# Ground track

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A ground track or ground trace is the path on the surface of a planet directly below an aircraft's or satellite's trajectory. In the case of satellites, it is also known as a suborbital track, and is the vertical projection of the satellite's orbit onto the surface of the Earth (or whatever body the satellite is orbiting). [1]

## Contents

A satellite ground track may be thought of as a path along the Earth's surface that traces the movement of an imaginary line between the satellite and the center of the Earth. In other words, the ground track is the set of points at which the satellite will pass directly overhead, or cross the zenith, in the frame of reference of a ground observer. [2]

## Aircraft ground tracks

In air navigation, ground tracks typically approximate an arc of a great circle, this being the shortest distance between two points on the Earth's surface. In order to follow a specified ground track, a pilot must adjust their heading in order to compensate for the effect of wind. Aircraft routes are planned to avoid restricted airspace and dangerous areas, and to pass near navigation beacons.

## Satellite ground tracks

The ground track of a satellite can take a number of different forms, depending on the values of the orbital elements, parameters that define the size, shape, and orientation of the satellite's orbit. (This article discusses closed orbits, or orbits with eccentricity less than one, and thus excludes parabolic and hyperbolic trajectories.)

Typically, satellites have a roughly sinusoidal ground track. A satellite with an orbital inclination between zero and ninety degrees is said to be in what is called a direct or prograde orbit , meaning that it orbits in the same direction as the planet's rotation. A satellite with an orbital inclination between 90° and 180° (or, equivalently, between 0° and −90°) is said to be in a retrograde orbit . (Direct orbits are by far the most common for artificial satellites, as the initial velocity imparted by the Earth's rotation at launch reduces the delta-v needed to achieve orbit.)

A satellite in a direct orbit with an orbital period less than one day will tend to move from west to east along its ground track. This is called "apparent direct" motion. A satellite in a direct orbit with an orbital period greater than one day will tend to move from east to west along its ground track, in what is called "apparent retrograde" motion. This effect occurs because the satellite orbits more slowly than the speed at which the Earth rotates beneath it. Any satellite in a true retrograde orbit will always move from east to west along its ground track, regardless of the length of its orbital period.

Because a satellite in an eccentric orbit moves faster near perigee and slower near apogee, it is possible for a satellite to track eastward during part of its orbit and westward during another part. This phenomenon allows for ground tracks that cross over themselves in a single orbit, as in the geosynchronous and Molniya orbits discussed below.

### Effect of orbital period

A satellite whose orbital period is an integer fraction of a day (e.g., 24 hours, 12 hours, 8 hours, etc.) will follow roughly the same ground track every day. This ground track is shifted east or west depending on the longitude of the ascending node, which can vary over time due to perturbations of the orbit. If the period of the satellite is slightly longer than an integer fraction of a day, the ground track will shift west over time; if it is slightly shorter, the ground track will shift east. [2] [3]

As the orbital period of a satellite increases, approaching the rotational period of the Earth (in other words, as its average orbital speed slows towards the rotational speed of the Earth), its sinusoidal ground track will become compressed longitudinally, meaning that the "nodes" (the points at which it crosses the equator) will become closer together until at geosynchronous orbit they lie directly on top of each other. For orbital periods longer than the Earth's rotational period, an increase in the orbital period corresponds to a longitudinal stretching out of the (apparent retrograde) ground track.

A satellite whose orbital period is equal to the rotational period of the Earth is said to be in a geosynchronous orbit. Its ground track will have a "figure eight" shape over a fixed location on the Earth, crossing the equator twice each day. It will track eastward when it is on the part of its orbit closest to perigee, and westward when it is closest to apogee.

A special case of the geosynchronous orbit, the geostationary orbit, has an eccentricity of zero (meaning the orbit is circular), and an inclination of zero in the Earth-Centered, Earth-Fixed coordinate system (meaning the orbital plane is not tilted relative to the Earth's equator). The "ground track" in this case consists of a single point on the Earth's equator, above which the satellite sits at all times. Note that the satellite is still orbiting the Earth — its apparent lack of motion is due to the fact that the Earth is rotating about its own center of mass at the same rate as the satellite is orbiting.

### Effect of inclination

Orbital inclination is the angle formed between the plane of an orbit and the equatorial plane of the Earth. The geographic latitudes covered by the ground track will range from –i to i, where i is the orbital inclination. [3] In other words, the greater the inclination of a satellite's orbit, the further north and south its ground track will pass. A satellite with an inclination of exactly 90° is said to be in a polar orbit, meaning it passes over the Earth's north and south poles.

Launch sites at lower latitudes are often preferred partly for the flexibility they allow in orbital inclination; the initial inclination of an orbit is constrained to be greater than or equal to the launch latitude. Vehicles launched from Cape Canaveral, for instance, will have an initial orbital inclination of at least 28°27′, the latitude of the launch site—and to achieve this minimum requires launching with a due east azimuth, which may not always be feasible given other launch constraints. At the extremes, a launch site located on the equator can launch directly into any desired inclination, while a hypothetical launch site at the north or south pole would only be able to launch into polar orbits. (While it is possible to perform an orbital inclination change maneuver once on orbit, such maneuvers are typically among the most costly, in terms of fuel, of all orbital maneuvers, and are typically avoided or minimized to the extent possible.)

In addition to providing for a wider range of initial orbit inclinations, low-latitude launch sites offer the benefit of requiring less energy to make orbit (at least for prograde orbits, which comprise the vast majority of launches), due to the initial velocity provided by the Earth's rotation. The desire for equatorial launch sites, coupled with geopolitical and logistical realities, has fostered the development of floating launch platforms, most notably Sea Launch.

### Effect of argument of perigee

If the argument of perigee is zero, meaning that perigee and apogee lie in the equatorial plane, then the ground track of the satellite will appear the same above and below the equator (i.e., it will exhibit 180° rotational symmetry about the orbital nodes.) If the argument of perigee is non-zero, however, the satellite will behave differently in the northern and southern hemispheres. The Molniya orbit, with an argument of perigee near −90°, is an example of such a case. In a Molniya orbit, apogee occurs at a high latitude (63°), and the orbit is highly eccentric (e = 0.72). This causes the satellite to "hover" over a region of the northern hemisphere for a long time, while spending very little time over the southern hemisphere. This phenomenon is known as "apogee dwell", and is desirable for communications for high latitude regions. [3]

### Repeat orbits

As orbital operations are often required to monitor a specific location on Earth, orbits that cover the same ground track periodically are often used. On earth, these orbits are commonly referred to as Earth-repeat orbits, and are often designed with "frozen orbit" parameters to achieve a repeat ground track orbit with stable (minimally time-varying) orbit elements. [4] These orbits use the nodal precession effect to shift the orbit so the ground track coincides with that of a previous orbit, so that this essentially balances out the offset in the revolution of the orbited body. The longitudinal rotation after a certain period of time of a planet is given by:

${\displaystyle \Delta L_{1}=-2\pi {\frac {T}{T_{E}}}}$

where

• ${\displaystyle T}$ is the time elapsed
• ${\displaystyle T_{E}}$ is the time for a full revolution of the orbiting body, in the case of Earth one sidereal day

The effect of the nodal precession can be quantified as:

${\displaystyle \Delta L_{2}=-{\frac {3\pi J_{2}R_{e}^{2}cos(i)}{a^{2}(1-e^{2})^{2}}}}$

where

• ${\displaystyle J_{2}}$ is the body's second dynamic form factor
• ${\displaystyle R_{e}}$ is the body's radius
• ${\displaystyle i}$ is the orbital inclination
• ${\displaystyle a}$ is the orbit's semi-major axis
• ${\displaystyle e}$ is the orbital eccentricity

These two effects must cancel out after a set ${\displaystyle j}$ orbital revolutions and ${\displaystyle k}$ (sidereal) days. Hence, equating the elapsed time to the orbital period of the satellite and combining the above two equations yields an equation which holds for any orbit that is a repeat orbit:

${\displaystyle j\left|\Delta L_{1}+\Delta L_{2}\right|=j\left|-2\pi {\frac {2\pi {\sqrt {\frac {a^{3}}{\mu }}}}{T_{E}}}-{\frac {3\pi J_{2}R_{e}^{2}cos(i)}{a^{2}(1-e^{2})^{2}}}\right|=k2\pi }$

where

• ${\displaystyle \mu }$ is the standard gravitational parameter for the body being orbited
• ${\displaystyle j}$ is the number of orbital revolutions after which the same ground track is covered
• ${\displaystyle k}$ is the number of sidereal days after which the same ground track is covered

## Related Research Articles

In celestial mechanics, an orbit is the curved trajectory of an object such as the trajectory of a planet around a star, or of a natural satellite around a planet, or of an artificial satellite around an object or position in space such as a planet, moon, asteroid, or Lagrange point. Normally, orbit refers to a regularly repeating trajectory, although it may also refer to a non-repeating trajectory. To a close approximation, planets and satellites follow elliptic orbits, with the center of mass being orbited at a focal point of the ellipse, as described by Kepler's laws of planetary motion.

Tidal acceleration is an effect of the tidal forces between an orbiting natural satellite and the primary planet that it orbits. The acceleration causes a gradual recession of a satellite in a prograde orbit away from the primary, and a corresponding slowdown of the primary's rotation. The process eventually leads to tidal locking, usually of the smaller body first, and later the larger body. The Earth–Moon system is the best-studied case.

A geosynchronous orbit is an Earth-centered orbit with an orbital period that matches Earth's rotation on its axis, 23 hours, 56 minutes, and 4 seconds. The synchronization of rotation and orbital period means that, for an observer on Earth's surface, an object in geosynchronous orbit returns to exactly the same position in the sky after a period of one sidereal day. Over the course of a day, the object's position in the sky may remain still or trace out a path, typically in a figure-8 form, whose precise characteristics depend on the orbit's inclination and eccentricity. A circular geosynchronous orbit has a constant altitude of 35,786 km (22,236 mi).

A geostationary orbit, also referred to as a geosynchronous equatorial orbit (GEO), is a circular geosynchronous orbit 35,786 km (22,236 mi) in altitude above Earth's Equator and following the direction of Earth's rotation.

Sidereal time is a timekeeping system that astronomers use to locate celestial objects. Using sidereal time, it is possible to easily point a telescope to the proper coordinates in the night sky. In short, sidereal time is a "time scale that is based on Earth's rate of rotation measured relative to the fixed stars", or more correctly, relative to the March equinox.

An equatorial bulge is a difference between the equatorial and polar diameters of a planet, due to the centrifugal force exerted by the rotation about the body's axis. A rotating body tends to form an oblate spheroid rather than a sphere.

The orbital period is the amount of time a given astronomical object takes to complete one orbit around another object. In astronomy, it usually applies to planets or asteroids orbiting the Sun, moons orbiting planets, exoplanets orbiting other stars, or binary stars.

A geosynchronous transfer orbit or geostationary transfer orbit (GTO) is a type of geocentric orbit. Satellites that are destined for geosynchronous (GSO) or geostationary orbit (GEO) are (almost) always put into a GTO as an intermediate step for reaching their final orbit.

A geocentric orbit or Earth orbit involves any object orbiting Earth, such as the Moon or artificial satellites. In 1997, NASA estimated there were approximately 2,465 artificial satellite payloads orbiting Earth and 6,216 pieces of space debris as tracked by the Goddard Space Flight Center. More than 16,291 objects previously launched have undergone orbital decay and entered Earth's atmosphere.

The Molniya series satellites are military and communications satellites launched by the Soviet Union from 1965 to 2004. These satellites use highly eccentric elliptical orbits known as Molniya orbits, which have a long dwell time over high latitudes. They are suited for communications purposes in polar regions, in the same way that geostationary satellites are used for equatorial regions.

A Molniya orbit is a type of satellite orbit designed to provide communications and remote sensing 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. The name comes from the Molniya satellites, a series of Soviet/Russian civilian and military communications satellites which have used this type of orbit since the mid-1960s.

A Sun-synchronous orbit (SSO), also called a heliosynchronous orbit, is a nearly polar orbit around a planet, in which the satellite passes over any given point of the planet's surface at the same local mean solar time. More technically, it is an orbit arranged so that it precesses through one complete revolution each year, so it always maintains the same relationship with the Sun.

A graveyard orbit, also called a junk orbit or disposal orbit, is an orbit that lies away from common operational orbits. One significant graveyard orbit is a supersynchronous orbit well beyond geosynchronous orbit. Some satellites are moved into such orbits at the end of their operational life to reduce the probability of colliding with operational spacecraft and generating space debris.

In astronautics and aerospace engineering, the bi-elliptic transfer is an orbital maneuver that moves a spacecraft from one orbit to another and may, in certain situations, require less delta-v than a Hohmann transfer maneuver.

A Tundra orbit is a highly elliptical geosynchronous orbit with a high inclination, an orbital period of one sidereal day, and a typical eccentricity between 0.2 and 0.3. A satellite placed in this orbit spends most of its time over a chosen area of the Earth, a phenomenon known as apogee dwell, which makes them particularly well suited for communications satellites serving high-latitude regions. The ground track of a satellite in a Tundra orbit is a closed figure 8 with a smaller loop over either the northern or southern hemisphere. This differentiates them from Molniya orbits designed to service high-latitude regions, which have the same inclination but half the period and do not loiter over a single region.

The Moon orbits Earth in the prograde direction and completes one revolution relative to the Vernal Equinox and the stars in about 27.32 days and one revolution relative to the Sun in about 29.53 days. Earth and the Moon orbit about their barycentre, which lies about 4,670 km (2,900 mi) from Earth's center, forming a satellite system called the Earth–Moon system. On average, the distance to the Moon is about 385,000 km (239,000 mi) from Earth's center, which corresponds to about 60 Earth radii or 1.282 light-seconds.

A geosynchronous satellite is a satellite in geosynchronous orbit, with an orbital period the same as the Earth's rotation period. Such a satellite returns to the same position in the sky after each sidereal day, and over the course of a day traces out a path in the sky that is typically some form of analemma. A special case of geosynchronous satellite is the geostationary satellite, which has a geostationary orbit – a circular geosynchronous orbit directly above the Earth's equator. Another type of geosynchronous orbit used by satellites is the Tundra elliptical orbit.

Nodal precession is the precession of the orbital plane of a satellite around the rotational axis of an astronomical body such as Earth. This precession is due to the non-spherical nature of a rotating body, which creates a non-uniform gravitational field. The following discussion relates to low Earth orbit of artificial satellites, which have no measurable effect on the motion of Earth. The nodal precession of more massive, natural satellites like the Moon is more complex.

The nodal period of a satellite is the time interval between successive passages of the satellite through either of its orbital nodes, typically the ascending node. This type of orbital period applies to artificial satellites, like those that monitor weather on Earth, and natural satellites like the Moon.

## References

1. "suborbital track". AMetSoc.org Glossary of Meteorology. Retrieved 15 March 2022.
2. Curtis, Howard D. (2005), Orbital Mechanics for Engineering Students (1st ed.), Amsterdam: Elsevier Ltd., ISBN   978-0-7506-6169-0 .
3. Montenbruck, Oliver; Gill, Eberhard (2000), Satellite Orbits (1st ed.), The Netherlands: Springer, ISBN   3-540-67280-X .
4. Low, Samuel Y. W. (January 2022). "Designing a Reference Trajectory for Frozen Repeat Near-Equatorial Low Earth Orbits". AIAA Journal of Spacecraft and Rockets. 59. doi:10.2514/1.A34934.