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The Laputians astronomers were uneasy because their calculations and beliefs led them to believe that the earth would be eaten up by the sun. They did not understand the change in the stars or the placement of the sun, something that provoked fear and unease. Details can be found on pages 149 and 150 in the text.
Their apprehensions arise from several changes they dread in the celestial bodies: for instance, that the earth, by the continual approaches of the sun towards it, must, in course of time, be absorbed, or swallowed up; that the face of the sun, will, by degrees, be encrusted with its own effluvia, and give no more light to the world; that the earth very narrowly escaped a brush from the tail of the last comet, which would have infallibly reduced it to ashes; and that the next, which they have calculated for one-and-thirty years hence, will probably destroy us.