Every time I try to solve this question I get an answer that's not in the choices: Pluto follows an elliptical orbit with a = 20.232 Au (astronomical units) and b = 19.618 Au. Compute the distance the comet travels in one orbit.

I keep getting around 65 Au whenever I try to calculate the perimeter of the ellipse, and that's not one of my options.

Question

Every time I try to solve this question I get an answer that's not in the choices: Pluto follows an elliptical orbit with a = 20.232 Au (astronomical units) and b = 19.618 Au. Compute the distance the comet travels in one orbit.

I keep getting around 65 Au whenever I try to calculate the perimeter of the ellipse, and that's not one of my options.

agent0smith · Answer

Since a and b are almost equal, the perimeter would be approximately the perimeter of a circle with radius ~20: 2*pi*20 = 125.66Au; thus 65Au is much too small. Which formula are you using? Here are a few: http://www.mathsisfun.com/geometry/ellipse-perimeter.html Using the first (the approximation) I got 125.2 Au

anonymous · Answer

I used the same formula, but every time I plug it into my calculator I get 65 :/

agent0smith · Answer

Are you sure you're entering it correctly? I used the approximation and got 125

agent0smith · Answer

$$p = 2\pi \sqrt{\frac{ 20.232^{2}+19.618^{2} }{ 2 }} = 2\pi \sqrt{\frac{ 794.199748 }{ 2 }}$$

agent0smith · Answer

$$p=2\pi \sqrt{397.099874}$$