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Message started by frankuitaalst on 07/26/07 at 06:26:55

Title: Mars Trojans
Post by frankuitaalst on 07/26/07 at 06:26:55

A new asteroid 2007NS2 was found last 14/07/2007 .
This one shares an orbit with Mars in the L5 point . It brings the known number of Trojans to 4 . 2 others share the point L5 , while another is in the L4 point . Herunder is the link for the list of those asteroids
A simulation of this 4 asteroids in a rotating frame with Mars gives the following picture :
The new one 2007NS2 is the light green orbit . Mars is represented as the "line" at the bottom of the picture .
There are a few astonishing features here : look at the unusual orbit of the green asteroid at the left , also the orbit at the right doesn't represent a kindney bean .
Remarkable also is the fact that the concave side of the left asteroids is once away from the sun and once directed to the sun .

Title: Re: Mars Trojans
Post by Tony on 07/26/07 at 11:23:57

That was just discovered.  How did you find it so fast :o

Title: Re: Mars Trojans
Post by frankuitaalst on 07/26/07 at 12:03:33

I read an article in the following link ,deals with a lot of scientific themata

Title: Re: Mars Trojans
Post by Tony on 07/26/07 at 12:26:27

Thanks for the link.  There's 2 questions I have about that article.

1. Morbidelli says that perhaps Earth has no trojans because it is more massive than Mars and was not kicked around as easily.  But when it comes to gravity, the bigger rock has no advantage over the smaller rock.  Drop a big rock and a small rock from the roof and they hit the ground at the same time.  How would Earth's greater mass have prevented it from being knocked around?  Perhaps he's considering forces other than gravitational.

2. Could it be that Earth has pleanty of trojans, but we have a harder time discovering them because they are always 1 AU from Earth, unlike Mars trojans which can come much closer and have an opposition angle, making their phases full, hence much brighter, and much faster against the background of stars, making them easier to detect?

Title: Re: Mars Trojans
Post by frankuitaalst on 07/26/07 at 12:36:15

I can follow your arguments .
On 1. I think you're right , but I can also think that a smaller object can gain more momentum , ie the increment can be bigger as the planet is smaller or ...?
On 2: I think you're completely right as these objects are hardly detectable (the same applies for ev; trojans of Mercyry ) . A short time ago I read an article dealing with the stability of such orbits ( If I remember it was a simulation of test particiles put in these orbits ) . Wll try to retrieve it .  

Title: Re: Mars Trojans
Post by frankuitaalst on 07/26/07 at 12:50:28

The article I refered to can be found on :
In this article the authors show numerically that Earth , Venus and Mars can hold Trojans for millions of years .
Mercury has a problem however .

Title: Re: Mars Trojans
Post by frankuitaalst on 08/04/07 at 12:39:06

Running the 2007NS2 asteroid for more than 250 years gives the following animated frame ( rotating frame with Mars ) .
In the beginning much frames were "shoot" in order to show the orbit of the asteroid .
The orbit of the asteroid ( Tadpole ) seems remarkable stable .
The green lines around the asteroid are smaller celestial bodies ( Ceres , Hygiea....)

Title: Re: Mars Trojans
Post by frankuitaalst on 08/05/07 at 14:06:44

Here is a rather unusual vieuw of the Mars Trojans Simulation :
The sim was run for 50 years , showing the 4 Trojans of Mars in a rotating frame to Mars , but unlike normal the view was taken edge-on , not from "above " as usual .
The four asteroids come up as green lines ( 2007NS2 is the light green one ) .
The straight line  through the center should be the orbit of earth , while Mars is the pink slighty oval orbit left from the center .
The asteroids show themselves rather far from the center as they orbit Mars in about 60 .
Out of this frame it is clear that all of them have a rather big inclination ...

Title: Re: Mars Trojans
Post by frankuitaalst on 08/08/07 at 10:09:20

The recently discovered asteroid 2007NS2 is shown herunder in another rotating frame ( also viewed from the edge ) as in the above post , but this time rotated over 90 . Due to the different viewpoint the asteroid seems to have another orbit , but this is only an illusion , as the asteroid has a three dimensional orbit , which is projected . In this view it seems to form a figure eight .
The sim was run for 20 years .
2007NS2 is the light green one ; Mars is the elliptical orbit at the left . The dark green orbits are merely dwarf planets as Ceres , Pallas...etc.

Title: Re: Mars Trojans
Post by Tony on 08/08/07 at 10:22:10

These edge-on rotating frames are facinating.  Is that Jupiter to the far left?

Title: Re: Mars Trojans
Post by frankuitaalst on 08/08/07 at 10:25:12

The Rotating frame may be difficult to understand or may be confusing . The picture hereunder tries to clarify the procedure :
Suppose you're above the ecliptic plane in which al the planets rotate .
So you must be somewhere on the Z-axis. Suppose also you have a camera , looking down on the ecliptic ...
The image you get then is the normal image you are familiar with ...

But suppose that in your position you are able to rotate your camera very slow , so that you "follow" the orbit of Mars fi.
The resulting movie you get is the rotating frame fixed on Mars . Mars moves hardly in this picture ... The other planets move a lot . Eventually resonance orbits will show up as smooth closed lines .
This is the case for the Mars Trojans asteroids ...

Above we have positioned our camera in the Z-axis , looking down ( see the big red arrow ) . We created a movie in a rotating frame "from above ".

Suppose now that we have a second camara , also rotating with the same angular speed as the first one (ie also locked on Mars fi ) , but let the camera look sidewards , not to the bottom .
The movie we get is also a rotating frame movie , but this time "edge on ".
It may be clear that the movie we get will depend on the direction in which we look .
( see the red arrows along the X and the Y-axis ) .
The last gif was made looking along the Y-axis.

Title: Re: Mars Trojans
Post by frankuitaalst on 08/08/07 at 10:31:40

I don't know, can be Jupiter or Saturn or Neptune or Uranus . I'll make a bigger vieuw to find out .

Title: Re: Mars Trojans
Post by frankuitaalst on 08/08/07 at 10:44:26

Heres the same sim but on 50AU screen width .
Jupiter is the "small" pink orbit near the center , Saturns orbit is just above it .
At the bottom , also in pink should be Uranus and Neptune , while Pluto must be the dots above .

Title: Re: Mars Trojans
Post by frankuitaalst on 08/14/07 at 16:40:55

It looks as if the guys from harvard have updated their list with the new Trojan :
Do they read this forum ?  :)

Title: Re: Mars Trojans
Post by frankuitaalst on 08/17/07 at 03:28:23

I discovered I nice link to The Mars Trojans :

"Since the discovery of 5261 Eureka, the Minor Planet Center has recognized three other asteroids as Martian Trojans: 1999 UJ7 at the L4 point, 1998 VF31 at the L5 point,[1] and 2007 NS2, also at the L5 point.[2] At least six other asteroids have been discovered which are in near 1:1 resonances with Mars, but fail to exhibit trojan behavior. They are 2001 FR127, 2001 FG24, 2001 DH47, 1999 ND43, 1998 QH56 and 1998 SD4[3][4]"

If you hit the sublink 3 and 4 you get redirected to a nice site :)

Title: Re: Mars Trojans
Post by Tony on 08/17/07 at 22:36:15

Hey, that is a nice site. ::)

Title: Re: Mars Trojans
Post by abyssoft on 08/18/07 at 10:00:34

Definitely a cool link  ;D

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