When a Satellite Is near Earth, Its Orbital Trajectory May $V$

question 19

Multiple Choice

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 hyperbolic if $V > \frac { k } { \sqrt { D } }$ , parabolic if $\mathrm { V } = \frac { \mathrm { k } } { \sqrt { \mathrm { D } } }$ , and elliptical if $\mathrm { V } < \frac { \mathrm { k } } { \sqrt { \mathrm { D } } }$ , where $\mathrm { k } = 2.82 \times 10 ^ { 7 }$ is a constant and $\mathrm { D }$ is the distance in meters from the satellite to the center of Earth. Solve the problem.
-When a certain satellite was at a maximum distance of $57.6 \times 10 ^ { 6 }$ m from Earth's center, it had a velocity of 4873 m per sec. Determine the shape of its trajectory.

• A) elliptical
• B) parabolic
• C) hyperbolic

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