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Old 06-02-2019, 01:35 AM   #1
Default Can I get the Vector components xyz given only this information?

I have these 3 dates
and I know the position X Y Z of moon Amalthea relative to Jupiter
and then I know the Velocity Vectors V for each one.
I need to get the VX VY VZ components for each of the 3 date-times.
Do I have enough information to get those from what you see?
I believe I need the instantaneous values.
I am aware of VX = dx/dt, VY = dy/dt, VZ = dz/dt
and I know VX + VY + VZ = V
I am interested in the math behind finding those components given what I have.
If you know the procedure can you tell me what it is? or shed some light on how I might solve the problem if its possible?
thank you.

1979 MAR 05 00:00:00
-178932.619 km -28063.045 km -17448.755 km V = -29.804114 km/sec

1979 MAR 05 00:02:00
-178337.419 km -30878.143 km -18771.071 km V = -29.231286 km/sec

1979 MAR 05 00:04:00
-177688.033 km -33683.859 km -20087.682 km V = 28.649604 km/sec

thank you.
I do have the answers if someone knew how to do it. I can check to see if your right.

Last edited by ncc1701d; 06-02-2019 at 01:45 AM.
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Old 06-02-2019, 01:48 AM   #2
Passed the Turing Test
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If I understand correctly, you have XYZ position information and a speed, and you want XYZ velocity information.

This can get really complicated if you care about a perfect answer.

However I would say simply knowing that the orbit is nearly circular and nearly equatorial is enough information to have a pretty good idea of the velocity vector.
You need to know what coordinate frame those XYZ values are in though.

Edit: I'm thinking you may actually care about a more accurate answer given your three times are less than an orbit apart.
I suspect you can in fact evaluate those three points together to get some orbital parameters out.

Last edited by Quick_Nick; 06-02-2019 at 01:55 AM.
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Old 06-03-2019, 01:16 PM   #3
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I think this article describes the required math. It's not easy. https://science.larouchepac.com/gaus...erProblem.html
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Old 06-06-2019, 02:32 PM   #4

thanks for the interesting problem to think about :-)

I can get the semimajor axis (a) and the standard gravitational parameter (mu) from the vis-viva equation;

v^2 = mu*(2/r - 1/a)

But then I get stuck!

Then I thought maybe it was an energy-conservation problem (Potential + Kinetic = Constant) but I'm not getting anywhere with that.

Since the times of the data points are given, I'm pretty sure that is necessary information. Needs some kind of insight regarding Kepler's 2nd law (radius sweeps out equal areas in equal times) maybe?

I think that the shape of an ellipse is completely determined by three points (pos vectors), so theoretically you should be able to find the equation of the ellipse and the tangent at a given point - but the math for doing that in 3D is looking really gnarly, so I'm not even thinking about that :-)

Anyway, I'm having fun playing with this one.

P.S. Your first two Velocity values are negative - typo?
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Old 06-06-2019, 06:08 PM   #5

the checkmarked answer I found here might provide the answer.

Although not sure its that simple yet. I am still researching.
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