbit is an ellipse with the Earth's centre at one focus. To describe a satellite completely you need to say how big that ellipse is, what shape it is, how it is tilted and turned in space, and where on it the satellite is. That takes six numbers, the orbital elements, plus the time they apply to (the epoch).

Earth equator plane reference direction RAAN ascending node inclination argument of perigee perigee satellite mean anomaly size: mean motion shape: eccentricity
Mean motion sets the orbit's size and eccentricity its shape; inclination tilts it against the equator; RAAN turns it to face a direction, measured to the northbound equator crossing; argument of perigee places the lowest point; mean anomaly says where the satellite is. Shape exaggerated; mean anomaly is drawn as an angle, though strictly it is a steadily turning clock hand.

The six, as a TLE writes them

Take Cartosat-3's TLE line 2 from CelesTrak:

`2 44804 97.4143 8.4285 0012177 27.7460 332.4422 15.19296575384848`

  • Mean motion — 15.19296575 orbits a day. This sets the size of the orbit: fewer orbits a day means a bigger orbit.
  • Eccentricity — 0.0012177. The shape: 0 is a perfect circle, and this one is very nearly circular.
  • Inclination — 97.4143°. The tilt of the orbit against the equator. Above 90° means the satellite travels slightly against the Earth's spin, which is typical of a sun-synchronous orbit.
  • Right ascension of the ascending node (RAAN) — 8.4285°. Which way the tilted orbit faces: the angle from a fixed direction in space to the point where the satellite crosses the equator going north.
  • Argument of perigee — 27.7460°. Where the lowest point (perigee) lies, measured along the orbit from that northward crossing.
  • Mean anomaly — 332.4422°. Where the satellite is: an angle that grows steadily from 0° at perigee to 360° over one orbit.

Why this matters on the tracker

Every position you see on this site is built from these six numbers. The orbit-type label, the altitude card and the ground track all come from them. If you know only inclination, you already know something useful: Cartosat-3, at 97.4°, passes close to both poles, so over many days it flies over all of India; the ISS, at 51.6°, never goes north of about 51.6° latitude. Each time this site downloads fresh TLEs, these six numbers are updated for every satellite.

See it live

In the Orbital Elements (TLE) block, line 2's third field is the inclination (about 97.4°) and its eighth is the mean motion (about 15.19). Open Cartosat-3

Key facts

  • Cartosat-3: inclination 97.41°, orbit 500 × 516 km, period 94.78 minutes (CelesTrak catalogue).
  • ISS: inclination 51.63°, orbit 414 × 424 km, period 92.95 minutes (CelesTrak catalogue).
  • Mean anomaly is 0° at perigee and 180° at apogee.
  • A TLE gives the elements plus an epoch, a drag term and a revolution count.

Go deeper

Textbooks usually give the six classical (Keplerian) elements as semi-major axis a, eccentricity e, inclination i, RAAN Ω, argument of perigee ω and mean anomaly M. A TLE swaps a for the mean motion n, because n is what tracking measures most directly; Kepler's third law links them: a = (μ / n²)^(1/3).

Worked example for Cartosat-3. n = 15.19296575 rev/day = 15.19297 × 2π / 86,400 ≈ 0.0011049 rad/s. With μ = 398,600.8 km³/s² (the WGS-72 value SGP4 uses), a ≈ 6,886 km. Its mean height is a − 6,378.135 ≈ 508 km. The eccentricity gives the spread: perigee radius = a(1 − e) ≈ 6,886 × 0.99878 ≈ 6,878 km and apogee radius = a(1 + e) ≈ 6,894 km, about 500 km and 516 km above the WGS-72 equator — the same 500 × 516 km that CelesTrak's catalogue lists.

Mean anomaly is not the true angle around the orbit; it is a clock hand that turns at a constant rate (M = M₀ + n·t). To get the actual angle, software solves Kepler's equation M = E − e·sin E for the eccentric anomaly E. For nearly circular orbits like Cartosat-3, the difference is tiny (at most about 2e radians, here roughly 0.14°).

AMSAT's guide counts seven numbers to define an orbit because it includes the epoch, and treats drag as an optional eighth. SGP4 also needs the TLE's BSTAR drag term.

Check yourself

Which orbital element tells you the highest latitude a satellite's ground track reaches?

Inclination. For a prograde orbit the ground track reaches latitudes up to the inclination, so the ISS at 51.6° stays between about 51.6° N and 51.6° S.

A satellite's TLE shows eccentricity 0.0000000. What shape is its orbit?

A circle (within the precision of the TLE), so its perigee and apogee heights are the same.

Name the element that changes steadily with time and tells you where the satellite is along its orbit.

Mean anomaly. It increases at a constant rate from 0° at perigee to 360° after one orbit.

Sources

  1. What Are Keplerian Elements? — AMSAT-NA (Bruce Paige)
  2. Frequently Asked Questions: Two-Line Element Set Format — CelesTrak (T.S. Kelso)
  3. GP element set (TLE) for CARTOSAT-3, catalogue number 44804 — CelesTrak
  4. SATCAT record: CARTOSAT-3 (44804) — CelesTrak
  5. SATCAT record: ISS (ZARYA) (25544) — CelesTrak
  6. Revisiting Spacetrack Report #3 (AIAA 2006-6753; Vallado, Crawford, Hujsak & Kelso) — CelesTrak