posted by Sara .
The distance between the Earth and Mars when the two panets are at opposition varies greatly because of the large eccentricity of Mar's orbit. The perihelion distance of a planet is given by rmin=a(1-e)and the aphelion distance by rmax=a(1+e) where a is the semimajor axis and e is the orbital eccentricity. Find the smallest and largest opposition distances assuming the Earth's orbit is a circle.
The eccentricity of Mar's orbit is .0934.
The semi-major axis is 141,643,675 miles.
Therefore, the perihelion distance is
r(p) = 141,643,675(1-.0934) = 128,414,418.
r(a) = 141,643,675(1+.0934) = 154,871,931.
The mean radius of the earth's orbit is
r = 92,960,242 miles.