Orbit Basics: the six numbers that define any satellite orbit
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Every satellite in the sky, from the International Space Station to GPS to Starlink, can be described by just six numbers. These six "orbital elements" tell you everything: how big the orbit is, what shape it takes, how it tilts relative to Earth, and where the satellite sits in its orbit right now. Once you understand these six, you can describe any orbit ever flown.
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What you'll learn
- What the six orbital elements are and what each one controls
- Why an orbit shape (a, e) is separate from its orientation in space (i, RAAN, ω)
- How mean anomaly (M) is the only one that changes with time for an unperturbed orbit
- How to read a real satellite's "TLE" (Two-Line Element set) once you know the elements
- Why orbits are ellipses, not circles, and what perigee and apogee mean
The six orbital elements, one by one
Semi-major axis (a) is the orbit's size: half the long axis of the ellipse. Bigger a means a larger, slower orbit. Eccentricity (e) is the orbit's shape: zero means a perfect circle, closer to one means a long stretched ellipse. Inclination (i) is the tilt of the orbital plane relative to Earth's equator. RAAN (right ascension of the ascending node) is where the orbit crosses the equator going north. Argument of perigee (ω) is where the closest point of the orbit sits, measured around the plane. Mean anomaly (M) is the satellite's current position along the orbit, expressed as if it were moving at a uniform rate around a circle. All six are required to describe an orbit completely.
Why orbits are ellipses
Newton showed that any object in gravitational orbit around a much more massive body follows a conic section: an ellipse, a parabola, or a hyperbola. Closed orbits (everything that stays bound) are ellipses. A perfect circle is just an ellipse with zero eccentricity. The Sun sits at one focus of every planet's elliptical orbit. Earth sits at one focus of every satellite's elliptical orbit. This was Kepler's first law, derived empirically in 1609 and proved analytically by Newton 70 years later.
Perigee, apogee, and what they mean for spacecraft
The closest point to Earth on an orbit is called perigee, the farthest is called apogee. A satellite moves fastest at perigee and slowest at apogee — that's Kepler's second law in action. For circular orbits (e = 0) the speed is constant. For highly elliptical orbits like Molniya (e ≈ 0.74), the speed varies by a factor of seven between perigee and apogee. Spacecraft designers exploit this: a Molniya satellite spends about 8 of its 12 hours sitting nearly motionless over the northern hemisphere because it's near apogee, then zips through perigee in 30 minutes on the other side.
Frequently asked questions
What are the six orbital elements?
Semi-major axis (a), eccentricity (e), inclination (i), right ascension of the ascending node (RAAN, Ω), argument of perigee (ω), and mean anomaly (M). Together they pin down a satellite's exact position and trajectory.
Which orbital element changes with time?
For an unperturbed two-body orbit, only mean anomaly (M) changes with time, at a steady rate set by the orbit size. In reality, perturbations like Earth's oblateness (J2) cause RAAN and argument of perigee to drift slowly too.
What is the difference between semi-major axis and altitude?
Semi-major axis is measured from Earth's center. Altitude is measured from Earth's surface. To go from one to the other, add or subtract Earth's radius (6,378 km at the equator). A satellite at 400 km altitude has a semi-major axis of about 6,778 km for a circular orbit.
What is eccentricity?
Eccentricity (e) measures how stretched an orbit is. e = 0 is a perfect circle. 0 < e < 1 is an ellipse, with higher values meaning a longer, more stretched shape. The Earth's orbit around the Sun has e ≈ 0.017 (nearly circular). A Molniya orbit has e ≈ 0.74. A parabolic escape trajectory has e = 1.
Why does the International Space Station orbit at 400 km specifically?
Below 400 km, atmospheric drag pulls satellites down quickly. Above 500 km, the South Atlantic Anomaly (a region of intense radiation) increases health risks for crew. 400 km is the compromise: long enough orbital lifetime that the ISS only needs occasional reboost burns, low enough that Soyuz and crew Dragon can reach it economically.
Related lessons
- Lesson 2: Altitude and Period — Higher orbits move slower. Drag the altitude slider and watch why.
- Lesson 3: Eccentricity and Speed — Same orbit, different speeds. Drag eccentricity, watch the satellite race through perigee and crawl through apogee.
- Lesson 4: Ground Tracks and Inclination — Watch the path a satellite traces on Earth's surface. Inclination changes everything.
Open it in the simulator
Delta-V Academy is a free interactive orbital mechanics simulator that runs entirely in your browser. The 10-lesson curriculum covers everything from these basics through space domain awareness, with three difficulty levels (novice, intermediate, advanced) plus a kid-friendly mode. Launch the simulator and try Lesson 1 interactively.
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