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 =

the working equation for the angular size is the product of the physical size and 360 degrees divided by the product of two pi and distance from earth. the minimum size would be 0.559 degrees while the maximum size would be 0.49 degrees. 

a sonic boom is a loud boom that breaks the sound barrier

explanation: