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The blog post seems to say the reentry time depends somewhat on (future, unknown) solar activity, contributing to the estimation error.

Why would this be? Is the solar wind strong enough to affect the velocity of a dense object such as this?

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Solar activity affects the outer layer of our atmosphere which expands with solar activity and affects the drag of satellites. This is how starlight lost a bunch of satellites last year.

The solar wind affects the atmosphere, specifically by raising it, such that the probe may experience more atmospheric drag.

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