Question #f33c5

1 Answer
Dwight
Feb 2, 2018

The aphelion of this very eccentric orbit would be 27.793 A.U.

Explanation:

Use Kepler's third law first to find the mean radius of the orbit (actually the semi-major axis of the ellipse). Since T is in (Earth) years and r is in A.U., we can use the simplification that k=1 in the formula:

#T^2 = kr^3# becomes #T^2 = r^3#

so, taking the cube root of each side, #r = T^(2/3) = 54^(2/3)=14.287 A.U.#

This is the mean radius (or semi-major axis), so the diameter (major axis) is twice this value:

#d=28.573 A.U.#

This value is the sum of the aphelion and perihelion, and so, the aphelion must be

#28.573 - 0.78 = 27.793 A.U.#

(Strange the question would ask for the answer to the nearest thousandth of an A.U. when the given information did not have this precision!)

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