SOLUTION: 4. the earth revolves around the sun along an ellipse. the sun lies in thefocus of the ellipse. the largest distance from the sun to the earth is 152.1million kilometers, and the s

Question 1167084: 4. the earth revolves around the sun along an ellipse. the sun lies in thefocus of the ellipse. the largest distance from the sun to the earth is 152.1million kilometers, and the shortest is 147.1 million kilometers. find thelength of the semi-minor axis of the ellipse and the eccentricity of the el-lipse. what is the distance between the two foci of the ellipse?
Answer by ikleyn(52875) (Show Source): You can put this solution on YOUR website!
.
The Earth revolves around the sun along an ellipse. The Sun lies in the focus of the ellipse. The largest distance from the Sun
to the Earth is 152.1 million kilometers, and the shortest is 147.1 million kilometers. Find the length of the semi-minor axis
of the ellipse and the eccentricity of the ellipse. What is the distance between the two foci of the ellipse?

Solution

Let "a" be the semi-major ahis and "e" be the linear eccentricity of the ellipse.


Then the largest distance from the Sun to the Earth is  a + e,

while the the shortest distance from the Sun to the Earth is  a - e.


Thus you have these equations


    a + e = 152.1  million kilometers,   (1)

    a - e = 147.1  million kilometers.   (2)



Add equations (1) and (2).  You will get

    2a = 152. + 147.1 = 299.1;  hence  a = 299.1/2 = 149.55 million kilometers.    ANSWER


Next, from equation (1)

    e = 152.1 - 149.55 = 2.55 million kilometers.                                  ANSWER


The distance between foci is 2e = 2*2.55 = 5.1  million kilometers.                ANSWER

Solved.

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