ORBITS
Types of orbits, explained step by step
Twelve three-letter codes say where a launch is going: LEO, SSO, MEO, MTO, GTO, GEO, GSO, STO, HEO, MOL, DSO and EEO. They describe the low orbit of the space stations and the Starlink satellites, the geostationary ring, the long ellipse above Siberia and the road to the Moon or to the Sun. Here each orbit is calculated in your browser with Kepler’s laws and drawn with lines and dots, as on the screen of a cathode-ray tube.
1.0 Five questions about an orbit
The codes in the parsec.ro glossary (in Romanian) do not form a single classification but several overlapping ones. Each answers a different question, so the same orbit can carry two codes at once: GEO is also GSO, SSO is also LEO.
1.1 Anatomy of an orbit
A few quantities are enough to answer all these questions. The drawing below is an elliptical orbit inclined to the equator. The equatorial plane is the gridded sheet, seen in perspective; the orbital plane is hatched, and the part of the orbit below the sheet is drawn fainter. The “Perspective” slider raises or lowers the point you look from, down to below the sheet; with a mouse you can also drag the drawing up and down. The other sliders change the orbit: the element you change is highlighted and its explanation opens in the list. Press the numbers to see the other elements.
1.2 Eccentricity: how flattened the orbit is
Eccentricity is a single number that says how far an orbit is from a circle. In the drawing, it is the distance between the centre of the ellipse and the point where the Earth sits, divided by the semi-major axis. A circle has an eccentricity of 0, and an ever flatter ellipse approaches 1. At 1 and above, the orbit no longer closes.
You can look at this in two ways. In the first, the semi-major axis stays the same and only the shape changes, so the period does not change at all. In the second, the perigee stays put and the eccentricity grows as the satellite gains more and more speed there: that is exactly what the upper stage of a rocket does, and the orbit passes in turn through several codes of the glossary.
2.0 The catalogue
The twelve codes of the glossary, ordered here by distance from the Earth, not alphabetically.
Each orbit is calculated on the spot. The satellite moves according to Kepler’s second law, fast at perigee and slow at apogee, and the Earth turns beneath it at its real rate, only sped up. For GEO, this means that the satellite stays above the same point on the equator all the time. For each code, the card also shows why someone would choose that orbit and what trade-off it involves. The definitions are reworded from the glossary; the flight data are calculated for the chosen examples.
Interactive catalogue of orbits
Figure 2.0-1.
LEO
Why it is chosen
The trade-off
Examples.
Two things stand out with the time marks on. On circular orbits, the dots are evenly spaced. On elongated orbits, they thin out near perigee and crowd together near apogee: on a Molniya orbit, the satellite spends over nine tenths of its time in the half of the orbit around apogee. The whole idea of the orbit rests on this: a satellite that “hangs” for hours above the north.
3.0 The classifier
The glossary defines orbits by thresholds: 2,000 km, 35,786 km, 150,000 km, a period of 12 hours or of one day. The program below applies the thresholds to an orbit you choose and prints the result, like a line printer on striped paper.
Move the sliders, type in the values or start from an example. Altitudes are measured from the surface of the Earth.
Figure 3.0-1. The orbit entered, with the GEO ring and the 2,000 km limit for reference. The dots are at equal time intervals, 24 per orbit. The apogee is placed above the northern hemisphere.
An escape trajectory has no apogee, so it cannot be set with the sliders. The button assumes that at perigee the satellite has exactly escape velocity, the lowest speed at which it escapes the Earth: the orbit becomes a parabola, and the classification is EEO. Then move the perigee and you will see escape velocity fall with altitude, from 11.01 km/s at 200 km to about 4.35 km/s at GEO altitude. For a hyperbola, with speed to spare, see section 1.2, the “Same perigee” option.
The program’s rules: an orbit is geosynchronous if its period is within 0.6% of the sidereal day; Molniya-type if its period is within 1.5% of half a sidereal day, its eccentricity above 0.5 and its inclination within 2° of 63.4°; sun-synchronous if its inclination is within 0.5° of the one calculated for its altitude. The tolerances are the program’s choice, not the glossary’s. In practice, an orbit also gets its code from the purpose of the mission: the same ellipse can be GTO for a satellite that will climb to GEO and HEO for one that stays on it.
4.0 The road to GEO
Almost no geostationary satellite is taken straight to GEO. The rocket leaves it on GTO, and the satellite makes the rest of the way on its own.
The rest of the way means two things: the orbit has to be circularised at apogee and turned into the plane of the equator. The turn costs more the farther the launch site is from the equator, because no rocket can go directly into an orbit with an inclination lower than the latitude of its launch pad. The cost is measured in Δv, the change in velocity the engines have to produce.
Figure 4.0-1. Δv counted from the parking orbit, with instantaneous burns. The whole plane change is made at apogee; real missions sometimes split it over several burns.
This is where one of the uses of the supersynchronous orbit comes from. If the upper stage raises the apogee above 35,786 km, the satellite moves even more slowly up there, and turning the plane costs less. In exchange, the first burn has to be bigger, and a third one is needed at the end to lower the apogee. Compare Baikonur with Kourou: for an inclination of 51.6°, the route via STO comes out cheaper for any apogee chosen on the slider, and for 5.2° it never does.
5.0 The ground track
The point on the Earth directly beneath the satellite draws a line on the map as the planet turns. Its shape shows the type of orbit at a glance.
On the Molniya track, the dots placed every 30 minutes bunch up at the two apogees, one above Russia and the other above North America. Three satellites spaced 8 hours apart cover the north permanently. A geostationary satellite, by contrast, is seen from Murmansk at most 12–13° above the horizon, and north of latitude 81° it cannot be seen at all.
6.0 Sun-synchronous: the clock of the orbit
SSO is the only orbit in the glossary defined relative to the Sun. Its plane is not fixed in space: it turns by almost one degree a day, exactly as fast as the Earth advances along its own orbit.
The turning uses no fuel. It is caused by the Earth’s equatorial bulge, which pulls on the inclined orbit as on a gyroscope. The effect depends on altitude and inclination, so for each altitude there is a single inclination that gives exactly the right rate. It is a little over 90°, which means the orbit is retrograde. Below, switch between a sun-synchronous orbit and one with a fixed plane, then run through the year.
Figure 6.0-1. Not to scale: the Earth and the satellite’s orbit are greatly enlarged. The small circles show the Earth and the satellite’s orbit every 30 days, starting from the March equinox.
What inclination is needed?
For 500 km the calculation gives 97.4°, and for 1,000 km, 99.5°: exactly the 97–99.5° range in the glossary. Sentinel-2, at 786 km and 98.62°, always crosses the descending node at 10:30 local solar time, a time ESA chose as a compromise between enough light and as little cloud cover as possible. The small difference between the calculation here and the real inclination comes from effects that the simple formula leaves out.
7.0 Sources
- Claudiu Tănăselia, Glosar (glossary, in Romanian), parsec.ro, section “Tipuri de orbite” (types of orbits). Definitions of all the codes, including ISS, CSS and LSS.
- ESA, Sentinel-2 Mission Orbit: 786 km, 98.62°, descending node at 10:30.
- Seradata, Falcon 9 launches GPS III-4 navsat, November 2020: transfer orbit of 402 × 20,183 km at 55°.
- Tiangong space station, Wikipedia: orbital elements of the Chinese station (386 × 392 km, 41.47°).
- J. T. McGraw, P. C. Zimmer, M. R. Ackermann, Ever Wonder What’s in Molniya? We Do., AMOS 2017: the geometry of the Molniya orbit and its two apogees.