# Altitude of Platform and Orbital Elements of Satellite (Especially for GATE-Geospatial 2022)

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## Altitude of Platform

The geometric distortion depends on not only the geometry of the sensor but also the altitude of the platform. Therefore, it is very important to measure the altitude of the platform for the consequent geometric correction.

The altitude of the platform is classified by the following two components:

- Rotation angles around the three axes: roll, pitch and yaw
- Jitter: random and unsystematic vibration which cannot be measured

The rotation angles; roll, pitch and yaw are defined as the rotation angles around the flight direction, the main wing and the vertical line respectively, as shown in below Figure which shows the satellite altitude parameters.

**Satellite altitude parameters**

For a frame camera, the rotation angles are single values common to a full scene of aerial photograph, while for a line scanner the altitude changes as a function of line number or time. In the case of satellites, the variation of the position and the altitude will be continuous, though in case of aircraft, the variation will not always be smooth, which makes the geometric correction more difficult.

### Altitude Sensors

Altitude control of a satellite is classified by two methods; spin control and three axis control. The former method is usually adopted for geosynchronous meteorological satellites which rotate itself together with rotating scanner. The latter method is mainly adopted for earth observation satellites such as Landsat which needs accurate look angle in the direction of the earth.

A gyro-compass is used for measurement of altitude variation over a short interval. Earth sensor detects the radiation of CO2 within the wavelength range of 14 - 16 mm emitted from the rim of the earth, from which two axis altitudes of roll and pitch can be measured with an accuracy of 0.3 - 1 degree. If the earth sensor is combined with a sun sensor and gyro-compass, the three-axis altitude can be measured with higher accuracy of 0.1 - 0.3 degree. Magnetic sensors can measure the three-axis altitude but with a slightly low accuracy. The responsivity of the above sensors is 2 Hz at maximum. If the high frequency altitude such as jitter is to be measured, the angular displacement sensor (ADS) is necessary.

**Typical Altitude Measurement**

## Orbital Elements of Satellite

A set of numerical values to define an orbit of a satellite or planet are called orbital elements. The independent orbital elements of the earth observation satellite are six elements of the Keplerian orbit.

A satellite can be considered to rotate around the earth in a plane, called the orbital plane, because the influence of gravity of the moon and the sun can be neglected as compared with the gravity of the earth.

A point in space can be expressed in the equatorial coordinate system as follows.

- The origin of equatorial coordinate system is the centre of the earth.
- The reference great circle: the equatorial plane
- The origin of astronomical longitude (right ascension) : the vernal equinox
- The astronomical longitude (right ascension) : 0 - 24 hours to the east from the vernal equinox.
- The astronomical latitude (declination) : angle from the equatorial plane (+ 90 degree in the north pole; -90 degree in the south pole)

### The Six Elements of Keplerian Orbit

- The semi-major axis (A) :
- Eccentricity of orbit (e) :
- Inclination angle (i) :
- Right ascension of ascending node (h)
- Argument of perigee (g)
- Time of passage of the perigee (t)

Below Figure shows the above elements. The shape and size of an orbit can be defined by A and e, while the orbit plane can be defined by i and h. The longer axis of the orbit ellipse can be determined by g. The position of a satellite can be located by T.