Understanding How the Hubble Re-Orients: The Mathematics Behind It

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The Hubble Space Telescope (HST) re-orients itself using tiny sensor gyroscopes that maintain a consistent orientation, helping it determine its position in space. For enhanced pointing accuracy, HST is equipped with star trackers integrated into its instruments. Additionally, the telescope utilizes reaction wheels, which are heavy spinning wheels that facilitate movement by conserving angular momentum. When these wheels are spun, they create a reaction that allows the telescope to adjust its orientation. This combination of gyroscopes and reaction wheels enables precise control over HST's positioning in orbit.
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How does Hubble Space Telescope (HST) re-orient itself; and what is an underlying mathematical description? http://en.wikipedia.org/wiki/Gyroscope"
 
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HST has tiny sensor gyroscopes which spin freely and so always point the same way it uses this to know which way is up.
For more accurate pointing it also star trackers built into some of the instruments.

It also has reaction wheels (also sometimes loosely called gyros) these heavy wheels spin like gyros and can be used to move the telescope. When the spin they tend to stay in the same plane and so when you push on them you move instead.
 
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