SME
Orbital Mechanics · Problem type
What i, Ω, ω and ν describe
Use this for “In which plane is the right ascension of the ascending node measured, and from where?”
Explore
The semi-major axis a is half the line from perigee to apogee; it alone sets the period.
The eccentricity e sets the shape: 0 is a circle, and near 1 a long, thin ellipse.
Assumptions
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Two-body motion: the orbit is a fixed ellipse with Earth’s centre at one focus.
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Angles are measured at Earth’s centre; x points to the vernal equinox and z to the north pole.
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The drawing is not to scale; its angles are.
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Related lessons
Orbital elements
Main lesson
Radius at a true anomaly (the orbit equation)
Use this for “An orbit has a = 24,471 km and e = 0.723. How far from Earth’s centre is the satellite at true anomaly 90°?”
Position after a time (Kepler’s equation)
Use this for “An orbit has a = 24,471 km and e = 0.723. Where is the satellite 1.684 h after perigee?”