# Astrophysics: Calculating the circumference of an ellipse

Homework Statement:
I'm new to this website. Could someone explain how to solve this equation, its the formula for an ellipse circumference :
Relevant Equations:
P = 2a(pi){1-(1/2)^2[(sqrta^2b^2)/a]^2- [(1*3)/(2*4)]^2{[(sqrta^2b^2)/a]/3}^4.....}
Substituting :
a = (9.15x10^7 mi)+(9.45x10^7mi) = 1.86x10^8 mi
b = ( a/2 ) = 9.3x10^7 mi

For this, I used six terms and got :

1.075x10^9 miles

Is my math wrong?

;

mjc123
Homework Helper
There seem to be a few mistakes in your formula. If I've got it right, "sqrta^2b^2" should be sqrt(a^2 - b^2). (Maybe just a typo on your part.)
{[(sqrta^2b^2)/a]/3}^4 should be {[(sqrt(a^2-b^2))/a]^4}/3
And I don't know where you're getting your a and b from. In this formula, a is the semi-major axis and b the semi-minor axis. Not (as you are using?) the sum and average of these. That's why you're getting an answer about a factor of 2 high.

Thanks for the feedback. Yes, I'm still learning how to type formulas, but what you wrote is what I meant. I was using the formula to find the length of earth's orbit around the sun w/out using Google. My apologies on the a and b numbers. I've found it extremely difficult to find the semi-minor axis of the orbit, given that the farthest and closest distances make a 180-degree angle.

mjc123