A mass placed in a gravitational field experiences a force.


If no other force acts on the mass, the total energy will
remain constant but energy might be converted from g.p.e. to k.e. 



Energy Possessed by a Satellite in Orbit 

Let the mass of the planet be M, the mass of the
satellite, m, and the radius of the orbit of
the satellite r. 

The force of gravity must be just equal to
the centripetal force needed to maintain the orbit . 

Therefore we can write 



This means that for a given radius of orbit, the satellite must have a speed
given by 



which tells us that, if the radius of the orbit decreases, the speed must
increase (to maintain the new orbit). 



Therefore, the kinetic energy, K possessed by the satellite is 



The potential energy possessed by the satellite is given by 



Looking at these last two equations, we see that 

1. if r decreases, K increases and P decreases
(it becomes a larger negative value) 

2. the decrease in P is more than the increase in K (so the total
energy decreases). 



Therefore, to fall from one orbit to a lower
orbit, the total energy must decrease. 

In other words, some work must be done
to decrease the energy of the satellite if it is to fall to a
lower orbit. 




The work done, w, is equal to the change in
the total energy of the satellite, 



This work results in a conversion of energy from gravitational potential
energy to internal energy of the satellite (it makes it hot!). 

Air resistance can thus reduce the speed of the satellite
along its orbit. 

This allows the satellite to fall towards the planet. 

As it falls, it gains speed. 

So, if a viscous drag (air resistance) acts
on a satellite, it will 

1. decrease the radius of the orbit and 

2. increase the speed of the satellite in its new orbit. 



In principle, the satellite could settle in a lower, faster
orbit but in practice it will usually be falling to a region
where the drag is greater. 

It will therefore continue to move towards the planet in a spiral path, as
shown. 
