Reply to this "Linear approximations are actually used fairly extensively in astronomy and its relative fields such as astrodynamics. One of its most frequent uses is in orbital mechanics, where the motions and orbits of both celestial bodies and spacecraft follow precise movements. For example, stations such as the ISS need to maintain their orbit in a predictable and steady motion in order for them to hold their altitude, and constantly recalculating the exact forces required repeatedly would create unwanted strain on the systems, so utilizing linear approximation makes it significantly easier and quicker for both computer and human calculation. Depending on the situation, quite a few formulae are used depending on the required outcome, but the vis-viva equation v v + dv/dr)r0 (r - r0) is the most significant as the ISS uses it to calculate changes in velocity from slight altitude drifting. These approximations are also used for calculating the motion of planets or stars, and although these celestial bodies follow a rough oval or circular shape, the precise motions that our planets follow are a lot more complex, so simply figuring out the short term direction using linearity makes it a lot easier to know where a particular celestial object will be, which in such a case would use the formula (t) 0 +wt. Furthermore, linear approximations are also used for a variety of smaller tasks, such as calculating the approximate landing site of a ship part after it detaches from the main craft, which in this case it would use the formula s(t) 0 + v0t, or even calculating the rough sizes of planets when only a basic estimate is required