Question

the orbiting velocity of an earth satellite is 8km/s. What will be the escape velocity

Answer 1

Answer :

Escape velocity = 8√2 km/s

                          = 11.312 km/s

Explanation :

 $\underline{\underline{\bf Orbital \ velocity :}}$

• The orbital velocity is the velocity at which a body revolves around the other one.
• It is given by,

                $\boxed{\bf V_{orbit}=\sqrt{\frac{GM}{r} } }$

       where

            G - Gravitational constant

            M - mass of the planet

             r - radius of the orbit

  $\underline{\underline{\bf Escape \ velocity:}}$

• The escape velocity is the minimum velocity required by a body to escape the gravitational field.
• It is given by,

                $\boxed{\bf V_{escape}=\sqrt{\frac{2GM}{r}}}$

          where

              G - gravitational constant

              M - mass of the planet

              r - radius of the planet

  $\underline{\bf Realtionship \ between \ V_{orbit} \ and \ V_{Escape}:}$

                   $\boxed{\bf V_{escape}=\sqrt{2}V_{orbit}}$

Given,

• Orbital velocity = 8 km/s

       =>  Escape velocity

                      $=\sqrt{2} \times 8 \\\\ =8\sqrt{2} \\\\ =8 \times 1.414 \\\\ =11.312 \ km/s$