Question

Earth moves in an elliptical orbit with the sun at one of the foci. The length of half of the major axis is kilometers, and the eccentricity is . Find the minimum distance (perihelion) and the maximum distance (aphelion) of Earth from the sun.

Answer 1

Complete question is;

Earth moves in an elliptical orbit with the sun at one of the foci. The length of half of the major axis is 149,598,000 kilometers, and the eccentricity is 0.0167. Find the minimum distance (perihelion) and the maximum distance (aphelion) of Earth from the sun

Answer:

Minimum distance = 147,099,713.4 km

Maximum distance = 152,096,286.6 km

Explanation:

The formula for the eccentricity of an ellipse is given by;

e = c/a

where;

c is distance from the center of the ellipse to the focus of the ellipse.

a is distance from the center of ellipse to a vertex.

From the question, we are given;

a = 149,598,000

e = 0.0167

Thus;

0.0167 = c/149,598,000

c = 0.0167 × 149,598,000

c = 2,498,286.6

Now, formula for the minimum distance (perihelion) is;

Minimum distance = a - c

Minimum distance = 149598000 - 2498286.6

Thus;

Minimum distance = 147,099,713.4 km

Similarly, formula for the maximum distance (aphelion) is;

Max distance = a + c

Max distance = 149598000 + 2498286.6

Maximum distance = 152,096,286.6 km