Need help with this trajectory

Can anyone provide me some help with a trajectory I have found on the
Internet, please. The following link shows a picture of the
trajectory.
What is this about? Is it some kind of space craft?
Any idea?


http://www.sueddeutsche.de/wissen/ar...7820/zoom_0_0/


Thanx for your help
Stephan

In article , Stephan says...

Can anyone provide me some help with a trajectory I have found on the
Internet, please. The following link shows a picture of the
trajectory.
What is this about? Is it some kind of space craft?
Any idea?

http://www.sueddeutsche.de/wissen/ar...7820/zoom_0_0/


Almost certainly not a spacecraft. The plane or nodal change partway through
the spiral, is an extremely difficult maneuver to arrange either by gravity
or propulsive effort, and there are more efficient ways to reach the depicted
end state if that is the goal. It might be possible to make it work with a
close flyby of a massive body in an inclined orbit, but I doubt it.


--
*John Schilling * "Anything worth doing, *
*Member:AIAA,NRA,ACLU,SAS,LP * is worth doing for money" *
*Chief Scientist & General Partner * -13th Rule of Acquisition *
*White Elephant Research, LLC * "There is no substitute *
* for success" *
*661-951-9107 or 661-275-6795 * -58th Rule of Acquisition *

John Schilling wrote:
In article , Stephan
says...

Can anyone provide me some help with a trajectory I have found on
the
Internet, please. The following link shows a picture of the
trajectory.
What is this about? Is it some kind of space craft?
Any idea?

http://www.sueddeutsche.de/wissen/ar...7820/zoom_0_0/

Almost certainly not a spacecraft.

This seems to be part of some sort of museum contest:
http://www.sueddeutsche.de/wissen/artikel/867/47820/
My German isn't good enough to figure it out.

But the trajectory looks like the phase space trajectory of
a chaotic dynamical system. Not sure which one though.
Possibly the Lorenz equation:
http://www.apmaths.uwo.ca/~bfraser/n...renzchaos.html

Tom

John Schilling wrote:
In article , Stephan says...

Can anyone provide me some help with a trajectory I have found on the
Internet, please. The following link shows a picture of the
trajectory.
What is this about? Is it some kind of space craft?
Any idea?

http://www.sueddeutsche.de/wissen/ar...7820/zoom_0_0/


Almost certainly not a spacecraft. The plane or nodal change partway through

Almost 100% certainly one, namely SMART-1. Theres a ESA image on the ESA
site its ripped (and recoloured) from. I don't see the image on teh web
ATM but you can see it on page 10 of this brochure -
http://esamultimedia.esa.int/docs/Sm...t_A404Ju02.pdf

the spiral, is an extremely difficult maneuver to arrange either by gravity
or propulsive effort, and there are more efficient ways to reach the depicted
end state if that is the goal. It might be possible to make it work with a
close flyby of a massive body in an inclined orbit, but I doubt it.


You mean like a satllite spiralling away under continuos thrust from
a massive Planet with a relatively massive Moon and uses said Moons
gravity to enter orbit around it ?

--
Sander

+++ Out of cheese error +++

In article , Sander Vesik says...

John Schilling wrote:
In article , Stephan says...

Can anyone provide me some help with a trajectory I have found on the
Internet, please. The following link shows a picture of the
trajectory.
What is this about? Is it some kind of space craft?
Any idea?

http://www.sueddeutsche.de/wissen/ar...7820/zoom_0_0/


Almost certainly not a spacecraft. The plane or nodal change partway through

Almost 100% certainly one, namely SMART-1. Theres a ESA image on the ESA
site its ripped (and recoloured) from. I don't see the image on teh web
ATM but you can see it on page 10 of this brochure -
http://esamultimedia.esa.int/docs/Sm...t_A404Ju02.pdf


OK, it's an artist's conception of a spacecraft trajectory. It also appears
at:

http://sci.esa.int/science-e/www/obj...objectid=30535

As do status reports giving periodic plots of the instantaneous orbit, e.g.

http://sci.esa.int/science-e/www/obj...objectid=35925

The image in question, is not an accurate depiction of the actual trajectory.
The eccentricity is far too high, unless we are viewing the thing at an angle
of at least 65 degress off normal, in which case the moon is too far out of
plane. The change in the line of apsides prior to the close flyby is too
small regardless of what assumptions we make about the viewing angle. And
it looks like the perigee is too low and the number of orbits insufficient.

At a guess, ESA's PR folks found a direct portrayal of the actual orbit too
confusing for brocure or top-level web page use, and had someone "clarify"
it by some transformation I can only guess at. As mentioned above, they at
least had to skew the view angle, exaggerate the lunar plane change to make
that part of the maneuver more visually obvious, and take out the apsidal
rotation to make the early orbits line up.

It is not, as shown, a trajectory an actual spacecraft can fly, unless maybe
you have a high-performance nuclear thermal rocket and are trying to show off
how profligately you can waste delta-V.


--
*John Schilling * "Anything worth doing, *
*Member:AIAA,NRA,ACLU,SAS,LP * is worth doing for money" *
*Chief Scientist & General Partner * -13th Rule of Acquisition *
*White Elephant Research, LLC * "There is no substitute *
* for success" *
*661-951-9107 or 661-275-6795 * -58th Rule of Acquisition *

John Schilling wrote:

The image in question, is not an accurate depiction of the actual trajectory.
The eccentricity is far too high, unless we are viewing the thing at an angle
of at least 65 degress off normal, in which case the moon is too far out of
plane.

Eccentricity can be gauged by how far earth is from center. On my screen
the outer ellipse has a 92 mm axis, earth is 30 mm from center - that's
an eccentricity of about .7. Yeah, I'd agree a viewpoint about 65
degrees off normal.

ESA gradually changed SMART 1's inclination to enable Lunar capture.
From 0 to 7 degrees inclination IIRC. But the moon was about 28 degrees
off equatorial at that time.

Evidently a lunar gravity assist did most of the inclination change.
Inertia would carry SMART-1 past the moon's orbital plane, so I'd expect
it to have a greater than 28 degree inclination after the gravity
assist. The "artist's conception" seems to show something like that.


The change in the line of apsides prior to the close flyby is too
small regardless of what assumptions we make about the viewing angle.

Their other orbit illustration seems to show line of apsides rotating
ten or twenty degrees over a year's time. That doesn't seem to
contradict the illustration. Remember, we're viewing it 65 degrees off
normal. The right most points aren't necessarily perigees.


And
it looks like the perigee is too low and the number of orbits insufficient.

At a guess, ESA's PR folks found a direct portrayal of the actual orbit too
confusing for brocure or top-level web page use, and had someone "clarify"
it by some transformation I can only guess at. As mentioned above, they at
least had to skew the view angle, exaggerate the lunar plane change to make
that part of the maneuver more visually obvious, and take out the apsidal
rotation to make the early orbits line up.

It is not, as shown, a trajectory an actual spacecraft can fly, unless maybe
you have a high-performance nuclear thermal rocket and are trying to show off
how profligately you can waste delta-V.




--
Hop David
http://clowder.net/hop/index.html

In article , Hop David says...


John Schilling wrote:

The image in question, is not an accurate depiction of the actual trajectory.
The eccentricity is far too high, unless we are viewing the thing at an angle
of at least 65 degress off normal, in which case the moon is too far out of
plane.

Eccentricity can be gauged by how far earth is from center. On my screen
the outer ellipse has a 92 mm axis, earth is 30 mm from center - that's
an eccentricity of about .7. Yeah, I'd agree a viewpoint about 65
degrees off normal.

ESA gradually changed SMART 1's inclination to enable Lunar capture.
From 0 to 7 degrees inclination IIRC. But the moon was about 28 degrees
off equatorial at that time.

Evidently a lunar gravity assist did most of the inclination change.
Inertia would carry SMART-1 past the moon's orbital plane, so I'd expect
it to have a greater than 28 degree inclination after the gravity
assist. The "artist's conception" seems to show something like that.

You're using common sense here, and it doesn't work. There is no inertia
to orbit *elements* like inclination, only the actual position vectors.
Since the flyby/gravity assist necessarily occurs near the point of plane
crossing, there is no lower bound on the absolute inclination or the
inclination change. And, in fact, SMART-1's last flyby before lunar capture
put it in an Earth orbit with an inclination of twenty degrees. Less than
that of the Moon, but sufficient to allow capture at the next flyby (again,
at a plane crossing so the two can meet in position despite different
inclinations).

It would be extremely and needlessly difficult to force the inclination
*higher* than that of the Moon, and this was not done, but the stylized
depiction of the orbit if taken literally shows a post-encounter inclination
of at least thirty-five to forty degrees.

So, vertical scale exaggerated by a factor of two or more for clarity, or
some similar transformation.


The change in the line of apsides prior to the close flyby is too
small regardless of what assumptions we make about the viewing angle.

Their other orbit illustration seems to show line of apsides rotating
ten or twenty degrees over a year's time. That doesn't seem to
contradict the illustration. Remember, we're viewing it 65 degrees off
normal.

The last set of osculating elements given before the flyby, show apsidal
rotation of ninety degrees in three months, or seven orbits. It's tricky
reading the dates, because they use European date convention and don't
present the data in chronological order, but it's there.

And a ninety degree shift over seven orbits, at that eccentricity, means
that each orbit will cross each other orbit on the inbound and outbound
legs. That's not an artifact of viewing angle, it's either there or it
isn't, and it isn't in the stylized view.

Again, presumably transformed for clarity, because tangled spaghetti
doesn't look good in the brochures.


--
*John Schilling * "Anything worth doing, *
*Member:AIAA,NRA,ACLU,SAS,LP * is worth doing for money" *
*Chief Scientist & General Partner * -13th Rule of Acquisition *
*White Elephant Research, LLC * "There is no substitute *
* for success" *
*661-951-9107 or 661-275-6795 * -58th Rule of Acquisition *

John Schilling wrote:
In article , Sander Vesik says...

John Schilling wrote:
In article , Stephan says...

Can anyone provide me some help with a trajectory I have found on the
Internet, please. The following link shows a picture of the
trajectory.
What is this about? Is it some kind of space craft?
Any idea?

http://www.sueddeutsche.de/wissen/ar...7820/zoom_0_0/


Almost certainly not a spacecraft. The plane or nodal change partway through

Almost 100% certainly one, namely SMART-1. Theres a ESA image on the ESA
site its ripped (and recoloured) from. I don't see the image on teh web
ATM but you can see it on page 10 of this brochure -
http://esamultimedia.esa.int/docs/Sm...t_A404Ju02.pdf


OK, it's an artist's conception of a spacecraft trajectory. It also appears
at:

http://sci.esa.int/science-e/www/obj...objectid=30535

As do status reports giving periodic plots of the instantaneous orbit, e.g.

http://sci.esa.int/science-e/www/obj...objectid=35925

The image in question, is not an accurate depiction of the actual trajectory.
The eccentricity is far too high, unless we are viewing the thing at an angle
of at least 65 degress off normal, in which case the moon is too far out of
plane. The change in the line of apsides prior to the close flyby is too
small regardless of what assumptions we make about the viewing angle. And
it looks like the perigee is too low and the number of orbits insufficient.

It didn't look too far fetched to me, then again, I'm hardly an expert
at judging this. Also, the 2D osculating orbit charts are not too dissimilar
in scale. The funky looking orbit - or at least part of it - looks similar
on this graph -

http://sci.esa.int/science-e/www/obj...objectid=36085

given that it gives distances I assume it is an actual graph (even if
from a slightly odd POV) and not artists concept.


At a guess, ESA's PR folks found a direct portrayal of the actual orbit too
confusing for brocure or top-level web page use, and had someone "clarify"
it by some transformation I can only guess at. As mentioned above, they at
least had to skew the view angle, exaggerate the lunar plane change to make
that part of the maneuver more visually obvious, and take out the apsidal
rotation to make the early orbits line up.

It is not, as shown, a trajectory an actual spacecraft can fly, unless maybe
you have a high-performance nuclear thermal rocket and are trying to show off
how profligately you can waste delta-V.


I guess I stand (or rather, sit) corrected.

--
Sander

+++ Out of cheese error +++

This actually looks like some work I saw last year on minimum energy
transfers between planets (or some such). It was being studied at Caltech
and JPL to come up with ways to transfer to and from near earth and other
planets using gravitational equipotentials (sun, earth, moon, other
planets). It was not at all straight forward or obvious, but the concepts
were intriguing. It was also slow transit but with almost no expenditure of
propellant it had merit. I saw a presentation by one of the researchers at
a AIAA meeting about six months ago. If I find the article I will try to
post the title.

Ron

"Stephan" wrote in message
m...
Can anyone provide me some help with a trajectory I have found on the
Internet, please. The following link shows a picture of the
trajectory.
What is this about? Is it some kind of space craft?
Any idea?


http://www.sueddeutsche.de/wissen/ar...7820/zoom_0_0/


Thanx for your help
Stephan

http://www.sueddeutsche.de/wissen/ar...7820/zoom_0_0/

Reminds me of Cassini's reference trajectory for its primary mission.
You can check - it's on the Cassini web site somewhere.

Jan