# Highly Elliptical Orbits (Revisit Period, Shape, Size, Velocity, Period, Inclination, and Atmospheric Condition and Altitude) (Especially for GATE-Geospatial 2022)

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- Highly Elliptical Orbits (HEO) satellites orbit the Earth in an orbital plane with an inclination between 50 and 70°. The period of a HEO satellite is approximately 12 hours and the shape of the orbit is highly elliptical.
- During the HEO satellite՚s orbit, it comes very close the planet for part of its orbit, causing its velocity to increase. Then it travels very far away from the Earth and its orbital velocity decreases. As a result, it spends much of its time in the portion of the orbit that is at a very high altitude.

## Details of High Elliptical Satellite Orbit

- A HEO satellite is placed in an orbit in such a way that it will spend the greatest amount of time over a specific area of the planet. Thus, if a HEO communications satellite is launched to provide communications in the arctic region, its orbit would be configured so that is spends the bulk of its time in orbit above these latitudes. This is especially useful in providing communications and navigation services from a satellite. One example of HEO satellites is the Global Positioning System, which uses a fleet of HEO satellites to provide constant coverage of the entire planet and which can provide precise locational data to any point on the surface of the Earth.
- As a satellite revolves around the Earth, the sensor “sees” a certain portion of the Earth՚s surface. The area imaged on the surface, is referred to as the swath. Imaging swaths for spaceborne sensors generally vary between tens and hundreds of kilometers wide. As the satellite orbits the Earth from pole to pole, its east-west position would not change if the Earth did not rotate.
- However, as seen from the Earth, it seems that the satellite is shifting westward because the Earth is rotating (from west to east) beneath it. This apparent movement allows the satellite swath to cover a new area with each consecutive pass. The satellite՚s orbit and the rotation of the Earth work together to allow complete coverage of the Earth՚s surface, after it has completed one complete cycle of orbits.

**Earth rotation, satellite orbit and satellite swath makes possible to image the entire Earth՚s surface coverage**

- If we start with any randomly selected pass in a satellite՚s orbit, an orbit cycle will be completed when the satellite retraces its path, passing over the same point on the Earth՚s surface directly below the satellite (called the nadir point) for a second time. The exact length of time of the orbital cycle will vary with each satellite.

## Revisit Period

- The interval of time required for the satellite to complete its orbit cycle is not the same as the “revisit period.” Using steer able sensors, a satellite-borne instrument can view an area (off-nadir) before and after the orbit passes over a target, thus making the ‘revisit’ time less than the orbit cycle time.
- The revisit period is an important consideration for several monitoring applications, especially when frequent imaging is required (for example, to monitor the spread of an oil spill, or the extent of flooding) . In near-polar orbits, areas at high latitudes will be imaged more frequently than the equatorial zone due to the increasing overlap in adjacent swaths as the orbit paths come closer together near the poles.

## Shape

- Satellites orbit their primary body in a shape that is called an ellipse. An ellipse can be thought of as a circle that is somewhat “out of round,” although the technical definition of an ellipse is “a closed plane curve generated by a point moving in such a way that the sums of the distances from two fixed points are a constant.”
- The characteristics of an ellipse are probably best understood when compared to a circle.
- A perfect circle has a single point in its centre. Each point on the circle is an equal distance from this point, known as the focus of the circle. Any line that connects two sides of the circle and passes through the focus are equal in length.
- An ellipse is a circle that is slightly stretched in one dimension. An ellipse has two focal points. The sum of the distances from any point to each focal point will always remain constant. A line that connects two sides of the ellipse and passes through both focal points is called the major axis of the ellipse. A line perpendicular to the major axis that passes through the point directly between the focal points is the minor axis of the ellipse.
- The degree to which an ellipse is stretched is described as the eccentricity of the ellipse. The eccentricity can be described as the ratio between the length of the major axis and the distance between the foci of the ellipse. The foci in highly eccentric ellipse are spread farther apart than those of an ellipse with a lower eccentricity. The value of eccentricity ranges from 0 (a perfect circle) and approaches a value of 1 as the ellipse becomes more eccentric. A satellite՚s orbit around the Earth is in the shape of an ellipse, and the Earth՚s centre of mass is at one of the focal points of the ellipse.
- A satellite orbit can be described by the eccentricity of the orbit. Satellite orbits range from nearly circular orbits (with a low eccentricity) to very highly elliptical orbits (with a high eccentricity) . A satellite with a nearly circular orbit maintains a relatively constant altitude above the Earth՚s surface, while the altitude of a satellite with a very highly elliptical orbit is constantly changing.
**Circular satellite orbits have low eccentricity while elliptical orbits have greater eccentricity**

## Size

- Another of the orbital elements used to describe a satellite՚s orbits is the semi-major axis, which is defined as half the distance of the major axis. In general, the larger the semi major axis, the larger the orbit.
- The larger the orbit, the greater the amount of energy required to place the satellite into the orbit. Thus, satellites with larger orbits with higher altitudes above earth are much more expensive to launch and maintain.

## Velocity

- As a satellite orbits the Earth in an elliptical orbit, its distance from the Earth՚s surface changes. The point in its orbit at which the satellite is closest to the Earth is called perigee. The point opposite to perigee, when the satellite is at its furthest point from Earth, is called apogee. As a satellite approaches perigee, its orbital velocity increases. At perigee, the satellites velocity is at its maximum.
- As it approaches apogee, its orbital velocity decreases. At apogee, the satellites velocity is at its minimum. Thus, satellites with a nearly circular orbit maintain a nearly constant orbital velocity, while satellites with highly elliptical orbits have a wider range of orbital velocities, speeding up as they get closer to Earth and slowing down as they move further away.

## Period

- The period of an orbit is the amount of time it takes for a satellite to complete one full orbit around its primary body. A general rule of orbital mechanics states that the closer an orbiting object is to its primary body, the higher its velocity. In addition, the closer a satellite is to the Earth, the less distance it must travel to complete a single orbit. The result is a general relationship between a satellite՚s altitude and its period: the lower the altitude, the shorter its period.
- The lowest satellites orbit the earth with a period of approximately 87 minutes per orbit (if a satellite were placed any lower in the orbit the atmosphere would interfere so much that it could not maintain its orbit) . Other satellites at higher altitudes have orbital periods that are longer than a full 24-hour day.

## Inclination

- Inclination of a satellite orbit describes the tilt of the orbit plane with respect to the equatorial plane. An orbit with inclination angle of 0° would orbit the Earth in the same plane as the Equator. This is known as an equatorial orbit, and a satellite in this type of orbit follows the Earth՚s equator.
- An orbit with an inclination angle of would orbit the Earth crossing the North and South Poles in a plane that is perpendicular to the equatorial plane. This type of orbit is known as a polar orbit. Other satellites are in orbits with inclinations between 0 and 90°.

## Atmospheric Condition and Altitude

- Atmospheric condition is different depending on the altitude. This factor is considered in the selection of platforms or sensors. Here, air pressure, air density and temperature are considered.
- Dependence of air pressure on altitude is based on the hydro-static equilibrium of balance between the vertical pressure of the atmosphere and gravity. The atmospheric constituents without water vapour are assumed constant in volume ratio with 78.08 % nitrogen, 20.95 % oxygen, and argon 0.93 % up to about 100 km regardless of time and place. It gives an average molecular weight at 28.97 for the atmosphere and the average molecular mass of 4.810 x 10 - 26 kg.
- When temperature is constant with respect to altitude, the air pressure decreases as an exponential function, which gives about an 8 km altitude for a decrease of air pressure to 1/e, as shown in Figure below.

**Altitudinal distribution of air pressure and air density**

- However, since the actual atmosphere varies in temperature with altitude, the air pressure can be calculated from the hydro-static equilibrium with a given temperature. For general purposes, the standard model atmosphere has been specified with respect to the average temperature distribution and the vertical air pressure. Also the average model With respect to latitude and season has been specified, although the actual temperature sometimes has a difference of 10 - 20°K. Therefore the measurement of temperature using radio-sonde is necessary for high accuracy. The vertical structure of the atmosphere is composed of the following layers.
- Troposphere: from the ground surface to 10 - 17 km,
- Stratosphere: from 10 - 17 km to about 50 km
- Mesosphere: from about 50 km to about 90 km
- Thermosphere: from about 90 km to 500 km

- The classification of the above layers depends on the distribution of thermal energy and thermal transportation. The vertical decrease of temperature in the troposphere is 9.8°K km
^{-1}for dry atmosphere, but 6.5°K km^{-1}for the actual atmosphere because of water vapour. - The border between the troposphere and the stratosphere is called tropopause. The tropics tropopause is rather constant at 17 km in altitude while the middle latitude tropopause depends on seasonal change and jet stream with 10 - 17 km in altitude as shown in below Figure.

**Seasonal distribution of thermal energy and thermal transpiration**