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Orbital Mechanics

Posted by: campbelp2002 - Thu Dec 23, 2004 7:49 pm
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Orbital Mechanics 

Could an object spiral into the Sun?
Of course! 64%  64%  [ 16 ]
No way! 28%  28%  [ 7 ]
I used to think so, but now I don't. 0%  0%  [ 0 ]
I didn't think so before, but now I do. 8%  8%  [ 2 ]
Total votes : 25

Orbital Mechanics 
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Post    Posted on: Fri Dec 31, 2004 4:05 pm
SawSS1Jun21 wrote:
Peter, I think your original position is justified, but you will never sway Ekke by sweating him over "spiral"

You got that right.

My originl point was the lower energy requirement to throw waste out of the solar system than throwing it into the Sun. Then the whole idea the stuff could fall into the Sun for almost free appeared.

Real orbits are chaotic and change all the time. In low Earth orbit they "decay" due to atmospheric drag and "spiral" down. I am speaking of pure mathematical two body orbits, which in theory are totaly stable.


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Post    Posted on: Fri Dec 31, 2004 4:21 pm
Ekkehard Augustin wrote:
Too much - along an elliptical orbit the velocity is changing permanently.

Correct.

Ekkehard Augustin wrote:
Besides - at german site there is to be read that the escape velocity at the sun is 618.02 km/s.

That sounds about right.


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Post    Posted on: Fri Dec 31, 2004 5:27 pm
Your answer to SawSS1June21 explicitly shows a fundamental difference between you and me:

a) You are considering a two-body-system
b) I am considering our real system which allows energy and impulse moving over to other objects and includes spacecrafts and vehicles.

Another point mentioned earlier by me is that orbit.xls doesn't allow external changes of the red vector (the reason may be that it is representing acceleration).

One additonal point I should add perhaps is that from my point of view no Jupiter-fly-by or anny other fly-by is required to throw waste into the sun and that this doesn't require the engines of a vehicle to be working permanently.

There is one differnece between throwing it into the sun and moving it out of the solar system - the sun would melt it entirely and it would be mixed with the general solar matter. It would be destroyed down to its atoms. To move it out of the system would keep it intact as it is on earth and it takes decades until it has left our system. And there is and there will be much vehicle traffic to the outer regions of the system - Mars. Jupiter, Satrun, Neptune, Pluto...

Another point is, that it could be sent back to us from those regions by the same causes responsible for incoming new comets.To move waste there reqiures exact previous reconnaissance of what is going on out there.

All this I should have said in the other thread perhaps but first there is going on the mathematical dicussion and second I hjad to explain here that I don't consider the interstellar option and the reasons to not do so.



Dipl.-Volkswirt (bdvb) Augustin (Political Economist)


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Post    Posted on: Sun Jan 02, 2005 2:30 pm
This poll is badly worded, but if you rephrase it as "can an object spiral into the sun without an external force constantly acting on it" then the answer is clearly NO.

Also, if the object is a small man-made pod launched from earth then I don't think there are any natural forces (such as tidal forces or atmospheric drag) in place that could cause a spiraling orbit, at least not in any reasonable amount of time. If there were, we wouldn't have a stable solar system in the first place...

Note that I'm CS student with very little actual knowledge of orbital mechanics, but it seems pretty straight forward to me.


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Post    Posted on: Sun Jan 02, 2005 4:46 pm
Hello, cyr,

what is "CS"?

If spiral courses are possible this no way would mean that the solar system couldn't be stable.

The general point would be then that there are two kinds of courses at least: 1. stable orbits; 2. spiral and other courses. And in fact the comet SOHO-6 has fallen into the sun.

At least one external force is working permanently all the object: sun's gravity.

Each orbit mathematically consists on a special and functional relationship between tangential velocity and vertical velocity or - in more mathematical terms - between two vectors. The comet fallen into the sun shows that this relationship can be broken - the comet fallen into Jupiter shows this too. In these both cases the gravitational vector got too large.

I don't insist on calling the courses in the cases of the fallen comets "spirals" - but they fell into the other bodies without any engine working.

And in the other thread I mentioned other examples of spirals - accretion disks around neutron stars for example which I don't want to discuss this time because I want to go on with the mathematics.



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Post    Posted on: Sun Jan 02, 2005 5:21 pm
Hi cyr,

You understood the question and answered it correctly. For someone who understands the wording is OK. For people who don't understand no amount of extra explanation in the poll would help.

Hi Ekkehard,

I think CS is Computer Science.

About "unstable" orbits. We probably need a very long discussion on stability of orbits. Just let me say that no orbit is unstable in the sense you are using. A craft does not leave one stable orbit and travel in an unstable state to another stable orbit. It simply changes the shape of it's stable orbit. Each orbit is stable, even if it is not circular.

And Comet SOHO-6 hit the Sun while traveling in a stable parabolic orbit with perihelion below the Sun's surface.


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Post    Posted on: Mon Jan 03, 2005 8:09 am
Peter,

in an mathematical sense an orbit is a course returning into itself around a mathematical point called a focus. As a mathematical point this focus doesn't have any extension to any of the three dimensions we are used to by our day-by-day-experiences.

But the sun is no mathematical point - it has extreme extension to all the three dimensions. This is physics - and it means that there are mathematical orbits that are no physical orbits.

I myself don't speak of "unstable" orbits in serious - an orbit is stable by definition. But a spacecraft is changing orbits - and it doesn't do that by tunneling, jumping or flctuating like electrons or quantums. This means that it doesn't go a course being a stable orbit.

Here is one point were you seem to be arguing by using definitions different to the definitions I have in mind. Perhaps this has to be worked out here.

To say that a spacecraft doesn't go along a stable orbit doesn't mean to say that the orbit(s) of the spacecraft are unstable themselves - if you do understand that I were calling the orbits unstable you looked at it from the orbits. And that's NOT the point I'm looking myself from - I am looking at it from the spacecraft. And the spacecraft is changing orbits - one example: a spacecrfat is launched and is orbiting Earth; then the engines fire again and the spacecraft leaves the orbit around Earth and goes into the interplanetary space to reach Mars; arrived at Mars the spacecraft is inserted into an orbit around Mars. In this example the spacecraft changes between three different orbits at least that haven't to do anything with each other except some transit points. All the orbits are stable themselves but the course of the spacecraft didn't keep any of them - it might keep the martian orbit but it didn't keep the earthian one and the transit course. So the spacecraft didn't go a stable orbit.

Another example of a spacecrafts that don't seem to go a stable orbit seen from the point of the spacecrafts are the two Yoyageers. They are leaving the solar system if nothing heepnes to them that forces them back into the system or on a course around the sun. But to leave the solar system means to NOT orbiting the sun - because the fact that orbits are stable does mean that the object orbting doesn't leave the system.

I have to repeat the example of Smart-1 to return to orbits in the mathematical sense and meaning. An orbit is a course returning into itself - Smart-1 didn't go such a course. Additionaly Smart-1 needed an insertion burn of its ion drive to get into its final orbit. And Smart will crash onto the moon one day as has been said by ESA I remember.

This all only is intended to put into question that we using the same definitions. There are several examples in mathematics that they use several different definitions in parallel. One example is that the coastal line of Great Britain is one-dimensional by definition - but on the other side this line can be considered to be of fractional dimensionality by another mathematical concept considered to be valid too. Both you and me should put in doubt and in question wether we are using the same definitions and mathematical concepts.

We are faced to some philosophics.



Dipl.-Volkswirt (bdvb) Augustin (Political Economist)



EDIT: I randomly found an issue in a serious and good web-article I have to look for again explaining why some comets are said to move along parabolic orbits. The reason isn't that they realy have an parabolic orbit - the reason is that the shape of there orbit is unknown and the data available are insufficient. In this case it is ASSUMED only that the orbit is parabolic. This is done to keep the error or mistake to be expected as low as possible.

This means that the data concerning a course can be so few that it's unknown what shape it has - elliptical, circular or hyperbolic.

Instead of "..data conserning... so few..." I could have said "...segment of...so small..." - the course of the vehicles in the example(s) above is made of segments of different orbits. And the ending segment of the course of a package going into the sun can be to small to allow conclusions about the shape of the course. It can go a long distance around the sun with the vertical distance to sun becoming smaller and smaller and smaller...until the package is going into the sun. Mathematically such a segment could be part of a spiral - that's the reason why I'm speaking of spirals. It's an approximative description of a shape only - for easy speaking.


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Post    Posted on: Mon Jan 03, 2005 7:56 pm
Hyperbolic orbits are really escape trajectories. They do not close on themselves like an ellipse but are still widely though of as orbits.

A parabola is the theoretical dividing line between a repeating ellipse and a non-repeating hyperbola. It never occurs exactly in real life.

Periodic comets are all in elliptical orbits. Non-periodic comets, including comets that hit the Sun, are in orbits that COULD be either elliptical or hyperbolic. Since the margin for error always includes the parabola, they are said to be parabolic. Astronomers have been looking for a comet with a clearly hyperbolic orbit or many years, but have never found one. If they did it would be clear evidence that some comets come from interstellar space, which would be interesting.

The most important point is that no astronomer has any doubt that comet orbits are either elliptical or hyperbolic.


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Post    Posted on: Tue Jan 04, 2005 8:46 am
Your last point doesn't say anything about the reasons why the astronomers don't have doubts and from what point and under which aspects they are thinking so.

To repeat it - I know all that and don't be arguing against it. SpaceShipOne for example was going in elliptical orbit the focusses of which have been calculated - one of them was deep within the body of Earth. If SSO would have tried to orbit really it would have crashed into the surface and the pilot would have died. It's an elliptical orbit - but stable? Hm - gravity will change within Earth's body but gravity is constant outside its body. SSO would have failed to go along the orbit completely - it wouldn't keep the orbit.

The astronomers take several data about a comet's course, do some calculations to get a more complete or the whole course, look at the mathematical description of the course and then say, what it is - they look at it mathematically.

But nothing of this included the course of a comet fallen into the sun - they didn't know of SOHO-6. SOHO-6 has been detected by SOHO only and not by any astronomer or any man else. That comet has been detected first when it fell into the sun - so nothing has been calculated, no results are available. May be someone at this forum knows calculations and results. Then I would be wrong and I would be interested in the calculations and results.

In principle astronomers consider most of the cometary orbits calculated to be too insignificant, too weak. They nearly always expect that the calculations will be prove to be too wrong. The calculations nearly always are within a sufficient range around the correct course to detect the comet when it returns but the comets are often NOT at tha coordinates that they are expected to be found at.

The reason is that the courses are calculated from observation and mathematically only - the astronomers don't have sufficient data about the masses required to calculate the courses using physics. From this it follows that they don't know which results they will get if they could base their calculations on gravity, energy, impulse and the like. Again - if someone here knows something different I would find it very interesting and be delighted to find it posted here. I myself up to did find only calculations based on mathematical course elements got by observations only.



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Post    Posted on: Tue Jan 04, 2005 2:57 pm
Here is an interesting link about Sun grazing comets and SOHO.
http://en.wikipedia.org/wiki/Sun-grazing_comet

And here is a quote from that document:

Quote:
Since the launch of the SOHO satellite in 1995, hundreds of tiny Kreutz Sungrazers have been discovered, many of which have actually plunged into the sun or been destroyed completely during their perihelion passage.


Here is a related link with detailed information about comet orbits:
http://en.wikipedia.org/wiki/Comet#Orbi ... cteristics
(EDIT)And in German:
http://de.wikipedia.org/wiki/Komet
Although the German version does not seem to have the same information about orbits.

And here is quote from that document:

Quote:
The first suggestion that Kepler's laws of planetary notion should also apply to the comets was made by William Lower in 1610. In the following decades, other astronomers, including Pierre Petit, Giovanni Borelli, Adrien Auzout, Robert Hooke, and Jean-Dominique Cassini, all argued for comets curving about the sun on elliptical or parabolic paths, while others, such as Christian Huygens and Johannes Hevelius, supported comets' linear motion.
The matter was resolved by the bright comet that appeared in November 1680. Astronomers throughout Europe tracked its position for several months. In his Principia Mathematica of 1687, Isaac Newton proved that an object moving under the influence of his inverse square law of universal gravitation must trace out an orbit shaped like one of the conic sections, and he demonstrated how to fit a comet's path through the sky to a parabolic orbit, using the comet of 1680 as an example.


It is true that comet orbits are often not in agreement with gravitational predictions. These differences, which can amount to several days error, are though to be due to out-gassing of the comet. Here is another quote from the above linked document:

Quote:
Bessel argued that the non-gravitational movements of Comet Encke were caused by jet forces created as material evaporated from the surface of the object . This idea was forgotten for more than a hundred years, before Fred Lawrence Whipple independently proposed the same idea in 1950.


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Post    Posted on: Thu Jan 06, 2005 4:50 am
The precise definition of "spiral" may also be called into question. Assume a two-body situation, start the projectile at a given distance from the sun with zero radial velocity and a tangential velocity less than orbital velocity at that distance, and the object will eventually crash into the sun. The path it takes will certainly look like what is popularly called a spiral, but will not be a true exponential spiral.


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Post    Posted on: Thu Jan 06, 2005 7:57 am
Hello, Garnetstar,

your answer sounds like you do understand my use of the term "spiral".

Hello, Peter,

I already read some of the links you posted before the post you're responding to - at least one of them is the source.

And at least the first of your quotes says that comets have fallen into the sun. This means that we really can throw something into the sun. It means too that the course of the object we throw into the sun will NOT be a straight line from the point we launch it from to the sun but a curve leading away from that line but going closer and closer to the sun and at least into the sun.

We are discussing the idea to throw something into the sun - nothing else.



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Last edited by Ekkehard Augustin on Thu Jan 06, 2005 11:28 am, edited 1 time in total.



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Post    Posted on: Thu Jan 06, 2005 11:03 am
Ugh.

Despite the wording of the poll question, my vote is in. After all, why not solve physical orbital problems democratically? :roll:

Cheers and the best of the new year to all you perpetual orbiters and spirallers out there.


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Post    Posted on: Thu Jan 06, 2005 11:32 am
I don't take the discussion negative - I find it challenging. The only thing is - issues should be checked, tested and experimented mathematically here instead of make it beliefs.

And there have been clarifyings by me as well as by Peter and others.

Does it sound negative to you?



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Post    Posted on: Thu Jan 06, 2005 3:06 pm
Garnetstar wrote:
… start the projectile at a given distance from the sun with zero radial velocity and a tangential velocity less than orbital velocity at that distance, and the object will eventually crash into the sun.

This is the idea that is SO popular and is just wrong!

A circular orbit has one and only one velocity. This velocity is EXACTLY the right one to balance gravity at the distance of the planet (or space craft) from the Sun and cause a circular orbit. If the speed were reduced by even the smallest amount then the velocity would be wrong and the planet would no longer be in a circular orbit. So far we agree.

Now think about this carefully. If the result of this slight change were a slow spiral into the Sun, then the Earth would have long ago spiraled into the Sun as the result of some tiny change in speed due to one of the many asteroid impacts known to have occurred in the distant past. And anyway, the Earth is not in a circular orbit. At no point along it’s orbit is it going at just the right speed and direction to maintain a circular orbit.

Think about this too. If the object were in a perfectly circular orbit and the speed were INCREASED just slightly, then it would be going too fast for the circular orbit. By you logic it should then spiral away from the Sun.

What REALLY happens when you change the speed of an object by accelerating it slightly along it’s circular orbit is you get an elliptical orbit tangent to the circular orbit at the point the velocity change occurred. If you speed up, the new elliptical orbit has perihelion tangent to the circular orbit and aphelion farther from the Sun. If you slow down then the aphelion is tangent to the circular orbit and perihelion is closer to the Sun. When the object reaches perihelion it has gained enough speed, by conservation of energy and Kepler’s 2nd law, to be going FASTER than a circular orbit at that distance. The result is that you are then in an elliptical orbit and at it’s perihelion that is tangent to a hypothetical circular orbit at that distance from the sun, but going too fast for that circular orbit. You are in EXACTLY the same situation as if you had started in the closer circular orbit and increased your speed. Also, as you move along the ellipse you cross an infinite number of hypothetical circular orbits at some angle. If you started in one of these hypothetical intermediate circular orbits and changed your speed AND direction just the right amount, you would enter the SAME elliptical orbit. If you changed your speed and direction by some other amount you would be in a different elliptical orbit. Or maybe a parabolic or hyperbolic orbit. If your speed were slow enough you would CURVE into the Sun along an elliptical path. If you speed were high enough AND in the correct direction, you would CURVE into the Sun along a parabolic or hyperbolic path. You would NOT spiral anywhere. All comets that crash into the Sun are CURVING in along paths that are OBSERVED to be parabolic.

You seem to be thinking of a circular orbit as a delicate and unstable balance of forces, like standing a stick on end. In physics this is an unstable equilibrium. If the stick is balanced perfectly then it will stand up forever, but if you disturb it even slightly then forces build to push it down. You should instead compare it to a pendulum. This is known in physics as a stable equilibrium. If it starts motionless and you disturb it slightly, then it oscillates around the original position, just the way an object in an elliptical orbit oscillates between being closer to and farther from the Sun. In fact, physics (advanced physics, not the introductory physics taught in classes for non-science students) uses the same mathematical formulation for orbital and pendulum motion. And the physics books always show how the orbital equations reduce to circles, ellipses, parabolas and hyperbolas, if the correct energy levels are input. The books NEVER show the equations reducing to a spiral, because they don’t and can’t. I have posted links to online documents that show just that, but to no effect it would seem.
(EDIT) Here is a link:
http://en.wikipedia.org/wiki/Orbit#Anal ... tal_motion
Look near the end of the "Analysis of orbital motion" section and just before the start of the "Orbital parameters" section.


Last edited by campbelp2002 on Thu Jan 06, 2005 6:33 pm, edited 3 times in total.



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