If something causes final orbital speed of the satellite to be decreased (final orbital speed < initial orbital speed), why its circular motion changes to elliptical motion? Assuming that the initial speed of the satellite satisfies the condition to set circular motion.
Solve the 2-body problem in closed form. Find circular speed. Increase this speed; you get an outer ellipse. Decrease the speed you get an inner ellipse. The equations show it.
Dear Raju,
As the Gravity Probe B experiment has shown, there is a gravito-magnetic force that acts upon satelites due to the Earth's spin and its orbital motion.
The Earth becomes a gravitational dipole and the force it gives is changing the orbit shape and orientation.
https://en.wikipedia.org/wiki/Gravitoelectromagnetism
Raju,
A circular orbit is a special case of the more general elliptical orbit that results from motion around a single mass.
A small perturbation from a circular orbit *always* leads to an ellipse. You do not need to invoke gravito-magnetic effects. Simple Newtonian mechanics is enough - and closed elliptical orbits are a feature of inverse-square laws - such as Newtonian gravity.
http://www.dartmouth.edu/~phys44/lectures/Chap_4.pdf
(eq.9 onwards)
Hi, I agree with Hames, any perturbation can modify the orbital parameters and increase the eccentricity of the orbit. A circular orbit remains circular only in a pure Keplerian model, i.e. the Earth is considered as a point mass neglecting all the terms of the Earth's potential so as atmospheric drag, the influence of the Moon, etc...
If you mean spontaneous change, then by any external force, usually a gravitational force by any body with non-negligible gravitational influence.
If you mean an intentional change, e.g. change of the space probe orbit from circular to elliptical (e.g. from parking LEO to GTO), then by own propulsion system that will apply an well defined impulse in proper moment in time and in proper direction.
If I can add slightly to what has already been said, actually there is no such thing as a perfectly circular orbit, it's a bit of a mathematical abstraction. Yes, it can be circular to a very large degree of precision, but let's say you are in a 1500 km altitude circular orbit. Your apogee altitude to the perigee altitude may be only a centimeter higher (1500.00001 km to 1500.00000km) and that is still a very slight eccentricity (6.35 e-10). Of course, in a practical sense you can ignore the slight difference and say that within certain bounds, it's a circular orbit. And you can set those bounds large enough so that the perturbations don't matter for a particular orbit.
Solve the 2-body problem in closed form. Find circular speed. Increase this speed; you get an outer ellipse. Decrease the speed you get an inner ellipse. The equations show it.
Thank you very much, all. Your answers really helped me to reach on above conclusion.
Any change in the initial velocity (the one that results in a circular orbit) or delta-v will result in an elliptical orbit even it is just slightly, actually no orbit is perfectly circular due gravimetric perturbations from the moon and the sun.
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