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Question 23302: The Earth is closest to the sun in January. The closest point, or perihelion, is 1.47 x 10^8km from the sun. The Earth is farthest from the sun in july. The farthest point or Aphelion, is 1.52 x 10^8 km from the sun. Write an equation of the ellipse that models the Earth orbit around the sun. Assume that the centre of the ellipse is at the origin and that the major axis is along the x-axis.
-------------------------Earth
Perihelion.___sun_________.Aphelion -----------> assuming this is the ellipse.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! I'm going to drop the 10's for the moment and just use 1.47 and 1.52.
The major axis is 2a = 1.47+1.52 = 2.99
So, a = 2.99/2 = 1.495 and a^2 = 2.235025
c=1.495-1.47= 0.025
To find "b" for an ellipse b^2=a^2-c^2
b^2=2.235025-0.025^2=2.234400
Therefore the equation of your ellipse, which has the form
x^2/a^2 + y^2/b^2 = 1 is
x^2/(1.495X10)^2 + y^2/[1.494657X10]^2 = 1
x^2/[2.235025X10^2] + y^2/[2.234400X10^2] = 1
Cheers,
stan H.
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