If \upsilon _\text{e} is the escape velocity and \upsilon _\text{o} is the orbital velocity of satellite of orbit close to the Earth's surface, then these are related by :

  • Option 1)

    \upsilon _\text{o} = \upsilon _\text{e}

  • Option 2)

    \upsilon _\text{e} = \sqrt {2\upsilon _\text{o} }

  • Option 3)

    \upsilon _\text{e} = \sqrt 2 \upsilon _\text{o}

  • Option 4)

    \upsilon _\text{o} = \sqrt 2 \upsilon _\text{e}

 

Answers (1)

escape velocity = \sqrt\frac{24M}{R}

orbital velocity close is earth's surface (V0) = \sqrt\frac{4M}{R}

\therefore \frac{Ve}{Vo}=\sqrt{2} or Ve=\sqrt{2} \ V_{0}


Option 1)

\upsilon _\text{o} = \upsilon _\text{e}

The option is incorrect.

Option 2)

\upsilon _\text{e} = \sqrt {2\upsilon _\text{o} }

The option is incorrect.

Option 3)

\upsilon _\text{e} = \sqrt 2 \upsilon _\text{o}

The option is correct.

Option 4)

\upsilon _\text{o} = \sqrt 2 \upsilon _\text{e}

The option is incorrect.

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