Mercury moves in an elliptical orbit with the sun at one of the foci.The length of the half of the major axis is 56,996,838 kilometers,and the eccentricity is 0.2056.Find the maximum distance (aphelion)of Mercury from the sun.Round your answer to nearest kilometer.
A)55,856,901 km
B)11,718,550 km
C)58,136,775 km
D)68,715,388 km
E)45,278,288 km

Question

Mercury moves in an elliptical orbit with the sun at one of the foci.The length of the half of the major axis is 56,996,838 kilometers,and the eccentricity is 0.2056.Find the maximum distance (aphelion)of Mercury from the sun.Round your answer to nearest kilometer. ​
A)55,856,901 km
B)11,718,550 km
C)58,136,775 km
D)68,715,388 km
E)45,278,288 km

Quizplus · Accepted Answer

The formula for the distance of a planet from the sun in terms of its eccentricity (e) and the length of half of its major axis (a) is:

distance = a(1+e)

We are given a = 56,996,838 km and e = 0.2056.

Plugging these values into the formula, we get:

distance = 56,996,838(1+0.2056)
distance = 68,715,387.89 km

Rounding this to the nearest kilometer, we get the maximum distance (aphelion) of Mercury from the sun as 68,715,388 km.

Therefore, the answer is D, 68,715,388 km.

Mercury Moves in an Elliptical Orbit with the Sun at One