Molniya orbit

For other uses, see Molniya.

A Molniya orbit is a type of highly elliptical orbit with an inclination of 63.4 degrees and an orbital period of precisely one half of a sidereal day. Molniya orbits are named after a series of Soviet/Russian Molniya (Russian: "Lightning") communications satellites which have been using this type of orbit since the mid 1960s.

A satellite placed in a Molniya orbit spends most of its time over a designated area of the earth as a result of "apogee dwell". Molniya orbits can be computed for any celestial body for which the dominant effects on bodies orbiting it are due to:

• Secular variations in the longitude of the ascending node;
• the argument of perigee due to the celestial body's oblateness.

Properties

Much of the area of the former Soviet Union, and Russia in particular, is located at high latitudes. To broadcast to these latitudes from a geostationary orbit would require considerable power due to the low grazing angles. A polar orbiting satellite is better suited to communications in these regions because it looks directly down on them, but a typical near-circular sun-synchronous orbit would put the satellite over Russia for short periods of time, during which it would move in two directions, north/south and to the west as the Earth turns, making tracking difficult. Likewise, an inclined equatorial orbit could be used to move the satellite northward on one-half of its orbit, but the satellite would pass over the country very quickly, so although tracking could be reduced to the east-west direction using an equatorial mount, a large number of satellites would be required to give constant coverage.

The solution to this problem is to make the orbit highly elliptical. The speed of a satellite in its orbit is a declining function of the distance from the focus, in this case the center of the Earth. So by making the satellite come close to the Earth during one part of its orbit this area will be passed over quite quickly, while at the other side of the orbit, when it is more distant, it will cover the distance slowly. By orbiting eastward, the satellite's angular speed is close to the Earth's rotation speed, and makes its location as seen from the ground move only a small amount for an extended period of time.

Due to the Earth's rotation, the apogee point is different for each orbit. In order to eliminate "useless" apogees when the satellite is far enough north but located too far east or west, the orbits are set up with periods which are some integer fraction or multiple of a day, making their apogee point repeatedly appear over the same location on a schedule. The most typical Molniya-type orbits have a period of 12 hours, making them appear over Russia daily, on every second orbit, for about eight hours. Only three such satellites are needed to give 24 hour coverage. The otherwise similar Tundra orbit has an orbital period of 24 hours.

In general, the oblateness of the earth perturbs the argument of perigee, so that even if the apogee started near the north pole, it would gradually move unless constantly corrected with "station keeping" thruster burns. To avoid this expenditure of fuel, the Molniya orbit uses an inclination of 63.4°, for which these perturbations are zero.

Uses

The primary use of the Molniya orbit was for the communications satellite series of the same name. After two launch failures in 1964, the first successful satellite to use this orbit was Molniya 1-01 launched on August 23, 1965. The early Molniya-1 satellites were used for long-range military communications starting in 1968, but the satellites had a short lifespan and had to be constantly replaced. Its replacement, the Molniya-2, provided both military and civilian broadcasting, and was used to create the Orbita television network, spanning the Soviet Union. These were in turn replaced by the Molniya-3 design. There is some confusion in the existing sources about the naming, with some sources suggesting that all of the satellites on-orbit are of the Molniya-3 type, but referred to as Molniya-1 through -3 depending on their purpose.

The same orbits, with slight adjustments, were also used by some Soviet spy satellites, with the apogee point over the continental United States. Although geostationary orbits are useful for observing the continental United States, Soviet sensor technology sometimes required high-contrast observing angles which could only be achieved from higher latitudes. One such example is the US-KS early-warning satellite which watches for US missile launches, although improvements in these systems have since allowed them to move these to geostationary orbits.

The US has also made some use of the Molniya orbits for spy satellites of their own. The same long loitering time over high latitudes which makes them useful for broadcasting communications in Russia makes them just as useful for listening to Russian communications. Electronic intelligence satellites called Jumpseat and their successors called Trumpet are also reported to use Molniya orbits. Another use is the Satellite Data System (SDS), which relays data from spy satellites operating over Russia back to the US download sites for processing. SDS allows for real-time data collection from the low-flying KH-11 reconnaissance satellites, passing by in their polar orbits below. Although the KH-11 can also use geostationary relays, these are not useful when passing over high latitudes.

A Molniya orbit is not suitable for manned spacecraft because it repeatedly crosses the high-energy Van Allen belt.

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Derivation

In order to ensure that the position of the apogee is not severely affected by orbit perturbations, an inclination close to 63.4 degrees is chosen. This results in the argument of perigee remaining nearly constant for a long period of time.

The change per day of argument of perigee for earth orbits is as follows (just considering the effect of the Earth's oblateness (J₂) on the orbit - which is the dominating perturbation):

$\Delta \omega _{day}=4.98^{\circ }\left({\frac {R_{E}}{a}}\right)^{\frac {7}{2}}{\frac {5\cos ^{2}i-1}{\left({1-\varepsilon ^{2}}\right)^{2}}}$

where:

• $R_{E}\,$ is earth's radius,
• $a\,$ is length of semi-major axis,
• $i\,$ is the inclination, and
• $\varepsilon \,$ is orbital eccentricity.

The equation becomes zero for an inclination of 63.4 degrees.

References

• Orbital Mechanics by Robert A. Braeunig
• Molniya-1 spacecraft by Mark Wade of Encyclopedia Astronautica

See also

• List of orbits
• Elliptic orbit

External links

• Real time satellite tracking for a typical Molniya satellite
• 3D Molniya constellation viewer (Java applet)
• illustration of the communication geometry provided by satellites in 12-hour Molniya orbits (video)