The computer translates right ascension and declination to the position of the telescope on its mount - a coordinate transformation that involves lots of spherical trigonometry (see p. 35).
The software built into the computer is called firmware and contains a built-in catalogue of stars and deep-sky objects, plus algorithms to compute the position of the Moon and planets, so that you can choose objects by name.
Computerized telescopes are a testimony to the low price of powerful computers. The Celestron NexStar 5, for example, has four CPUs in an internal network. Comparable computing power would have cost millions of dollars in the 1960s and would have filled several rooms. What's more, the telescope can be connected to an external computer - typically a laptop PC - for even more brainpower.
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