The satellites are revolving around a planet in circular orbits by themselves (no external source to maintain their speed). Are we able to make them revolve in elliptical orbits by themselves?
Do satellites change their way according to what conservation of angular momentum says
WITHOUT ANY EXTERNAL SYSTEM OF CONTROL?
If you solve the equations for two bodies interacting via gravity (or indeed any inverse square law force) then the bound orbits are all elliptical - a circle is a special case of an ellipse with zero eccentricity. So any object in an elliptical orbit will remain in that orbit forever. No external forces are needed. To see how the orbit is calculated have a look at the question Kepler problem in time: how do two gravitationally attracted particles move?.
To try and make this answer a bit more interesting than just yes I'll mention a few other interesting points:
Elliptical orbits are only stable with an inverse square force, or possibly also a harmonic force though I'm not sure about this. There is a theorem called Bertrand's theorem that tells us this.
Real satellites don't orbit in an inverse square force, because you need to take into account the gravitational forces between the satellites. For artificial satellites orbiting the Earth this is entirely negligable, but if you look at the planets orbiting the Sun none of them travel in perfect ellipses because of this effect. For example the eccentricity of Earth's orbit around the Sun changes continually mostly due the the gravitational force between Earth and Jupiter.
Even in a system of just two bodies the orbit still isn't a perfect ellipse because the Newton inverse square force law is actually only an approximation and is modified by effects due to General Relativity. So even in a two body system orbits aren't perfectly elliptical. You may have heard that the precession of Mercury is due to this, though actually only a small part of the precession is due to General Relativity.
Finally, a two body system radiates gravitational waves, so if you wait long enough the orbits will decay and the two bodies will collide. However unless the system is an extreme one like a binary pulsar the timescales required for this are long compared to the age of the universe.
the dynamics of two bodies in gravitational interaction forbids closed orbits that are not elliptical (or circular as a special case). So the only thing you have to do is put the satellite high enough (to minimize friction from the atmosphere), and give it a large enough tangential speed. The higher the satellite, the smaller the tangential speed you need to give it. After that, the satellite will move in a closed elliptical orbit, it has no other choice. (well, if the speed is too large, it will leave earth in a hyperbolic orbit, if it is too low, it will fall back to Earth).
The motion of a satellite in orbit is governed by
When there is no (or negligible) drag, these two are satisfied by an elliptical orbit. Kepler studied this at length, by observing the motion of the planets. He formulated his famous laws:
Obviously, the first law can be generalized to orbital motion of any two objects where one is heavier than the other (when the masses become comparable the orbit is still an ellipse but the heavier object is no longer exactly at the focus: instead the center of mass will be).
The second law is almost a direct statement of conservation of angular momentum; and the third law describes how fast an object needs to move to remain in a particular orbit. It is easy to see that for a circular orbit, you end up with the orbital period being proportional to $R^{3/2}$.
If you start out in a circular orbit and you want to go to an elliptical orbit, you can:
