The velocity needed for the rocket or other projectile to orbit around the Earth is called the 'first cosmic velocity' (v₁). The velocity required to escape the Earth is called the 'second cosmic velocity' (v₂). The minimum velocity has to attain to leave the solar system from the Earth is called the 'third cosmic velocity' (v₃). In terms of the radius of the Earth R, the speed Earth orbiting around the Sun v and the gravitational acceleration near the Earth surface g, find
a) The 'first cosmic velocity' (v₁)
b) The 'second cosmic velocity' (v₂)
c) The 'third cosmic velocity' (v₃)
Finally, estimate the values of v₁, v₂ and v₃ using values from the formula page and the expressions obtained above.