The orbit of earth is an ellipse with eccentricity 1/60 with the sun at one focus the major axis being approximately 186 × 106 miles in length. Find the shortest and longest distance of the earth from the sun.
Let the orbit of the earth be the ellipse
Its major axis = 2a = 186 × 106 miles (given)
i.e., a = 93 × 106 miles and e = 1/60 (given)
Let the sum be at the focus S(ae, 0). Then the earth will be at shortest and longest distance from the sun when the earth is at the extremities of the major axis which are respectively nearest and farthest from this focus S.
∴ Shortest distance of the earth from the sun
= SA where S is (ae, 0) and A is (a, 0)
= a – ae = a(1 – e)
= 91450000 miles
and longest distance of earth from the sun
= SA’, where S is (ae, 0) and A’ is (–a, 0)
= a + ae
= a(1 – e)
= 94550000 miles
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