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

question 239

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.
-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 a
Satellite traveling at a velocity of 5696 meters per second to escape Earth's gravitational influence when $\mathrm { D } = 167 \times 10 ^ { 6 } \mathrm {~m} .$

• A) \(- 3514 \mathrm {~m}\) per sec
• B) \(5765 \mathrm {~m}\) per sec
• C) \(7878 \mathrm {~m}\) per sec
• D) \(5627 \mathrm {~m}\) per sec

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Definitions:

Unit Conversion Cost

The cost associated with converting raw materials into a finished product on a per-unit basis.

Equivalent Units

A concept used in cost accounting to express the amount of work done in terms of fully completed units of output during a period.

Conversion Costs

Conversion costs are the sum of direct labor and manufacturing overhead costs that are required to convert raw materials into finished products.

Direct Materials

Raw materials that are directly used in the manufacturing process of a product and can be directly traced to the goods being produced.