Escape Velocity

1
Escape Velocity
2
Contd

• Consider a projectile of mass m, leaving the
  surface of a planet (or some other astronomical
  body) with escape velocity v. It has a kinetic
  energy k given by

3
Contd

• The projectile also has potential energy U given
  by

4
Contd

• When the projectile reaches maximum height v0
• since v(instantaneous velocity) is the
  derivative of altitude with respect to time.
  Therefore k 0. Also as r the
  potential energy goes to zero. Based on the
  principal of conservation of energy , the total
  energy of the projectile at the planets surface
  must also have been zero. Therefore,

5
Contd
6
Escape speed
7
Escape speed

• The escape speed does not depend on the direction
  in which a projectile is fired.However, attaining
  the speed is easier if the projectile is fired in
  the direction the launch site is moving as Earth
  rotates about its axis.

8
Escape speed

• Rockets are launched eastward at Cape
  Conaveral to take advantage of the Capeseastward
  speed of 1500km/h.