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The eccentricity of earths orbit is 0.0167. What is the ratio of its maximum speed to its minimum speed in its orbit?

I solved it in the following way:

Let its maximum and minimum speed be v1 and v2 respectively. Let a and b be the semi length of the major and minor axis respectively. Let e be its eccentricity.

v is inversely proportional to a and b. I took this assumption because at points closest to the centre of the elliptical path the velocity is maximum.

Hence,

v1/v2 = a/b

Now for an ellipse, (1 – e^2) = (b/a)^2

By solving I get,

a/b = 1.00014

Therefore,

v1/v2 = 1.00014

But the book answer is 1.033. Is there any mistake?

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# Homework Help: Eccentricity of elliptical path of earth

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