Molniya orbit

For other uses, seeMolniya (disambiguation).

Figure 1: The Molniya orbit. Usually the period fromperigee+2 hours to apogee +10 hours is used to transmit to the northern hemisphere.

Figure 2: TheSDSconstellation, which uses satellites in a mixture of geostationary and Molniya orbits. The constellation of Molniya-orbiting satellites uses three satellites on different orbital planes, with apogees comparable to those of the geostationary satellites.

AMolniya orbit(Russian:Молния,IPA:[ˈmolnʲɪjə],"Lightning" ) is a type of satelliteorbitdesigned to provide communications andremote sensingcoverage over highlatitudes.It is ahighly elliptical orbitwith aninclinationof 63.4degrees,anargument of perigeeof 270 degrees, and anorbital periodof approximately half asidereal day.The name comes from theMolniyasatellites, a series ofSoviet/Russiancivilian and militarycommunications satelliteswhich have used this type of orbit since the mid-1960s.

The Molniya orbit has a long dwell time over thehemisphereof interest, while moving very quickly over the other. In practice, this places it over eitherRussiaorCanadafor the majority of its orbit, providing a highangle of viewto communications and monitoring satellites covering these high-latitude areas.Geostationary orbits,which are necessarily inclined over theequator,can only view these regions from a low angle, hampering performance. In practice, a satellite in a Molniya orbit serves the same purpose for high latitudes as a geostationary satellite does for equatorial regions, except that multiple satellites are required for continuous coverage.

Satellites placed in Molniya orbits have been used for television broadcasting, telecommunications, military communications, relaying, weather monitoring,early warning systemsand some classified purposes.

History

The Molniya orbit was discovered by Soviet scientists in the 1960s as a high-latitudecommunications alternative togeostationary orbits,which require large launch energies to achieve a highperigeeand tochange inclinationto orbit over the equator (especially when launched from Russian latitudes). As a result,OKB-1sought a less energy-demanding orbit.Studies found that this could be achieved using a highly elliptical orbit with anapogeeover Russian territory.The orbit's name refers to the "lightning" speed with which the satellite passes through the perigee.

The first use of the Molniya orbit was by thecommunications satelliteseriesof the same name.After two launch failures, and one satellite failure in 1964, the first successful satellite to use this orbit, Molniya 1-1, launched on 23 April 1965.The early Molniya-1 satellites were used for civilian television, telecommunication and long-range military communications, but they were also fitted with cameras used for weather monitoring, and possibly for assessing clear areas forZenit spy satellites.The original Molniya satellites had a lifespan of approximately 1.5 years, as their orbits were disrupted byperturbations,and they had to be constantly replaced.

The succeeding series, the Molniya-2, provided both military and civilian broadcasting and was used to create theOrbitatelevision network,spanning the Soviet Union. These were in turn replaced by the Molniya-3 design.A satellite called Mayak was designed to supplement and replace the Molniya satellites in 1997, but the project was cancelled,and the Molniya-3 was replaced by theMeridiansatellites, the first of which launched in 2006.The SovietUS-Kearly warning satellites,which watch for American rocket launches, were launched in Molniya orbits from 1967, as part of theOkosystem.

From 1971, the AmericanJumpseatandTrumpetmilitary satellites were launched into Molniya orbits (and possibly used to intercept Soviet communications from the Molniya satellites). Detailed information about both projects remains classified as of 2019.This was followed by the AmericanSDSconstellation, which operates with a mixture of Molniya and geostationary orbits. These satellites are used to relay signals from lower flying satellites back to ground stations in the United States and have been active in some capacity since 1976.A Russian satellite constellation called Tyulpan was designed in 1994 to support communications at high latitudes, but it did not progress past the planning phase.

In 2015 and 2017 Russia launched twoTundrasatellites into a Molniya orbit, despite their name, as part of itsEKSearly warning system.

Animation ofEKS

Equatorial view

Polar view

Earth fixed frame,front view

Earth fixed frame,side view

Kosmos 2510·Kosmos 2518·Kosmos 2541·Kosmos 2546·Earth

Uses

Figure 3: Groundtrack of a Molniya orbit. In the operational part of the orbit (four hours on each side of apogee), the satellite is north of 55.5° N (latitude of, for example, central Scotland, Moscow and southern part of Hudson Bay). A satellite in this orbits spends most of its time over the northern hemisphere and passes quickly over the southern hemisphere.

Much of the area of the formerSoviet Union,andRussiain particular, is located at high northern latitudes. To broadcast to these latitudes from a geostationary orbit (above the Earth'sequator) requires considerable power due to the lowelevation angles,and the extra distance and atmospheric attenuation that comes with it. Sites located above 81° latitude are unable to view geostationary satellites at all, and as a rule of thumb, elevation angles of less than 10° can cause problems, depending on the communications frequency.

A satellite in a Molniya orbit is better suited to communications in these regions, because it looks more directly down on them during large portions of its orbit. With an apogee altitude as high as 40,000 kilometres (25,000 mi) and an apogee sub-satellite point of 63.4 degrees north, it spends a considerable portion of its orbit with excellent visibility in the northern hemisphere, from Russia as well as from northern Europe, Greenland and Canada.

While satellites in Molniya orbits require considerably less launch energy than those in geostationary orbits (especially launching from high latitudes),their ground stations need steerable antennas to track the spacecraft, links must be switched between satellites in a constellation and range changes cause variations in signal amplitude. Additionally, there is a greater need forstation-keeping,and the spacecraft will pass through theVan Allen radiation beltfour times per day.

Southern hemisphere proposals

Similar orbits with an argument of perigee of 90° could allow high-latitude coverage in the southern hemisphere. A proposed constellation, theAntarctic Broadband Program,would have used satellites in an inverted Molniya orbit to providebroadband internet serviceto facilities inAntarctica.Initially funded by the now defunctAustralian Space Research Program,it did not progress beyond initial development.

Molniya constellations

Permanent high-latitude coverage of a large area of Earth (like the whole of Russia, where the southern parts are about 45°N) requires a constellation of at least three spacecraft in Molniya orbits. If three spacecraft are used, then each spacecraft will be active for a period of eight hours per orbit, centered around apogee,as illustrated in figure 4. Figure 5 shows the satellite's field of view around the apogee.

The Earth completes half a rotation in twelve 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, the apogees were placed over Russia and North America, but by changing theright ascension of the ascending nodethis can be varied.The coverage from a satellite in a Molniya orbit over Russia is shown in figures 6 to 8, and over North America in figures 9 to 11.

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 separated by 7.97 hours.Since each satellite has an operational period of approximately eight hours, when one spacecraft travels four hours after its apogee passage (see figure 8 or figure 11), then the next satellite will enter its operational period, with the view of the earth shown in figure 6 (or figure 9), and the switch-over can take place. Note that the two spacecraft at the time of switch-over are separated by about 1,500 kilometres (930 mi), so that the ground stations only have to move their antennas a few degrees to acquire the new spacecraft.

Diagrams

• 
  Figure 4: A constellation of three Molniya spacecraft providing service for the Northern hemisphere.Pis the orbital period. A green line corresponds to service for Asia and Europe with the visibility of figures 6–8. A red line corresponds to service for North America with the visibility of figures 9–11.
• 
  Figure 5: Illumination zones (at least 10° elevation) from a Molniya orbit. At apogee, the green illumination zone applies. At three hours before or after apogee, the red zone applies. At four hours before or after apogee, the blue zone applies. The plane of the figure is the longitudinal plane of apogee rotating with the Earth. In the eight-hour period centered at the apogee passage, the longitudinal plane is almost fixed, the longitude of the satellite varies by only ±2.7°. The views of the Earth from these three points are displayed in figures 6–11.
• 
  Figure 6: View of the Earth four hours before apogee from a Molniya orbit under the assumption that the longitude of the apogee is 90°E. The spacecraft is at an altitude of 24,043 km over the point 92.65°E 47.04°N.
• 
  Figure 7: View of the Earth from the apogee of a Molniya orbit under the assumption that the longitude of the apogee is 90°E. The spacecraft is at an altitude of 39,867 km over the point 90°E 63.43°N.
• 
  Figure 8: View of the Earth four hours after apogee from a Molniya orbit under the assumption that the longitude of the apogee is 90° E. The spacecraft is at an altitude of 24,043 km over the point 87.35°E 47.04°N
• 
  Figure 9: View of the Earth four hours before apogee from a Molniya orbit under the assumption that the longitude of the apogee is 90°W. The spacecraft is at an altitude of 24,043 km over the point 87.35°W 47.04°N.
• 
  Figure 10: View of the Earth from the apogee of a Molniya orbit under the assumption that the longitude of the apogee is 90°W. The spacecraft is at an altitude of 39,867 km over the point 90°W 63.43°N.
• 
  Figure 11: View of the Earth 4 hours after apogee from a Molniya orbit under the assumption that the longitude of the apogee is 90°W. The spacecraft is at an altitude of 24,043 km over the point 92.65°W 47.04°N.

Comparison ofTundra orbit,QZSS orbitand Molniya orbit - equatorial view

Front view

Side view

Earth fixed frame,Front view

Earth fixed frame,Side view

Tundra orbit·QZSS orbit·Molniya orbit·Earth

Properties

A typical Molniya orbit has the following properties:

• Argument of perigee: 270°
• Inclination: 63.4°
• Period: 718 minutes
• Eccentricity: 0.74
• Semi-major axis:26,600 km (16,500 mi)

Argument of perigee

The argument of perigee is set at 270°, causing the satellite to experience apogee at the most northerly point of its orbit. For any future applications over the southern hemisphere, it would instead be set at 90°.

Orbital inclination

In general, theoblatenessof the Earthperturbstheargument of perigee($\omega$), so that it gradually changes with time. If we only consider the first-order coefficient$J_{2}$,the perigee will change according to equation1,unless it is constantly corrected with station-keeping thruster burns.

${\dot {\omega }}={\frac {3}{4}}\cdot nJ_{2}\cdot \left({\frac {R_{E}}{a}}\right)^{2}{\frac {4-5\sin ^{2}{i}}{(1-e^{2})^{2}}}$(1)

where$i$is the orbital inclination,$e$is the eccentricity,$n$is mean motion in degrees per day,$J_{2}$is the perturbing factor,$R_{E}$is the radius of the earth,$a$is the semimajor axis, and${\dot {\omega }}$is in degrees per day.

To avoid this expenditure of fuel, the Molniya orbit uses an inclination of 63.4°, for which the factor$4-5\sin ^{2}{i}$is zero, so that there is no change in the position of perigee over time.An orbit designed in this manner is called afrozen orbit.

Orbital period

To ensure the geometry relative to the ground stations repeats every 24 hours, theperiodshould be about half asidereal day,keeping the longitudes of the apogees constant.

However, theoblatenessof the Earth also perturbs the right ascension of theascending node($\Omega$), changing thenodal periodand causing theground trackto drift over time at the rate shown in equation2.

${\dot {\Omega }}=-{\frac {3}{2}}\cdot nJ_{2}\cdot \left({\frac {R_{E}}{a}}\right)^{2}{\frac {\cos {i}}{(1-e^{2})^{2}}}$(2)

where${\dot {\Omega }}$is in degrees per day.

Since the inclination of a Molniya orbit is fixed (as above), this perturbation is${\dot {\Omega }}=-0.3$degrees per day. To compensate, the orbital period is adjusted so that the longitude of the apogee changes enough to cancel out this effect.

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 setas high as possible.However, the perigee needs to be high enough to keep the satellite substantially above theatmosphereto minimize drag (~600km), and the orbital period needs to be kept to approximately half a sidereal day (as above). These two factors constrain the eccentricity, which becomes approximately 0.737.

Semi-major axis

The exact height of a satellite in a Molniya orbit varies between missions, but a typical orbit will have a perigee altitude of approximately 600 kilometres (370 mi) and an apogee altitude of 39,700 kilometres (24,700 mi), for a semi-major axis of 26,600 kilometres (16,500 mi).

Modelling

To track satellites using Molniya orbits, scientists use the SDP4simplified 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.

See also

• List of orbits
• Tundra orbit

External links

• Illustration of the communication geometry provided by satellites in 12-hour Molniya orbits(video)