Why is an sattelite's motion not circular?

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Satellite motion is primarily elliptical due to the gravitational force obeying an inverse square law, making circular orbits a special case with zero probability in reality. While geostationary orbits are often considered circular, they are affected by Earth's non-spherical gravity and perturbing forces, resulting in slight deviations. Most orbits are not perfectly circular because achieving such a state requires a precise balance of forces, which is rarely possible. Additionally, some satellites are intentionally placed in non-circular orbits to optimize coverage over specific regions. Overall, the complexity of gravitational interactions leads to the predominance of elliptical orbits in satellite motion.
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Why is an sattelite's motion not circular? I mean if there is a force that adjust the orbit every instant shouldn't the orbit be circular?
 
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If a force is exerted, then an orbit can be confined to circular.
Most orbits, however, are ballistic.
 
I don't think I understand the question. Not circular meaning what? Are you thinking of a specific example you encountered? In any case, most bound orbits are elliptical (of which a circular orbit is a special case). Unbound orbits are typically hyperbolic. This is a consequence of the strength of the gravitational force obeying an inverse square law with radial distance.

Friction can reduce the total mechanical energy of a satellite to decrease, causing its orbit to decay. This can cause an unbound orbit to become bound, and causes bound elliptical orbits to become more circular with time.

A geostationary orbit is certainly circular...and is used for telecommunications satellites.
 
That orbits (in the Newtonian two body problem) are conic sections comes straight out of the mathematics. The only thing special about circular orbits is that they never occur in reality. There are always perturbing forces, and gravity is not Newtonian. Even in a purely Newtonian, two point mass universe, circular (and parabolic) orbits are a zero probability event in the sense that the set of all circular and parabolic orbits are a zero measure subspaces of the space of all orbits.Edited to add:
Geostationary orbits are neither circular nor geostationary. Very close, but not quite. The subsatellite point follows a figure eight. The non-spherical nature of the Earth's gravity and third body effects (moon and sun) make it impossible to have a perfectly circular orbit.
 
grizzlyjoker said:
Why is an sattelite's motion not circular? I mean if there is a force that adjust the orbit every instant shouldn't the orbit be circular?
Uniform circular motion occurs when the centripetal force is always directed perpendicular to the velocity. Objects in space are not always constrained to move perpendicular to the gravity force.
 
Most orbits are almost circular, they are elliptical because to be a perfect circle would require a perfect balance of forces eg. the Earth's orbit around the sun is only around 1% off a perfect circle.

However some satellites are deliberately put into high non-circular orbits, for instance a Molniya puts a satelite high and sow over russia for most of it's orbit then low and fast over the south pacific - this maximises the time the satelite is available over the country of choice.
 
I have recently been really interested in the derivation of Hamiltons Principle. On my research I found that with the term ##m \cdot \frac{d}{dt} (\frac{dr}{dt} \cdot \delta r) = 0## (1) one may derivate ##\delta \int (T - V) dt = 0## (2). The derivation itself I understood quiet good, but what I don't understand is where the equation (1) came from, because in my research it was just given and not derived from anywhere. Does anybody know where (1) comes from or why from it the...
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