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

question 152

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

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Definitions:

Cost of Capital

The rate of return that a company must pay on its investments to satisfy its debtors and equity holders, influencing investment and financing decisions.

Use of Funds

Use of funds refers to the detailed explanation of how a company or individual intends to spend the money raised from investors, loans, or other sources.

Marginal Tax Rate

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Weighted Average Cost

A method used to calculate the average cost of goods available for sale, which is weighted by the quantity of goods at each purchase price.