How do we know orbits go in an elliptic shape? I never really understood how we found out the orbits our planets follow are elliptical and not in a circle.
 A: With a triangular sextant (https://www.sciencesource.com/archive/Image/Tycho-Brahe--Triangular-Sextant--1582-SS21473734.html) and a lot of patience.
A: From a mathematical/philosophical standpoint, we can conclude that all orbits are eccentric to some extent, without needing to do any observation at all.
A truly perfectly circular orbit (eccentricity equal to exactly zero) at some orbital radius requires an exact orbital speed with infinite precision. Velocities are continuous, so the probability of a body having any particular velocity is zero - the chance of picking any particular value from a continuum of values is always zero. The probability that any body has exactly the orbital speed needed to have an orbit with an eccentricity of exactly zero is, in fact, zero. Any body in orbit almost surely does not have the correct velocity to be in a perfect circular orbit, the probability that it does is 0. All orbits are eccentric to varying degrees. The probability of finding an orbiting body with any exact eccentricity value is zero, whether that value is $0.0128475000...$ or $0.00000000...$ . You will almost never find a body with an orbital eccentricity of precisely zero.
