Terra's sorta Second moon (Cruithne)

[Cham]

What is the relation between MeanLongitude and MeanAnomaly ? This is what's causing me some troubles. %$#@& astronomy conventions !

EDIT : Please, I need a confirmation that MeanLongitude := MeanAnomaly + AscendingNode + ArgOfPericenter in Celestia.

[chris]

What is the relation between MeanLongitude and MeanAnomaly ? This is what's causing me some troubles. %$#@& astronomy conventions !

EDIT : Please, I need a confirmation that MeanLongitude := MeanAnomaly + AscendingNode + ArgOfPericenter in Celestia.

Yes, this is exactly what MeanLongitude is (in Celestia and everywhere else.)

--Chris

[granthutchison]

Martin:
Are you allowing for the fact that the velocity of both bodies is varying continuously during the course of an orbit?

Grant

[Cham]

Martin:
Are you allowing for the fact that the velocity of both bodies is varying continuously during the course of an orbit?

Grant

Yes, and this is the tricky mathematical part. I have to parametrize the trajectory with an azimuthal angle ([tex]\phi_{Earth}[/tex]), defined for the Earth, say, and use [tex]\phi_{Cruithne}(t(\phi_{Earth}))[/tex] for the other body. So I need to numericaly solve an integral to define that function. I'm not sure I'll succeed with this analytical approach.

[chris]

could it be that the anonymous author of the Wiki article
http://en.wikipedia.org/wiki/3753_Cruithne
used Celestia for displaying the orbits, without crediting Celestia?

The animations were created with Celestia, and this is noted in 'Source' section of the page that appears when you click on them. The author (of the images; multiple people have contributed to the text) is listed as 'Jecowa'.

To anyone interested in better understanding the motion of Cruithne:
Although there's no plotted, you can clearly see the kidney bean motion of Cruithne if you follow earth and phase-lock to the Sun:
- Select Earth
- Follow
- Select Sun
- Phase lock (press ':')

Now, what would be nice is if one could press a key in Celestia to start a plot of the currently selected object in the current observer frame.

--Chris

[Cham]

Now, what would be nice is if one could press a key in Celestia to start a plot of the currently selected object in the current observer frame.

--Chris

Absolutly ! Is this possible ?

[t00fri]

could it be that the anonymous author of the Wiki article
http://en.wikipedia.org/wiki/3753_Cruithne
used Celestia for displaying the orbits, without crediting Celestia?

The animations were created with Celestia, and this is noted in 'Source' section of the page that appears when you click on them. The author (of the images; multiple people have contributed to the text) is listed as 'Jecowa'.

Aha, good. I am obviously not a heavy user of Wiki .

Now, what would be nice is if one could press a key in Celestia to start a plot of the currently selected object in the current observer frame.

--Chris

My saying since years...Last time a few posts up:

I thought that meanwhile I have convinced everybody that unlike present Celestia rendering, orbits are frame dependent. Therefore, I assumed that it is definitely on the todo list for after version 1.6 that we will at last implement frame dependent orbit rendering.

Fridger


We are all hoping that after version 1.6.0, Celestia will at last be able to display orbits correctly in various reference frames...

Fridger

Fridger

[t00fri]

My idea was simply to substract both trajectories, as this :

[tex]{\bf r}_{Cruithne relative to Earth} = {\bf r}_{Cruithne relative to Sol} - {\bf r}_{Earth relative to Sol}[/tex]

However, to plot the trajectory, I need to define the time variable.

How about determining the Galilei transformation matrix [tex]\Lambda(t)[/tex] by the requirement
[tex]\vec{x}(t)^T_{Earth} \,\Lambda(t) =\{0,0,0\}[/tex]

and then transforming the positional vector of Cruithne as follows:
[tex]\vec{x}(t)_{bean\ shape} = \vec{x}(t)^T_{Cruithne} \, \Lambda(t)[/tex]

Plot it! That's all...

Obviously, applying my above frame transformation matrix [tex]\Lambda(t)[/tex] and the Galilei invariance to your vectorial difference
[tex]{\bf r}_{Cruithne relative to Sol} - {\bf r}_{Earth relative to Sol}[/tex]

gives
[tex]{\bf r}_{Cruithne relative to Earth} = \Lambda {\bf r}_{Cruithne relative to Sol} - \Lambda {\bf r}_{Earth relative to Sol}[/tex]
[tex]= {\bf r}_{Cruithne relative to Sol} - {\bf r}_{Earth relative to Sol}[/tex]

i.e. what you were using .

Fridger

PS:

as I noted I finally have edited this post 23 times . This was due to a VERY odd bug in the LaTeX parser!

[granthutchison]

Martin:
Are you allowing for the fact that the velocity of both bodies is varying continuously during the course of an orbit?

Grant

Yes, and this is the tricky mathematical part. I have to parametrize the trajectory with an azimuthal angle ([tex]\phi_{Earth}[/tex]), defined for the Earth, say, and use [tex]\phi_{Cruithne}(t(\phi_{Earth}))[/tex] for the other body. So I need to numericaly solve an integral to define that function. I'm not sure I'll succeed with this analytical approach.

OK, good. I notice that Cruithne's orbit in the Wiki animation changes shape during one orbital cycle while it traces out the bean shape; this may well be a real periodic evolution which will further complicate your calculations. I also notice that the "bean" curve is closed in the animation: that's not realistic.

Grant

[jogad]

Hello

Very interesting. I like very much even if I don’t understand all technical and mathematical details.

Here is something for those who are like me and just want to see it in Celestia.

Just unzip these two files in Celestia. The first one is a ssc file and goes in the ‘extras’ folder and the second is a script file and goes to the ‘scripts’ folder.
Once unzipped run Celestia and launch ‘cruithne.celx’ from the File/Scripts submenu.

Data of the ssc file are from http://ssd.jpl.nasa.gov/sbdb.cgi?sstr=3753
 

[t00fri]

Very nice, Jogad!

Fridger

[Cham]

Indeed, this is a very good script, Jogad.

EDIT : Is there a way to simplify the first part of the script, to use CELX only ?

Code: Select all

function CEL(source)
   local script = celestia:createcelscript(source)
   while script:tick() do
      wait(0)
   end
end


CEL([[
{
  seturl { url "cel://PhaseLock/Sol:Earth/Sol/2008-12-09T11:43:52.18332?x=ADOsgcq2EDT7/////////w&y=iyy4V7/bjkFp&z=AI4Dp5qVeobw/////////w&ow=-0.053687&ox=-0.059524&oy=0.731694&oz=0.676904&select=Sol&fov=23.455702&ts=10000000.000000&ltd=0&p=0&rf=1693111&lm=2017986560&ver=2" }
}
]])


terre = celestia:find("Sol/Earth")
cruithne=celestia:find("Cruithne")
celestia:unmarkall()
cruithne:mark("yellow","diamond")
terre:mark("cyan","circle")

[jogad]

Hi,

Thank you very much. I am very happy if I can help a little.

To simplifiy the script, really I don't know. My knowledge of scripts is quite zero and I used this ugly (but helpful) URL just to avoid scripting.

Any improvement is welcome. Particulary if somebody knows how to display the track.

Cheers

[chris]

Now, what would be nice is if one could press a key in Celestia to start a plot of the currently selected object in the current observer frame.

--Chris

Absolutly ! Is this possible ?

Not yet, but you'll be able to do something like it in the next version of Celestia.

--Chris