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Let G be the universal gravitational constant and mp be the mass of the planet a satellite is orbiting. Which equation could be used to find the velocity of the satellite if it is placed in a geostationary orbit?
Which factor is not needed when calculating the velocity of a satellite orbiting a planet?
the mass of the planet
the orbital radius of the satellite
the universal gravitational constant
the mass of the satellite
Let G be the universal gravitational constant and mp be the mass of the planet a satellite is orbiting. Which equation could be used to find the velocity of the satellite if it is placed in a low Earth orbit?
Transcribed Image Text:The image presents four mathematical expressions, likely representing velocity formulas involving gravitational parameters. One of the options is highlighted, indicating it may be the correct or selected answer. Here are the expressions:
1. \( \bigcirc \quad v = \frac{1}{(200 \text{ km})} \sqrt{Gm_p} \)
2. \( \bigodot \quad v = \sqrt{\frac{Gm_p}{(7,000 \text{ km})}} \)
3. \( \bigcirc \quad v = \frac{1}{(7,000 \text{ km})} \sqrt{Gm_p} \)
4. \( \bigcirc \quad v = \sqrt{\frac{Gm_p}{(200 \text{ km})}} \)
Explanation of Variables:
- \( v \) is the velocity.
- \( G \) is the gravitational constant.
- \( m_p \) represents the mass of the planet or central body.
- The numeric values in parentheses (e.g., 200 km, 7,000 km) represent distances, possibly from the center of the planet or orbit radius.
The highlighted option (second expression) suggests a specific scenario or formula relevant to orbital velocity or gravitational calculations.
![The image shows a set of equations related to the calculation of velocity using gravitational parameters. Each equation follows the formula format:
\[ v = \sqrt{\frac{Gm_p}{r}} \]
where \( Gm_p \) is the product of the gravitational constant and the mass of the planet, and \( r \) is the radius in kilometers. Each equation is accompanied by a selectable option (radio button), with one option highlighted to indicate selection. The equations are:
1. \[ v = \sqrt{\frac{Gm_p}{15,522 \text{ km}}} \]
2. \[ v = \sqrt{\frac{Gm_p}{7,324 \text{ km}}} \]
- This option is currently selected.
3. \[ v = \sqrt{\frac{Gm_p}{42,164 \text{ km}}} \]
4. \[ v = \sqrt{\frac{Gm_p}{48,115 \text{ km}}} \]
There are no graphs or additional diagrams associated with the image. The focus is on the mathematical expressions and the selection interface.](https://content.bartleby.com/qna-images/question/9167482e-441e-4d4b-828a-88c1aa93bc1d/46539cbb-55da-4a00-9c33-c076ce76e76a/h5givvf_processed.png)
Transcribed Image Text:The image shows a set of equations related to the calculation of velocity using gravitational parameters. Each equation follows the formula format:
\[ v = \sqrt{\frac{Gm_p}{r}} \]
where \( Gm_p \) is the product of the gravitational constant and the mass of the planet, and \( r \) is the radius in kilometers. Each equation is accompanied by a selectable option (radio button), with one option highlighted to indicate selection. The equations are:
1. \[ v = \sqrt{\frac{Gm_p}{15,522 \text{ km}}} \]
2. \[ v = \sqrt{\frac{Gm_p}{7,324 \text{ km}}} \]
- This option is currently selected.
3. \[ v = \sqrt{\frac{Gm_p}{42,164 \text{ km}}} \]
4. \[ v = \sqrt{\frac{Gm_p}{48,115 \text{ km}}} \]
There are no graphs or additional diagrams associated with the image. The focus is on the mathematical expressions and the selection interface.
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