The first artificial satellite to orbit the earth was Sputnik I. Its highest point above earths surface was 947 km, and its lowest point was 228 km. The center of the earth was at one focus of the elliptical orbit. The radius of the earth is 6378 km. Find the eccentricity of the orbit.

Explanation

As show in the fiugure, Sputink setellite is travelling on the ellptical orbit having equation
`(x^(2))/(a^(2))+(y^(2))/(b^(2))=1`
with the centre of earth A at the focus.
AC=AD= Radius of earth =6378 km
Accroding the question, the highest point of Spuntik abvoe earth's surface si E and the lowest point is B. Therefore,
`BC=228 km and Ed =947 km`
From the figure,
`AB=a-ae=AC+BC=6378+228=6606`
and `AE=a+ae=AD+ED=6378+947=7325`
`:. (a+ae)/(a-ae)=(7325)/(6606)`
`:. (1+e)/(1-e)=(7325)/(6606)`
`:. e=(7325-6606)/(7325+6606)=(719)/(13931)+ 0.05161`