SOLUTION: The orbit of Earth around the sun is in the shape of an ellipse where the sun is at one of the foci, and whose length of the major axis is 185.8 million miles. If the distance of t

Question 1142988: The orbit of Earth around the sun is in the shape of an ellipse where the sun is at one of the foci, and whose length of the major axis is 185.8 million miles. If the distance of the sun from the center of the orbit is 1.58 million miles, find the least and greatest distance of Earth from the sun.
Found 2 solutions by ikleyn, rothauserc:
Answer by ikleyn(52800) (Show Source): You can put this solution on YOUR website!
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From the condition, the linear eccentricity of the ellipse is c = 1.58 million miles. The major semi-axis of the ellipse is a = = 92.9 miles. The greatest distance from the sun to Earth is the sum a + c = 92.9 + 1.58 = 94.48 million miles. ANSWER The least distance from the sun to the Earth is the difference a - c = 92.9 - 1.58 = 91.32 million miles. ANSWER

Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
The semi-major axis a is half of the greatest width of the ellipse.
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a = 185.8/2 = 92.9 million miles
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Linear eccentricity c - is the distance from the focal point to the center of the ellipse
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c = 1.58 million miles
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Eccentricity of ellipse e is the ratio of the linear eccentricity c to the length of the semi-major axis a
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e = c/a = 1.58/92.9 = 0.017
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The greatest distance(Apogee) of Earth from the sun is
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A = a * (1+e) = 92.9 * 1.017 = 94.4793 is approximately 94.48 million miles
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The least distance(Perigee) of Earth from the sun is
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P = a * (1-e) = 92.9 * 0.983 = 91.3207 is approximately 91.32 million miles
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