Ground track
A ground track or ground trace is the
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
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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.[note 1]
Direct and retrograde motion
Typically, satellites have a roughly
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
A satellite whose orbital period is equal to the rotational period of the Earth is said to be in a
A special case of the geosynchronous orbit, the
Effect of inclination
Orbital
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:
where
- is the time elapsed
- 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:
where
- is the body's second dynamic form factor
- is the body's radius
- is the orbital inclination
- is the orbit's semi-major axis
- is the orbital eccentricity
These two effects must cancel out after a set orbital revolutions and (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:
where
- is the standard gravitational parameter for the body being orbited
- is the number of orbital revolutions after which the same ground track is covered
- is the number of sidereal days after which the same ground track is covered
See also
- Course (navigation)
- Ground tracking station
- Pass (spaceflight), the period in which a spacecraft is visible above the local horizon
- Satellite revisit period, the time elapsed between observations of the same point on Earth by a satellite
- Satellite watching, as a hobby
- Subsolar point
- Terminator (solar), the moving line that separates the illuminated day side and the dark night side of a planetary body
Notes
- ^ This article discusses closed orbits, or orbits with eccentricity less than one, and thus excludes parabolic and hyperbolic trajectories.
- ^ 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.
References
- ^ "suborbital track". AMetSoc.org Glossary of Meteorology. Retrieved 15 March 2022.
- ^ ISBN 978-0-7506-6169-0.
- ^ ISBN 3-540-67280-X.
- S2CID 236275629.
- Lyle, S. and Capderou, Michel (2006) Satellites: Orbits and Missions Springer ISBN 9782287274695pp 175–264
External links
- Satellite Tracker at eoPortal.org
- satview.org
- heavens-above.com
- https://isstracker.pl ISS Tracker
- Satellite Ground Track, GPS BII-10 at the Wayback Machine (archived 2020-09-30) Small Satellites (software code)
- infosatellites.com
- n2yo.com