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.

When the artificial satellite Explorer IV was at a maximum distance D of 42.5 × 10⁶ m from Earth’s center, it had a velocity V of 2090 m per sec. Determine the shape of its trajectory.

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