The equation of an ellipse is x2/a2+y2/b2=1, where a and b are positive constants, a ³...

The equation of an ellipse is x2/a2+y2/b2=1, where a and b are positive constants, a ³ b. The foci of this ellipse are located at (c, 0), and (-c, 0), where c = (a² – b²)^1/2. The eccentricity, e, of this ellipse is given by e=c/a, while the length of the ellipse’s perimeter is

\int_0^((\pi )/(2)) 4a(1-e^(2)sin^(2)\theta )^((1)/(2))d\theta .

If 0 < e < 1, this integral cannot be integrated in terms of “well-known” functions. However, fnInt, may be used to approximate the integral.

The path of the earth lies in a plane, and follows an ellipse, with the sun at one of its foci. It takes one year for the earth to orbit the sun. The closest the earth comes to the sun is 91.5 million miles, and the furthest is 94.5 million miles.

1. For the earth and sun configuration, what are the values of a, b, c, and e?

2. How far does the earth travel in one orbit of the sun?

3. What is the average speed of the earth, around the sun, in miles per second? Why is this the average speed?

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genius_generous answered 1 year ago

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