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Problem with orbit model



 
 
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  #1  
Old January 27th 04, 02:06 AM
Makhno
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Default 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  
Old January 27th 04, 02:36 AM
Mark Folsom
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Default

"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  
Old January 27th 04, 03:21 AM
Greg Neill
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Posts: n/a
Default

"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  
Old January 27th 04, 06:56 AM
John O'Flaherty
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Default

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  
Old January 27th 04, 12:42 PM
Dave
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Posts: n/a
Default


"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  
Old January 27th 04, 01:34 PM
Sally
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Posts: n/a
Default


"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  
Old January 27th 04, 08:18 PM
Makhno
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Posts: n/a
Default

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  
Old January 27th 04, 08:20 PM
Makhno
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Posts: n/a
Default

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  
Old January 27th 04, 08:30 PM
Makhno
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Posts: n/a
Default

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  
Old January 27th 04, 10:19 PM
Greg Neill
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Posts: n/a
Default

"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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