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Sun vector is the vector from the center of earth to center of sun. Actually it is from the satellite to the sun but for all practical purposes we can assume it is from earth to sun (distance between earth and sun 149,597,870 km and earth and satellite around 700 km + radius of the earth for LEO satellites). Before dirtying our hands for the calculation, let’s look at how the equatorial plane and ecliptic planes are defined and what is vernal equinox.
[[File:SunVector4.png|frame|center|Ecliptic plane and ECI frame. Image reproduced from [https://commons.wikimedia.org/wiki/File:Earths_orbit_and_ecliptic.PNG here]]]
* '''Equatorial Plane:''' It is the plane perpendicular to the axis of rotation of earth. It is midway between North and South pole and divides the earth into two Hemispheres – Northern and Southern.
* '''Ecliptic Plane:''' The plane which is coplanar with the Earth’s orbit around Sun. The axis of Earth is tilted by 23.4 degrees with respect to this ecliptic plane. This tilt is the reason we have seasons.<ref>https://www.windows2universe.org/earth/climate/cli_seasons.html</ref> Isn’t that Cool and Hot and Rainy?
==Determination of Light/Eclipse region ==
Here we are defining the dark region as umbra and rest is taken as the light region. We wish to calculate how long will the satellite be in Umbra. You can see from the figure that umbra region is formed by simply drawing the common tangents of earth and sun.
[[File:UmbraUmbra3.png|framethumb|center|1000px|Definition of the eclipse region. Image reproduced from [https://en.wikipedia.org/wiki/Umbra,_penumbra_and_antumbra here]]]
Let’s define first some of the parameters first.<br \>
Rs = Radius of Sun. <br \>
∅ = angle between sun vector and the vector formed be apex of umbra and satellite.<br \>
ru can be calculated by forming similar triangle.
The region of umbra would be when it follows two conditions:[[File:Equation76.png|frame|center]][[File:Umbra2.png|frame|center|Obtaining condition for satellite to be in umbra region]]
The knowledge of eclipse region is important from the power subsystem point of view. In this region there will no solar panel in the sunlight so the satellite functionalities have to depend solely on batteries. Also, in this region the sun vector can’t be calculated using the sun sensor. Any output coming on the sun sensor would be noise and we should not calculate sun vector using sun sensor in this region. <br \>
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If you are done reading this page, you can go back to [[Attitude Determination and Control Subsystem]]
==References==
