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     We saw in the previous section that to put a mass in orbit requires giving it angular momentum through the application of a torque. To take it out of orbit or to put it in a lower orbit requires a torque in the opposite sense to take angular momentum away. This is why retro-rockets fired against the direction of motion are used to bring manned satellites back to Earth, or to effect the landing of a spacecraft on the Moon.

     But we can also get interesting effects by the redistribution of angular momentum which can occur as a result of collisions.

     To illustrate this we obviously need more than one "particle" so let us take our single satellite (this time in a circular orbit for simplicity) and instantaneously break it up into say a million parts and allow the parts to have a very small random velocity component relative to all the other parts (say 1mm per hour). Clearly there will be collisions between the parts, albeit at a relatively low frequency. However, during a collision (in which the total angular momentum of the colliding parts is conserved), one part is likely to end up with more angular momentum at the expense of the other parts. That part with more is pushed into a higher orbit while that with less drops into a lower orbit. But now the orbital periods are not synchronised since the period of the part with the lower orbit is now smaller than that in the higher orbit.

     The final result is that the million parts are distributed throughout a ring and, because they are now dispersed, the mean distance between the parts is now many orders of magnitude greater than before so the frequency of collisions has dropped to almost negligible proportions. Hence this configuration becomes a stable one.

     We can see examples of this in our own planetary system such as the rings of Saturn and the asteroid belt. Indeed the planetary system itself comprising only a few bodies could be viewed as such though it would be wrong to do so because collisions are almost non-existent. (It is more likely for the planets to have been formed from the material in a previous disc by accreting matter and getting rid of angular momentum by heating up and emitting photons).


     We see other examples in binary star systems where two stars are in orbit round each other. During the lifetime of a star it sometimes expands about a hundred fold to become a Red Giant star. If such a star is part of a close binary system where the other star is a nearby compact object (or even a black hole), as our primary star expands material can spill over from the larger star and fall towards the compact star. Since these two stars are orbiting each other this material possesses angular momentum and is conserved by the material going into orbit round the small star in the form of a ring. Through collisions this ring spreads out and, as more material is deposited, so the ring grows in size to form a disc. This is known as an accretion disc. The material in the outer part of the disc contains most of the angular momentum of the disc and as these outer parts get closer to the primary star the matter in them can exert a torque on the material in the primary star itself and thus loose some of the angular momentum which then can cause the disc to stop growing.

     Hence a dynamic equilibrium situation can be reached whereby the material transferred from the primary star and deposited in the disc falls in towards the compact star whilst its angular momentum is transferred outwards via the process described (called viscosity).

     This is a simplification because, amongst other things, the transfer of material is not necessarily constant and such things as the star's magnetic field also has to be taken into account.

     An obvious question is where does the matter end up? It largely depends on the nature of the compact object. If it is a black hole it will never appear again. If not it may end up on the surface of the compact star itself and cause all sorts of interesting things to happen as a result. However sometimes this material is ejected back into space along two very energetic jets from the poles of the compact objects.

     If we could actually see such a disc/jet object with our own eyes it would be very dramatic. All we have at the moment are artists impressions which are founded on computer models which themselves are based on all the astrophysical data that we have from these exotic objects.

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The University of Birmingham 

Physics and Astronomy Department, The University of Birmingham