When a satellite is near Earth, its orbital trajectory may trace out a hyperbola, a parabola, or an ellipse. The type of trajectory depends on the satellite’s velocity V in meters per second. It will be

where k = 2.82 × 10⁷ is a constant and D is the distance in meters from the satellite to the center of Earth.

If a satellite is scheduled to leave Earth’s gravitational influence, its velocity must be increased so that its trajectory changes from elliptical to hyperbolic. Determine the minimum increase in velocity necessary for Explorer IV to escape Earth’s gravitational influence when D = 42.5 × 10⁶ m. Round to the nearest whole number.

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parabolic if V = hyperbolic if V> elliptical if V <- or VD