1. The problem statement, all variables and given/known data What fraction of its "year" (i.e. the period of its orbit) does a planet spend traversing the half of its orbit closest to the sun? Give the answer in terms of the eccentricity ε of the planet's orbit. This is problem 15 from page 852 of Adam's Calculus 3ed. No detailed solution available. 2. Relevant equations Partial area integral of an ellipse. 3. The attempt at a solution Just divide (area of ellipse to the "right" of latus rectum)/(total area of ellipse) according to Kepler's law. However I get stuck in "impossible" integrals. The answer is (1/2)-(ε/π). S.A.