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One way to align a spacecraft into a certain manner while in orbit around a body is the use a Magnetorquer. Does Mars have enough of a magnetic field to allow such a device to operate?

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No, a magnetorquer would be useless in orbit around Mars.

Mars has a surface field strength of maybe a few tens of nanoteslas. That's less of a magnetic field strength than a cassette tape. To make things worse, there isn't one single magnetic field, but a collection of weak remnant fields. Mars used to have a global magnetic field a few billion years ago, but today the remaining local fields barely even cover their relatively small areas.

Sources:

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