Books describing first-hand experience of astrophysicists finding planets without skipping actual maths
The discovery and recapture of Ceres, and the brilliant discovery and use by Gauss of the Normal distribution, the method of least squares, and a method that would now be thought of as a type of fast fourier transform to predict the position of the planet to within 0.5 degrees, based on just 6 observations is one of the great achievements of "pen and paper astronomy". Gauss, though we now think of him as a pure mathematician, held the post of Professor of Astronomy in Göttingen.

Discovery of the First Asteroid, Ceres: Historical Studies in Asteroid Research by Clifford Cunningham, ISBN 978-3-319-21777-2 tells this story in some detail, but ouch its not cheap! nearly £100 on dead trees.