Arocket of mass m is in circular orbit around the earth at a distance r from the center. (a) what tangential impulse, that is, m δv, must be given to the body so that it just escapes to infinity? (b) describe the resulting orbit. (c) compare with the radial impulse that must be given to a particle initially at rest at r if it is to acquire sufficient velocity to escape to infinity.

Answer and Solution:

As per the question:

Mass of rocket = m

Distance from the center = R

Now,

(a) For tangential impulse, the centripetal force of the rocket is provided by the gravitational force, thus:

where

= Centripetal force

= Gravitational force

Therefore,

Also, the velocity of the rocket after impulse is given as:

Now, the tangential impulse can be calculated as under:

At infinity, the energy is zero:

Now,

Impulse,

(b) Resulting orbit will follow a straight line path.

(c) On comparing the radial impulse, the energy that the impulse has provided is given by:

Impulse = mv =

increases it