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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:Umbra.png|frame|center]]
Let’s define first some of the parameters first.<br \>Rs = Radius of Sun.<br \>Re = Radius of Earth.<br \>r = Center distance between Earth and Sun.<br \>ru = Distance between center of earth and apex of umbra.<br \>α = Umbra apex half angle<br \>θ = angle between satellite position vector (from earth) and sun vector.<br \>∅ = angle between sun vector and the vector formed be apex of umbra and satellite.<br \>
ru can be calculated by forming similar triangle.
[[File:Umbra2.png|frame|center]]
If you are done reading this page, you can go back to [[Attitude Determination and Control Subsystem]]
==References==
