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

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 $V =$ $\frac { k } { \sqrt { D } }$ , and elliptical if $V < \frac { k } { \sqrt { D } }$ , where $k = 2.82 \times 10 ^ { 7 }$ is a constant and $\mathrm { D }$ is the distance in meters from the satellite to the center of Earth. Solve the problem.
-If a satellite is scheduled to leave Earthʹs gravitational influence, its velocity must be increased so that its trajectory changes from elliptical to hyperbolic. Determine the minimum increase in
Velocity necessary for a satellite traveling at a velocity of 4881 meters per second to escape Earthʹs
Gravitational influence when D = 194 × 106 m.

A) 4817 m per sec
B) 4945 m per sec
C) 6906 m per sec
D) -2856 m per sec