Molniya orbit Molniya or Highly Elliptical Orbit
Friday, February 15, 2019

# Molniya orbit

For other uses, see Molniya (disambiguation) .

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

Figure 2: Groundtrack of Molniya orbit. In the operational part of the orbit (4 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 in the northern hemisphere and passes quickly over the southern hemisphere.

Figure 3: The SDS constellation, which uses satellites in a mixtures of geostationary and Molniya orbits. The constellation of Molnia orbiting satellites uses three satellites on different orbital planes, and they have apogees comparable to those of the geostationary satellites.

A Molniya orbit ( Russian : Молния, IPA:  [ˈmolnʲɪjə]  ( listen ), “Lightning”) is a type of satellite orbit. 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. The high eccentricity provides a longer dwell time over the hemisphere of interest, compared to a more circular orbit. 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]

## Contents

• 1 History
• 2 Uses
• 3 Properties
• 3.1 Orbital inclination
• 3.2 Orbital period
• 3.3 Eccentricity
• 4 Modelling
• 5 Diagrams
• 7 References

## History[ edit ]

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/or assessing clear areas for spy satellites. [4] 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, [5] followed by the Mayak and Meridian satellites in 1997 and 2002 respectively. [6]

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. [7] [8] [9]

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. [6] [10]

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. [11] A single classified communication satellite launch in 1998 may be related to this constellation. [6]

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. [12]

## Uses[ edit ]

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), [13] , 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 , [14] [15] [16] and the spacecraft will pass through the Van Allen radiation belt four times per day. [13]

## Properties[ edit ]

A typical Molniya orbit, has:

• Semi-major axis: 26,600 km
• Eccentricity: 0.74
• Inclination: 63.4° [15]
• Argument of perigee: 280°
• 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° N. If three spacecraft are used, each spacecraft is active for periods of eight hours per orbit centered at apogee [3] as illustrated in figure 9.

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 Canada, but by changing the right ascension of the ascending node this could be varied. For example, if the apogee longitudes are 90° E and 90° W, the apogees will alternately serve Europe and Asia (see figures 3 to 5) and next North America (see figures 6 to 8).

The orbits of the three spacecraft should then have the same orbital parameters, but different right ascension of the ascending nodes, with their passes over the apogees (for example 90° W and 90° E) separated by 7.97 hours. [3] [17] Since each satellite has an operational period of 8 hours, when one spacecraft travels four hours after its apogee passage (see figure 5 or figure 8), the next satellite will enter its operational period. The next satellite will have a view of the earth shown in figure 3 (or figure 6) 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. [18]

### Orbital inclination[ edit ]

In general, the oblateness of the Earth perturbs the argument of perigee (

$\displaystyle \omega$

ω

\displaystyle \omega

), so that even if the apogee started near the north pole, it would gradually move, according to equation 1 , unless constantly corrected with station-keeping thruster burns.

$\displaystyle \Delta \omega =-2\pi \;\frac J_2\mu p^2\;3\left(\frac 54\sin ^2i-1\right)$

Δ
ω
=

2
π

J

2

μ

p

2

3

(

5
4

sin

2

i

1

)

\displaystyle \Delta \omega =-2\pi \;\frac J_2\mu p^2\;3\left(\frac 54\sin ^2i-1\right)

(1)

where

$\displaystyle \mu$

μ

\displaystyle \mu

is the gravitational constant,

$\displaystyle J_2$

J

2

\displaystyle J_2

is the perturbing factor, and

$\displaystyle p$

p

\displaystyle p

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. [14] [15] At this inclination the factor

$\displaystyle \left(\frac 54\sin ^2i-1\right)$

(

5
4

sin

2

i

1

)

\displaystyle \left(\frac 54\sin ^2i-1\right)

is zero, so there is no change in perigee over time.

### Orbital period[ edit ]

To ensure the geometry relative to the ground stations repeats every 24 hours the nodal 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 (

$\displaystyle \Omega$

Ω

\displaystyle \Omega

), which would cause the ground track to drift over time at the rate shown in equation 2 .

$\displaystyle \Delta \Omega =-2\pi \;\frac J_2\mu p^2\;\frac 32\cos i$

Δ
Ω
=

2
π

J

2

μ

p

2

3
2

cos

i

\displaystyle \Delta \Omega =-2\pi \;\frac J_2\mu p^2\;\frac 32\cos i

(2)

Since the inclination of a Molniya orbit is set, this perturbation is

$\displaystyle \Delta \Omega =-0.0742$

Δ
Ω
=

0.0742

\displaystyle \Delta \Omega =-0.0742

degrees per orbit. To compensate, the orbital period is adjusted so that the longitude of the apogee changes enough to cancel out this effect. [15]

### Eccentricity[ edit ]

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. [15]

## Modelling[ edit ]

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. [19]

## Diagrams[ edit ]

• Figure 2: 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 3–8

• Figure 3: 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 4: 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 5: 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 6: 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 7: 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 8: 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.

• Figure 9: A constellation of three Molniya spacecraft providing service for the Northern hemisphere. P is the orbital period. A green line corresponds to service for Asia and Europe with the visibility of figures 3–5. A red line corresponds to service for North America with the visibility of figures 6–8.

• Elliptic orbit
• List of orbits
• Tundra orbit

## References[ edit ]

1. ^ a b c Kolyuka, Yu. F.; Ivanov, N.M.; Afanasieva, T.I.; Gridchina, T.A. (28 September 2009). Examination of the Lifetime, Evolution and Re-Entry Features for the “Molniya” Type Orbits (PDF). 21st International Symposium of Space Flight Dynamics. Toulouse, France: Mission Control Center 4, Korolev, Moscow. p. 2. Retrieved 22 May 2018.

2. ^ Anatoly Zak. “Russian communications satellites” . Russian Space Web. Retrieved 22 May 2018.
3. ^ a b c d Stojče Dimov Ilčev. Global Satellite Meteorological Observation (GSMO) Theory, Volume 1 . Springer International Publishing. p. 57. ISBN   978-3-319-67119-2 .
4. ^ Hendrickx, Bart. “A History of Soviet/Russian Meteorological Satellites” (PDF). Bis-Space.com. Antwerpen, Belgium. p. 66.
5. ^ Martin, Donald H. (2000). Communication Satellites . AIAA. pp. 215–. ISBN   9781884989094 . Retrieved 1 January 2013.
6. ^ a b c Mark Wade. “Molniya orbit” . Astronautix. Retrieved 6 June 2018.
7. ^ Forden, Geoffrey (May 3, 2001). “Reducing a Common Danger: Improving Russia’s Early-Warning System” (PDF). Cato Policy Analysis No. 399. Cato Institute : 5.
8. ^
Podvig, Pavel (2002). “History and the Current Status of the Russian Early-Warning System” (PDF). Science and Global Security. 10: 21–60. doi : 10.1080/08929880212328 . ISSN   0892-9882 . Archived from the original (pdf) on 2012-03-15.
9. ^ “Russia blinded by loss of missile detection satellite” . Moscow Times. 26 June 2014.
10. ^ William Graham (23 September 2017). “Atlas V launches NROL-42 spy satellite” . NASA spaceflight.
11. ^ Jeffrey T Richelson (2002). The Wizards of Langley. Inside the CIA’s Directorate of Science and Technology. Boulder: Westview press. ISBN   0813340594 .
12. ^ Anatoly Zak. “Nord:Connecting the north” . Russian Space Web. Retrieved 6 June 2018.
13. ^ a b “Soviet orbital trick” . Geek Times. Retrieved 23 May 2018.
14. ^ a b Wiley J. Larson and James R. Wertz (ed.). Space Mission Analysis and Design. Microcosm.
15. ^ a b c d e Kidder, Stanley Q.; Vonder Haar, Thomas H. (18 August 1989). “On the Use of Satellites in Molniya Orbits of Meteorological Observation of Middle and High Latitudes” . Journal of Atmospheric and Oceanic Technology. 7. p. 517.
16. ^ King-Hele, D. G. (1975). “The Orbital Lifetime of Molniya Satellites” . Jbis-journal of The British Interplanetary Society. 28: 783–796.
17. ^ Kidder, Stanley Q.; Vonder Haar, Thomas H. (18 August 1989). “On the Use of Satellites in Molniya Orbits of Meteorological Observation of Middle and High Latitudes” . Journal of Atmospheric and Oceanic Technology. 7. p. 519.
18. ^ R. L. Sturdivant, E. K. P. Chon (2016). “Systems Engineering of a Terabit Elliptic Orbit Satellite and Phased Array Ground Station for IoT Connectivity and Consumer Internet Access” . IEEE. 4: 9947.
19. ^ Hoots, Felix R.; Ronald L. Roehrich (31 December 1988). “Models for Propagation of NORAD Element Sets” (PDF). United States Department of Defense Spacetrack Report (3). Retrieved 16 June 2010.

• Real time satellite tracking for a typical Molniya satellite
• Illustration of the communication geometry provided by satellites in 12-hour Molniya orbits (video)
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Gravitational orbits
Types
General Box Capture Circular Elliptical / Highly elliptical Escape Graveyard Horseshoe Hyperbolic trajectory Inclined / Non-inclined Osculating Parabolic trajectory Parking Synchronous semi sub Transfer orbit Geosynchronous Geostationary Sun-synchronous Low Earth Medium Earth High Earth Molniya Near-equatorial Orbit of the Moon Polar Tundra Areosynchronous Areostationary Halo Lissajous Lunar Heliocentric Heliosynchronous
Parameters
ShapeSize e   Eccentricity a   Semi-major axis b   Semi-minor axis Q, q   Apsides i   Inclination Ω   Longitude of the ascending node ω   Argument of periapsis ϖ   Longitude of the periapsis M   Mean anomaly ν, θ, f   True anomaly E   Eccentric anomaly L   Mean longitude l   True longitude T   Orbital period n   Mean motion v   Orbital speed t0   Epoch
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