A spaceship is launched into a circular orbit close to the earth's surface . What additional velocity has now to be imparted to the spaceship in the orbit to overcome the gravitational pull. Radius of earth `= 6400 km`, `g = 9.8m//s^(2)`.

Explanation

Let `v_0` and `v_e` denote the orbital velocity and escape velocity of the spaceship.
` therefore v_0 = sqrt(gR) = sqrt(9.8 xx 6400 xx 1000) = 8 km//s`
and ` v_e = sqrt(2gR) = sqrt(2 xx 9.8 xx 6400 xx 1000) = 11.2 km//s`
` therefore ` Additional velocity required ` = v_e - v_0`
` therefore Delta v = sqrt(2gR) - sqrt(gR) = (11.2 - 8.0) km//s = 3.2 km//s `