It always felt fishy to me, even before I started doing planetary photography. Due to other reasons, like capturing the moons’ movement, and the interplay of shadows, I always tried to keep the videos short.
However, the subject is evergreen wherever there are newcomers. So, now I made the math, and since we are people, not mathboys, here’s a handy little table one can play with or scroll below, the same calculator loads into this article.
So the math is really simple. But since we are not mathematicians but engineers, I mean amateur astronomers, we can take shortcuts. We can safely ignore Jupiter’s axial tilt. We can safely ignore Jupiter’s oblateness, since we expect the greatest motion blur at the equator, right in the middle — because the way we see Jupiter is like viewing the trigonometric circle from the outside, so a sin/cos function applies. In the middle, all the movement goes sideways, while towards the edges, some, then all the movement is perceived as a recess while the surface area stays on the same pixel.
That said, we hope to find the maximum length of the video that yields no more than the motion blur set as the threshold.