Pluto moves in an elliptical orbit with the sun at one of the foci. The length of half of the major axis is $5.906 \times 10 ^ { 9 }$ kilometers, and the eccentricity is $0.2488$. Find the perihelion distance of Pluto from the sun. Round your answer to the nearest kilometers.
A) $7,375,412,800$ kilometers
B) $4,436,587,201$ kilometers
C) $4,436,587,200$ kilometers
D) $8,873,174,399$ kilometers
E) $8,873,174,401$ kilometers

Question

Quizplus · Accepted Answer

We can use the formula for the distance from a focus in terms of the major axis and eccentricity, which is $a(1-e)$. Since half of the major axis is given as $5.906 	imes 10^9$, the full major axis is $2(5.906 	imes 10^9) = 1.1812 	imes 10^{10}$. We can then find $a$ using the formula $a = \frac{1}{2} \cdot 	ext{major axis}$, so $a = 5.906 	imes 10^9$. Plugging in these values, we get $a(1-e) = (5.906 	imes 10^9)(1-0.2488) \approx 4,436,587,200$ kilometers. Rounded to the nearest kilometer, our answer is $\boxed{	extbf{(C)}\ 4{,}436{,}587{,}200}$.

Pluto Moves in an Elliptical Orbit with the Sun at One