A missile is fired radially from the surface of earth (radius 6.4 xx 10^(6) m) at a satellite, orbiting the earth. The satellite appears stationary vertically upwards from the point where the missile is launched. Its distance from the centre of the earth is 25.4 xx 10^(6)m. Will the missile actually hit the satellite?

A missile is fired radially from the surface of earth (radius 6.4 xx 1

1.	A missile is fired radially from the surface of earth (radius 6.4 xx 10^(6) m) at a satellite, orbiting the earth. The satellite appears stationary vertically upwards from the point where the missile is launched. Its distance from the centre of the earth is 25.4 xx 10^(6)m. Will the missile actually hit the satellite?
Answer» SOLUTION :At time of launch of missile, it has the following velocities. (i) An orbital angular velocity equal to orbital angular velocity of earth and (ii) vertical velocity to reach geo-stationary satellite. When missile is moving TOWARDS satellite, no torque is acting on it, hence angular momentum of missile-earth system MUST be CONSERVED. With the increase in height `r`, the moment of inertia of missle, `I = mr^(2)` increase as a result of it, its angular velocity decrease because `I omega = a` constant. As the orbital angular velocity of satellite remains unchanged so the missile will not be hitting the satellite.