Hill's Equations

[huddi]

Hi,

I'm trying to program a pathprediction for a docking maneuver situation.
The Hill's equation (also known as Clohessy-Wiltshire) should - as I understand -
exactly do this.

This is how it is in Orbiter:
-target (blue dot) is in a circular orbit
-interceptor (red dot) about 500m behind target
-green line is 300sek prediction after Hill's equation
-red line is 300sek linear prediction

So we follow an exactly straight line to the target.
I've got the equations out of "the vallado" third edition.
I'm pretty sure that they're right.
How could I interpret this?

Thanks!
Huddi

---------- Post added 10-27-2009 at 01:00 AM ---------- Previous post was 10-26-2009 at 07:56 PM ----------

When I start at the destination of the target the equations do provide a pretty good estimate. But they should as well work the other way round?!

 

[tblaxland]

Your image is missing.

Nonetheless, I am skeptical about a straight in approach from directly behind the target. Orbital mechanics dictate that you will drop below the target as you catch up and approach the target from below. The only time I have seen a straight line solution from Hills equations is when executing a constant delta height manoeuvre.

 

[Andy44]

To approach from directly behind the target in a tangential intercept, you have to start from a higher altitude and do a retro burn.

If you use SyncOrbit MFD you are doing this all the time without really thinking about it. But Hill's Equations still apply.

 

[huddi]

Okay, so there must be something wrong with my calculations-
but I just cannot find the mistake :/.

Maybe the coordinate system?! I've got
x: in Orbitvelocity direction
y: crossproduct(x,z)
z: points towards earth

This is my code to that:

        GetRelativeVel(this->GetSurfaceRef(),KoSyFront);
        oapiGetRelativePos(this->GetSurfaceRef(),this->GetHandle(),&KoSyDown);
        KoSyRight=crossp(KoSyFront,KoSyDown);

These are not those Vallado uses, but they (should be?) are colinear.
Of course I adjusted the equations to my variables.



This is what I get:
-First try: start from the targetposition (present position is about 0)
-Second try: start behind and under the target

so strangely the first try worked, but the second is horribly wrong.


It would be really nice, if you could help

 

[C3PO]

There's something wrong in that picture. If the interceptor is 'behind' the target and closing, the path should arc up instead of down.

You could try out Rendezvous MFD and see what it should look like: http://orbithangar.com/searchid.php?ID=1199

I'd love to see this work!

 

[huddi]

Thanks,
still this is not it... that was a drawingproblem

 

[tblaxland]

Maybe the coordinate system?! I've got
x: in Orbitvelocity direction
y: crossproduct(x,z)
z: points towards earth
[...]
These are not those Vallado uses, but they (should be?) are colinear.
Of course I adjusted the equations to my variables.

Check if Vallardo's coordinate system is right handed. The coordinate system you have defined there is left handed but most implementations of Hills equations are based on right handed. Just change y: crossproduct(z,x).

 

[huddi]

That was just a mistake in the example. I've got x=orbitdirection y=right z=down
I used the exact equations that are given.

Vallado uses: x= up y=orbitdirection z=left

So I put x=-z y=x z=-y
and back again. This should work?!