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If something were to happen that would cause the James Webb Telescope to be unable to downlink its data to earth, how long could it continue collecting observations before it would run out of storage space?

How large will the JWST's memory buffer be? I assume it doesn't write its data to a disk, or does it?

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This user guide seems to be reasonably recent (2017) and answers your question.

The solid state recorder (SSR) onboard JWST can hold at least 58.8 Gbytes of recorded science data.

JWST downlinks science data in two 4-hr contacts per day; each contact can transmit at least 28.6 Gbytes of recorded science data to the ground.

So it can hold about 1 day of data in the solid state recorder.

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