The Titan with a vision of the future

Long, long ago, a Titan named Helius had a vision of the earth's future: somewhere in the future the Vogons would come and destroy earth to construct a new intergalactic highway. Fearing of this, Helius flew into the sky and attained a zero velocity w.r.to earth (Gravity does not apply on Helios). He then threw an infinite number of fireballs in all directions with same speeds. the fireballs flew perpetually in space forming a network into which nothing can breach.

The envelope of the network is an ellipsoid which when drawn in 2D is an ellipse of eccentricity \(e\).If the ratio of the velocity with which Helius threw the balls to the escape velocity from earth at the point where helius threw the balls be \(0.6\), then find the \(1/e\).

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