The planets move around the sun in elliptical orbits with the sun at one focus.

Question

The planets move around the sun in elliptical orbits with the sun at one focus. The point in the orbit at which the planet is closest to the sun is called perihelion, and the point at which it is farthest is called aphelion. These points are the vertices of the orbit. With an eccentricity of 0.23, a certain planet's orbit is the most eccentric in the solar system. The length of the minor axis of its orbit is approximately 14,000,000,000 km. Find the distance between this planet and the sun at perihelion and at aphelion. (Round your answers to the nearest hundredth.)

Explanation / Answer

Eccentricity, e = (1 - b2/a2)1/2

=> semi-major axis, a = b/(1 - e2)1/2 = (1.4 * 1013) / (1 - 0.232)1/2 = 1.44 * 1013 m

Distance at perihelion, dp = a(1 - e) = 1.44 * 1013 * (1 - 0.23) = 1.11 * 1013 m

Distance at aphelion, da = a(1 + e) = 1.44 * 1013 * (1 + 0.23) = 1.77 * 1013 m

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