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cj
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Why are orbits elliptical?
Any ideas?
Any ideas?
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dextercioby said:Nope.Kepler's problem for Coulomb potential admits either hyperbolic or elliptical trajectories.
Daniel.
neurocomp2003 said:pick up a standard astronomy text and find out =] eg Carroll and Ostlie
dextercioby said:Nope.Kepler's problem for Coulomb potential admits either hyperbolic or elliptical trajectories.
Daniel.
tony873004 said:
I don't understand the "nope" part . But I agree with the rest.
I imagine you're responding to my post.
It's kinda the point I was trying to make. Everything is either hyperbolic or elliptical because circular or parabolic are perfect conditions that only exist on paper. If you think you have a perfectly circluar orbit, try expressing its eccentricity accurate to 15 digits.
The general solution to the differential equation of motion of a mass in a gravitational field is a conic section. See, for example:cj said:Any ideas?
No. They would be elliptical even without other planets.cj said:So it's the gravitational effect from other planets that
cause this deviation from perfection?
amt said:There is still no clear and concise answer to the original question though.
Sounds interesting. Do you happen to have a link or know of a text that goes into detail on this?Chronos said:An ellipse is a 2D circle that is rotated. If you attempt to translate such an ellipse into its circle equivalent a vector force, which happens to be G, drops right into your lap [ok, with some minor GR corrections].
This is not the reason for eccentricity. I'll try to prove this more formally. Not axiomatically or anything, but just a good convincing argument.Symbreak said:What people seem to have overlooked in this thread is that a circle is a conic section as well, where there is no eccentricity. Give the circle eccentricity (or slant the plane which cuts through the cone) and it becomes an ellipse. Even more, and we start getting parabolic and hyperbolic shapes.
The reason why the planets have a slight eccentricity is due to minor effects in the gravity of other planets (as said by others) but also due to the rectilinear movement of a planet at its formation. Also, large impacts of comets can cause the planet to deviate in its orbit, causing more eccentricity in its orbit round the sun.
Elliptical orbits are a result of the laws of gravitation and motion, specifically Kepler's laws. According to these laws, the shape of an orbit is determined by the balance between the gravitational pull of the central body and the velocity of the orbiting object. If the velocity is just right, the orbit will be circular. However, if the velocity is too high or too low, the orbit will be elliptical.
No, not all orbits can be considered elliptical. Orbits can also be circular or parabolic. A circular orbit has a constant radius, while a parabolic orbit has an escape velocity and does not loop back around the central body. However, in many cases, elliptical orbits are the most common and can be seen in the orbits of planets, comets, and satellites.
The speed of an object in an elliptical orbit is not constant. The object will move faster when it is closer to the central body due to the stronger gravitational pull, and slower when it is farther away. This is known as Kepler's second law, which states that the line connecting the object to the central body sweeps out equal areas in equal times.
No, not all elliptical orbits have the same shape. The shape of an ellipse is determined by its eccentricity, which is a measure of how elongated or flattened the ellipse is. An eccentricity of 0 represents a perfect circle, while an eccentricity of 1 represents a parabola. The eccentricity of an elliptical orbit can range from 0 to 1, with most orbits falling somewhere in between.
Yes, the shape of an orbit can change over time. This is due to external forces such as the gravitational pull of other objects or the effects of atmospheric drag. These forces can cause an object's orbit to become more or less elliptical, eventually leading to a circular or parabolic orbit. This is known as orbital decay and is commonly seen in the orbits of satellites and space debris.