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#1
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Problem with orbit model
Evening people,
I have created an orbital model predicting the positions of a particle in orbit around the Earth. The Sun is assumed stationary, and the Earth's position is given via interpolated heliocentric ephemeris. The particle's position is calculated from first principles (GM/r2 with a time increment). Trouble is, whichever orbit I inject the particle into, it ends up being unstable and either crashing into the planet, or spinning wildly away after only a few days. I noticed that the particle seems to receive an impulse exactly once every day - precisely the resolution of my ephemeris. This is true regardless of my time-increment size. What I don't understand is that the trajectory of the Earth appears to be very smooth, so if there's any 'jolt' in its movements it must be very slight. I was surprised at the effect this has had on the particle's trajectory. I can't think what else could be affecting the particle. Other than using more frequent ephemeris (which I believe won't make the orbit completely stable, just reduce the instability) I can't think of what to do if it's the ephemeris that's the problem. The data (range, theta, psi) are linearly interpolated. Any ideas? Am I making a common error? Could a slight change in the trajectory of the Earth cause a satellite in orbit to become unstable? Your thoughts would interest me. |
#2
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"Makhno" wrote in message
... Evening people, I have created an orbital model predicting the positions of a particle in orbit around the Earth. The Sun is assumed stationary, and the Earth's position is given via interpolated heliocentric ephemeris. The particle's position is calculated from first principles (GM/r2 with a time increment). Trouble is, whichever orbit I inject the particle into, it ends up being unstable and either crashing into the planet, or spinning wildly away after only a few days. I noticed that the particle seems to receive an impulse exactly once every day - precisely the resolution of my ephemeris. This is true regardless of my time-increment size. What I don't understand is that the trajectory of the Earth appears to be very smooth, so if there's any 'jolt' in its movements it must be very slight. I was surprised at the effect this has had on the particle's trajectory. I can't think what else could be affecting the particle. Other than using more frequent ephemeris (which I believe won't make the orbit completely stable, just reduce the instability) I can't think of what to do if it's the ephemeris that's the problem. The data (range, theta, psi) are linearly interpolated. Any ideas? Am I making a common error? Could a slight change in the trajectory of the Earth cause a satellite in orbit to become unstable? Your thoughts would interest me. Try a higher-order interpolator. A series of lines with little corners would certainly introduce little jerks. Mark Folsom |
#3
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"Makhno" wrote in message ...
I can't think what else could be affecting the particle. Other than using more frequent ephemeris (which I believe won't make the orbit completely stable, just reduce the instability) I can't think of what to do if it's the ephemeris that's the problem. The data (range, theta, psi) are linearly interpolated. Any ideas? Am I making a common error? Could a slight change in the trajectory of the Earth cause a satellite in orbit to become unstable? Your thoughts would interest me. Have you considered using a three-body integration scheme rather than the interpolated ephemeris? What kind of accuracy are you looking for? If it's just a demo and you're going for just a few orbits, something as simple as a leap-frog (Verlet) integrator may be just the ticket. If you're looking for something better, perhaps a Runge-Kutta-Fehlberg scheme with self-adjusting step sizes would do. http://math.fullerton.edu/mathews/n2003/RungeKuttaFehlbergMod.html What is your implementation language? |
#4
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On Tue, 27 Jan 2004 01:06:59 -0000, "Makhno" wrote:
Evening people, I have created an orbital model predicting the positions of a particle in orbit around the Earth. The Sun is assumed stationary, and the Earth's position is given via interpolated heliocentric ephemeris. The particle's position is calculated from first principles (GM/r2 with a time increment). Trouble is, whichever orbit I inject the particle into, it ends up being unstable and either crashing into the planet, or spinning wildly away after only a few days. I noticed that the particle seems to receive an impulse exactly once every day - precisely the resolution of my ephemeris. This is true regardless of my time-increment size. What I don't understand is that the trajectory of the Earth appears to be very smooth, so if there's any 'jolt' in its movements it must be very slight. I was surprised at the effect this has had on the particle's trajectory. I can't think what else could be affecting the particle. Other than using more frequent ephemeris (which I believe won't make the orbit completely stable, just reduce the instability) I can't think of what to do if it's the ephemeris that's the problem. The data (range, theta, psi) are linearly interpolated. Any ideas? Am I making a common error? Could a slight change in the trajectory of the Earth cause a satellite in orbit to become unstable? Your thoughts would interest me. Does the model assume that the particle is being dragged by the earth, or is the particle given its own momentum in the earth orbit? -- john |
#5
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"Greg Neill" wrote in message .. . "Makhno" wrote in message ... I can't think what else could be affecting the particle. Other than using more frequent ephemeris (which I believe won't make the orbit completely stable, just reduce the instability) I can't think of what to do if it's the ephemeris that's the problem. The data (range, theta, psi) are linearly interpolated. Any ideas? Am I making a common error? Could a slight change in the trajectory of the Earth cause a satellite in orbit to become unstable? Your thoughts would interest me. Have you considered using a three-body integration scheme rather than the interpolated ephemeris? What kind of accuracy are you looking for? If it's just a demo and you're going for just a few orbits, something as simple as a leap-frog (Verlet) integrator may be just the ticket. If you're looking for something better, perhaps a Runge-Kutta-Fehlberg scheme with self-adjusting step sizes would do. http://math.fullerton.edu/mathews/n2003/RungeKuttaFehlbergMod.html What is your implementation language? I haven't modelled planetary motion for a long time, but I have recently had to model the evolution of nuclear magnetisation, for which the Numerical Recipes adaptation of Runge-Kutta with adaptive step-size is adequate, and probably would be for planetary orbits too. In fact, I suspect the adaptive step size would not be necessary for planetary orbits. If you're using C, take a look at http://www.library.cornell.edu/nr/bookcpdf/c16-2.pdf otherwise take a look at http://www.nr.com/. The fortran version is also available on-line. DaveL |
#6
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"Mark Folsom" wrote in message ... Try a higher-order interpolator. A series of lines with little corners would certainly introduce little jerks. You mean like this? http://nso0.livjm.ac.uk/uninow/orrery/ Sally |
#7
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Try a higher-order interpolator. A series of lines with little corners
would certainly introduce little jerks. There's no lines with little jerks. I'm linearly interpolating the heliocentric angles and ranges. This means.....curves with jerks. Though you have to look hard for the jerks. |
#8
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Does the model assume that the particle is being dragged by the earth,
or is the particle given its own momentum in the earth orbit? The former. The particle is influenced by the Sun, Mars and Earth. Though Mars has next to no effect. |
#9
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Have you considered using a three-body integration scheme
rather than the interpolated ephemeris? I need real-time, or better than real time. I believe using a look-up table would be the best choice for predictable things like planets. What kind of accuracy are you looking for? If it's just a demo and you're going for just a few orbits, something as simple as a leap-frog (Verlet) integrator may be just the ticket. If you're looking for something better, perhaps a Runge-Kutta-Fehlberg scheme with self-adjusting step sizes would do. How would I use an integration method in orbital mechanics? Currently I'm adjusting the velocity, v, by dt * GM/(r^2) and then adjusting the position by vdt for every cycle, of length dt. |
#10
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"Makhno" wrote in message
... Have you considered using a three-body integration scheme rather than the interpolated ephemeris? I need real-time, or better than real time. I believe using a look-up table would be the best choice for predictable things like planets. No problem. You can integrate *years* worth of points in several seconds of computer time. What kind of accuracy are you looking for? If it's just a demo and you're going for just a few orbits, something as simple as a leap-frog (Verlet) integrator may be just the ticket. If you're looking for something better, perhaps a Runge-Kutta-Fehlberg scheme with self-adjusting step sizes would do. How would I use an integration method in orbital mechanics? Currently I'm adjusting the velocity, v, by dt * GM/(r^2) and then adjusting the position by vdt for every cycle, of length dt. That sounds like a simple Euler integration scheme. Do a Google search on Leapfrog Integrator. Also on Runge-Kutta or Runge-Kutta-Fehlberg. An integrator is a fancy way of saying it is an algorithm that solves the differential equations. Here's a link or two: http://www.physics.drexel.edu/courses/Comp_Phys/Integrators/leapfrog/ http://physics.ucsd.edu/students/cou...1/lecture02/le cture02.html We use multibody integration methods quite often for articles in The Orrery newsletter. If you're handy in the BASIC language, I might be able to set you up with a program that could be used as a starting point. -- ----------------------------------------------------------------------- Greg Neill, Editor The Orrery: Models of Astronomical Systems http://members.allstream.net/~gneill/ ----------------------------------------------------------------------- |
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