Some body moves at the perihelion of its orbit four times faster than at the aphelion. Find the eccentricity of its orbit

The easiest way to solve this problem is to remember that according to Kepler’s II law, a body in the course of its movement around the central mass (in this case, the Sun) describes equal areas for equal periods of time. At perihelion and aphelion, the body’s velocity is perpendicular to the direction to the center, so we can immediately get that at perihelion the body is four times closer to the Sun than at aphelion. The eccentricity of the orbit is: e = (4 – 1) / (4 + 1) = 0.6.