1. History

2. Uses

3. Properties
    Orbital inclination  Orbital period  Eccentricity 

4. Modelling

5. Diagrams

6. See also

7. References

8. External links

A Molniya orbit ({{lang-rus|Молния|p=ˈmolnʲɪjə|a=Ru-молния.ogg}}, "Lightning") is a type of satellite orbit, designed to provide coverage over high latitudes. It is a highly elliptical orbit with an inclination of 63.4 degrees, an argument of perigee of 270 degrees and an orbital period of approximately half a sidereal day.^[1] The name comes from a series of Soviet/Russian Molniya communications satellites which have been using this type of orbit since the mid-1960s.^[2]

The high inclination of Molniya orbits provides a high angle of view to communications and monitoring satellites covering high latitudes. It has a long dwell time over the hemisphere of interest, while moving very quickly over the other. Geostationary orbits, which are necessarily inclined over the equator, can only view these regions from a low angle, and are unable to view latitudes above 81 degrees.^[3]

History

The Molniya orbit was invented by Russian scientists in the 1960s as a high latitude communications alternative to geostationary orbits. They were limited in the amount of rocket power available and it is extremely energy intensive to both launch a satellite to 40,000 km, and change its inclination to be over the equator, especially when launched from Russia.^[4] As a result, OKB-1 sought a less energy-consuming orbit. Studies found that this could be achieved using a large elliptical orbit, with an apogee over Russian territory.^[2] The orbit's name, "quick as lightning", is in reference to the speed with which it passes through the perigee.^[5]

The first use of the Molniya orbit was by the communications satellite series of the same name. After two launch failures in 1964, the first successful satellite to use this orbit, Molniya 1-01, launched on April 23, 1965. The early Molniya-1 satellites were primarily used for long-range military communications, but were also fitted with cameras used for weather monitoring, and possibly for assessing clear areas for Zenit spy satellites.^[6] The original Molniya satellites had a lifespan of approximately 1.5 years, as their orbits were disrupted by perturbations, and they had to be constantly replaced.^[1]

Its successor, 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,^[7] followed by the Mayak and Meridian satellites in 1997 and 2002 respectively.^[8]

The Russian US-K early-warning satellites, which watch for US missile launches were launched in Molniya orbits from 1967, as part of the Oko system.^[9][10][11]

From 1971, the American Jumpseat and Trumpet satellites were launched into Molniya orbits, and possibly used to strategically intercept Soviet communications from the Molniya satellites. Detailed information about both projects remains classified as of 2018.^[8][12]

This was followed by the American SDS constellation, which operates with a mix of Molniya and geostationary orbits. These satellites are used to relay imagery from lower flying satellites back to ground stations in the United States and have been active in some capacity since 1976.^[13] A single classified communication satellite launch in 1998 may be related to this constellation.^[8]

A Russian satellite constellation called Nord (and later, Tyulpan) was designed to support mobile communications at high latitudes, in a similar manner to the Iridium constellation, but it did not progress past the planning phase.^[14]

Uses

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 (above the Earth's equator) would require considerable power due to the low elevation angles. A satellite in a Molniya orbit is better suited to communications in these regions because it looks directly down on them during large portions of its orbit. With an apogee altitude as high as 40,000 km, and a sub-satellite point of 63.4 degrees north, it spends a considerable portion of its orbit with excellent visibility of the Northern Hemisphere, from the Russian Federation but also from Northern Europe, Greenland and Canada.^[3]

While Molniya orbits require considerably less launch energy than geostationary orbits (especially from Russia),^[15] the ground station needs a steerable antenna to track the spacecraft, links must be switched between satellites, the range is varying, there is a greater need for station keeping,^[21][16][17] and the spacecraft will pass through the Van Allen radiation belt four times per day.^[15]

Properties

A typical Molniya orbit, has:

• Semi-major axis: 26,600{{nbsp}}km
• Eccentricity: 0.74
• Inclination: 63.4°^[16]
• Argument of perigee: 270°
• Period: 718 minutes^[1]

It is necessary to have a constellation of at least three spacecraft for permanent high elevation coverage of a large area, like the whole of Russia where some parts are as far south as 45°{{nbsp}}N. If three spacecraft are used, each spacecraft is active for periods of eight hours per orbit centered around apogee^[3] as illustrated in figure 11.

The Earth completes half a rotation in 12 hours, so the apogees of successive Molniya orbits will alternate between one half of the northern hemisphere and the other. For the original Molniya orbit, this places the apogees over Russia and North America, but by changing the right ascension of the ascending node this could be varied. The coverage from a satellite in a Molniya orbit over Russia is shown in figures 5 to 7, and North America in figures 8 to 10.

The orbits of the three spacecraft should then have the same orbital parameters, but different right ascensions of the ascending nodes, with their passes over the apogees (for example 90°{{nbsp}}W and 90°{{nbsp}}E) separated by 7.97 hours.^[3][18] Since each satellite has an operational period of approximately 8 hours, when one spacecraft travels four hours after its apogee passage (see figure 7 or figure 10), the next satellite will enter its operational period. The next satellite will have a view of the earth shown in figure 5 (or figure 8) and the switch-over can take place. Note that the two spacecraft at the time of switch-over are separated about 1500 km, so that the ground stations only have to move the antennas a few degrees to acquire the new spacecraft.^[19]

Orbital inclination

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, according to equation {{EquationNote|1}}, unless constantly corrected with station-keeping thruster burns.

where is the gravitational constant, is the perturbing factor, and is the semi-latus rectum.

To avoid this expenditure of fuel, the Molniya orbit uses an inclination of 63.4°, for which these perturbations are zero.^[20][16] At this inclination the factor is zero, so there is no change in perigee over time.

Orbital period

To ensure the geometry relative to the ground stations repeats every 24 hours the period should be about half a sidereal day, keeping the longitudes of the apogees passages constant.

However, the oblateness of the Earth also perturbs the right ascension of the ascending node (), changing the nodal period and causing the ground track to drift over time at the rate shown in equation {{EquationNote|2}}.

Since the inclination of a Molniya orbit is set, this perturbation is degrees per orbit. To compensate, the orbital period is adjusted so that the longitude of the apogee changes enough to cancel out this effect.^[16]

Eccentricity

The eccentricity of the orbit is based on the differences in altitudes of its apogee and perigee. To maximise the amount of time that the satellite spends over the apogee the eccentricity should be as high as possible.

However, the perigee needs to be high enough to keep the satellite above the atmosphere to avoid drag, and the orbital period needs to be approximately half a sidereal day. These two factors constrain the eccentricity, which becomes approximately 0.737.^[16]

Modelling

To track satellites using Molniya orbits, scientists use the SDP4 simplified perturbations model, which calculates the location of a satellite based on orbital shape, drag, radiation, gravitation effects from the sun and moon, and earth resonance terms.^[21]

Diagrams

See also

• Elliptic orbit
• List of orbits
• Tundra orbit

References

External links

• [https://www.youtube.com/watch?v=O_Iykeouj3g Illustration of the communication geometry provided by satellites in 12-hour Molniya orbits] (video)

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