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Thursday, October 20, 2011

How the Satellite Orbit is defined?

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A satellite orbit is generally described by Two Line Elements ( TLE for short )

A typical TLE set for Cartosat 2 Satellite looks like this. This a very rigidly specified format and can be directly used by most of the Orbit Generation programs.

1 29710U 07001B 11289.87789931 .00001006 00000-0 14407-3 0 2742
2 29710 97.8976 348.0802 0002117 70.9435 289.1994 14.78689525 25724
What do these numbers indicate?

Use the worksheet here to decode them.

and after using that link we get following list: ( Some parameters are additional parameters computed after decoding the TLEs )

Sat Name: CARTOSAT-2
CAT No. 37838
DRAG 0.00001006
BSTAR 14407-3
Inclination 19.7947
Right Ascension 62.7084
Eccentricity 0.0060638
Argument of perigee 17.8079
Mean Anomaly 342.4581
Mean Motion 14.2066792
Element Set 2742
Rev No. 25724
Epoch Time 11289.8779

SemiMajor Axis 7201.23183
Height above Equator 823.09
Period ( in seconds ) 6081.646441
Epoch Year ------------------> 2011
Epoch Day of year---------> 289
EpochTime ------------------> 21:04:10

Figure below shows them graphically.

We use a Practical example with an actual satellite graphic to bring more clarity.

First figure depicts Apogee, Perigee, Major and Minor axes, Ascending and Descending nodes, True Anomaly ( see last para/figure ), Argument of Perigee

The satellite orbit crosses equator at two points.. once while traveling from North to South and second time from South to North . These points are called as NODEs.. The first case N>>>S) is defined as DESCENDING node because the satellite is traveling downwards. The S>>>N node is called as Ascending node. ( In the figure Ascending node is in front while descending Node is behind Earth hence can’t be seen ). Inclination is defined as the angle between orbital plane and Equator at Ascending node measured towards East.
Figure below shows:

AScending Node the angle between Vernal Equinox ( also called 1st point of Aries , One of the points of ( Which was earlier In Aries Constellation )The line formed where the The Celetial Equator and Earth's Equator intersect. This is shown in the figure on Leftside.

Basically these numbers tell the status of satellite in its orbit around Earth. Orbit is always in a flat plane called orbital plane and the Earth is in its one of the foci. We will restrict ourselves withElliptical orbits.

Epoch time is the time for which the given numbers are measured. ( these numbers together are also called as State Vector because they depict the status of satellite in its dynamic path at that Epoch time.

The satellite can be put in any of the following orbits: ( classified with respect to angle between Orbital plane and Equator.)

Equatorial: Where the orbit is over equator. So the angle i ( = inclination ) in above 2nd figure will be = 0 deg.
Polar : Where the orbit is passing near poles. So the angle i will be = 90 deg.
Inclined Orbit : Is in between the above two .. there are other subcategories in this :prograde, Retrograde and a very special called as Molniya which has an inclination angle of 63.4 deg.

The Orbit in its orbital plane itself has different shapes. The Ellipse may be Thin, Fat, Circularetc. ( these are unscientific words used only for explanation ) This definition of shape is denoted by the Eccentricity. The Apogee and Perigee are the points in the ellipse which are nearest and farthest from the central body. The straight line between Apogee and Perigee will necessarily pass through the central body and that distance is called Major axis. The other perpendicular axis to Major axis in orbital plane passing through the centre of major axis isMinor axis. Eccentricity e is a constant defining the shape of the orbit (0=circular, Less than 1=elliptical)
The satellite can be anywhere in the orbital plane and it is denoted by small Omega sign ( calledArgument of perigee , the angle between perigee and satellite at the time of Epoch.

We had shownTRUE Anomaly in the figure whereas in the decoded list given above there isMEAN anomaly.

No, it is not typo.. TRUE and MEAN anomalies ARE different. Their representation is shown below. The second part shows how true anomaly changes throughout the orbit.

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