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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: Mon Jan 10, 2005 2:09 pm
New misunderstanding seem to be involved. I suuposed that to occur because I have been thinking about the chance that I do understand the english term "instantaneously" wrong perhaps.

I understand the term "instantaneously" to mean infinitesimal short period of time in english. This would involve infinitesimal short distances, velocities and accelerations too - and these really don't exist as has been proved by a special experiment. The experiment was to increase the kinetic energy of neutrons beginning at an initial level by as small amounts of additional energy as possible. If velocity wouldn't be discrete but continuos each amount of additional energy should cause an increase of velocity, acceleration - if in turn velocity is discrete there should be amounts of energy that don't cause acceleration. The result of the experiment was that the smallest possible amounts of additional energy didn't accelerate the neutrons - the acceleration required several smallest possible amounts and the new velocity wasn't in the immediate neighborhood of the old velocity.

May be I understand the english term "instantaneously" wrong - but if not you may be in error somewhere in the identifcation of theoretical values with real ones.

The average speed in your first example isn't 1 km/h for the reason you are stating - and the 60 km/h isn't the result of a measurement during an infinitesimal period of time.

To get the average it is required to add on all the velocities that have been valid during all the infinitesimal small periods of time that in sum are the time of the trip and then to divide by the time of trip. You cannot get it simply by the distance and it's a problem to include the periods of time after stopping the car completely.

The measurement of the 60 km/h is a measurement got by comparisons of distance between two moments. The amount of time between these two moments is very small but it is not infinitesimal - at least if the measurement method still is as I know it.

The stops at traffic lights don't have anything to do with physical speed - this really is a kind of economical speed. Physical speed is connected to physical motion.

But this is a very tricky point which tends to force us into philosophics.

It seems a little bit if I had to post graphics here which will take time - I have to draw them and to scan them in which isn't possible at the moment.



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Post    Posted on: Mon Jan 10, 2005 2:19 pm
Yes, you understand correctly the meaning of the word instantaneous. I don’t think you read my edit because I posted it just as you posted, but it says that there is nothing physically significant about 1 second. A speed of 10 meters per second is not meant to imply that the motion will continue for a full second. It just means that IF the motion did continue uniformly for 1 second that 10 meters of distance would be covered.

Yes, this is a philosophical question. Your error is not mathematical, it is philosophical. But your philosophical error results in using wrong vectors in your calculations. This is also why scientists were called natural philosophers in Galileo’s time. Science concerns the philosophy of understanding nature. Mathematics is just a tool. And this tool is only useful after the underlying science is agreed upon.

Did you visit the link I posted?
(EDIT)
http://library.thinkquest.org/10796/ch2/ch2.htm
This link does not take you directly to the page I wanted. You need to click on the "Visit Site" link.
(ANOTHER EDIT) I am having some trouble with the link. Sometimes it does not work. You need to get to the page called "Chapter 2, Velocity".


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Post    Posted on: Mon Jan 10, 2005 2:35 pm
Yes - as I already said I visited the link concerning the comets.

The problem at the moment is that you are calling vectors wrong that I got from an astronomer - Joachim Herrman - who in turn is calling Newton as a witness by quoting him. As I already said I cannot scan in something currently but there are graphics showing those vectors I'm using. What I do is simply a very close approximation but a look inmto Joachim Herrmann's book shows that I can do as I'm doing. And I allways see scientists doing so. And it's plausible.

Please list a name of an astronomer and a title of a book he wrote which I ccould buy here in Germany and which is written for an advanced public.



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

EDIT: Peter, in your EDIT you again are doing something different compared to what I'm doing. You are considering an unpropelled rock only - I in turn do what I have been speaking of much earlier: I have a vehicle which has been propelled by the space elevator and is going to be propelled again in the future. It has been accelerated artificially by the elevator and it will be accelerated artificially again in the future. If you leave away these artificial accelerations you get different results - and you cannot use them as arguments saying that I am wrong. To have the possibility to get results perhaps proving me to be wrong you have to use the same artificial accelerations as mine. But you don't.


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Post    Posted on: Mon Jan 10, 2005 2:55 pm
Not the comet link. This link:
http://library.thinkquest.org/10796/ch2/ch2.htm

And about the propulsion. I thought we already agreed that the space craft had to be on a collision course to the Sun at the time the package was released. I don't care what method is used to get on this course or what the space craft does after dropping the package to avoid hitting the Sun, but the package and space craft are on the same course at the moment of release.


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Post    Posted on: Mon Jan 10, 2005 3:21 pm
Garnetstar wrote:
The path, of course, will be a segment of an ellipse of high eccentricity, not a true spiral.[/i]

Exactly correct.


Last edited by campbelp2002 on Mon Jan 10, 2005 3:24 pm, edited 1 time in total.



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Post    Posted on: Mon Jan 10, 2005 3:23 pm
whonos wrote:
drag only from the interstellar medium would cause the orbit to decay over time periods longer than the age of the universe, so they can be ignored.

Exactly.


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Post    Posted on: Mon Jan 10, 2005 3:42 pm
Peter,

the spacecraft isn't yet at the point where the package is to be released at. This point is a special point where special conditions are fulfilled. And I want the vehicle to move there to be able to control and steer the vehicle and to get some data that are of use during my doing.

By the calculations I'm correcting currently (as far as I find time to do it) I get such data too. These calculations you are considering to be wrong for philosophical reasons. I really don't want to repeat to explain the meaning of my initial calculations of seconds and degree per second, cosinus etc. ... but it looks like the moment will come where it is required. They are an integral part of my concept of thinking.

I cannot explain it all to you yet because we seem to not agree on infinitesimality, "instantaneous" velocities, vectors etc..



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Post    Posted on: Mon Jan 10, 2005 3:51 pm
You still have not commented on this link.
http://library.thinkquest.org/10796/ch2/ch2.htm
If you don’t understand and use instantaneous velocities correctly in your second by second calculations, then you are wasting your time. The calculations will not represent physical reality.
(EDIT) Even with a rocket under power you need to use instantaneous velocities, instantaneous forces and instantaneous accelerations all correctly or your calculations are just wrong.


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Post    Posted on: Mon Jan 10, 2005 4:37 pm
Ekkehard Augustin wrote:
Please list a name of an astronomer and a title of a book he wrote which I ccould buy here in Germany and which is written for an advanced public.

Here is a link in German.
http://de.wikipedia.org/wiki/Geschwindigkeit

Here is a very good link, but only in English:
http://theory.uwinnipeg.ca/mod_tech/node14.html

I entered “instantaneous velocity” into a free online translator and got “Unmittelbare Geschwindigkeit”. I then typed “Unmittelbare Geschwindigkeit” into a google search and got many results. I don’t speak German well enough to tell which of these would be of help, but I am sure you could do the same search and find a good document.

(EDIT) I see from the German link above that a better word to search would be “Momentangeschwindigkeit“. A search on that word gave me this:
http://www.physik.uni-muenchen.de/leifi ... geschw.htm
You may be able to find better pages with your own search.
Notice that none of these links is about astronomy. There is nothing astronomical about the concept of instantaneous velocity, it is a general physics of motion concept. The same physics applies to orbits and cars and runners.

(ANOTHER EDIT)
This German link looks VERY good.
http://www.physik.uni-muenchen.de/leifi ... schw01.htm
It looks more like a projectile motion example. Similar to suborbital flight, but closer to an orbital example than the others above.

(3rd EDIT) I just noticed that the last 2 links are from the same site. Probably an online Physics course.


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Post    Posted on: Tue Jan 11, 2005 7:46 am
Peter,

I know the term "Momentangeschwindigkeit" very well but we're not talking about "Momentangeschwindigkeit" - I had a look into the book that says the orbital velocity of Earth to be 29.8 km/s. This velocity I am using in my initial calculations. The book doesn't call these 29.8 km/s "Momentangeschwindigkeit" - it's calling it "mittlere Bahngeschwindigkeit". The term "Bahngeschwindigkeit" is "velocity along course" or "velocity along orbit" in English - the term "mittlere" now is "in the middle of (several numbers)", "medium", "average" (and the like) in English.

This "mittlere Bahngeschwindigkeit" doesn't have anything to do with your example of the car moving by 60 km/s and stopping after 1 km. The average velocity in your example including times of 0 km/h velocities is simply a statistical average during a trip, tour or journey caused by human control. The "mittlere Bahngeschwindigkeit" isn't of that nature and cannot be compared neither to the 60 km/h nor to the 1 km distance - the "mittlere Bahngeschwindigkeit" is an average during one completion of the whole orbit. There are two points at this orbit where Earth really is going by this velocity. The vehicle in my experiment can be considered to have the velocity too at these to points as long as it is not artificial accelerated additionaly.

The "mittlere Bahngeschwindigkeit" is the result of two independent causes - gravitational acceleration and original velocities the materials Earth is made of had before sun has been formed. These orginal velocities didn't be cause by the gravitational acceleration of sun. Partially at least they are caused by the Impulse Conservation Theorem - other materials had lost impulse before our sun and her system have been formed and this impulse has been moved over to materials our solar system is consisting of. I say PARTIALLY - but this is sufficient. For this reason I cannot only - I MUST seperate Earth's velocity into at least two components.

But this already has been discussed in this thread. I don't know why you don't accept it - the theories about the formation of planetary systems and about their history and the history of the dusts and materials within our galaxy really say this. That means that regardless of we talking about instantaneous or average velocities these velocities are the result of two components at least.

Believe me I know what "Momentangeschwindigkeit" really is and how to calculate it mathematically but mathematics say that this "Momentangeschwindigkeit" in general is to be suspected to be changing permanently - each value of it is valid during an infinitesimal short period of time. The term "period of time" in principle is wrong because "infinitesimal short" is indicating an extremely close approach to a POINT on the time-beam. "mittlere Bahngeschwindkeit" instead isn't changing. And the methods by which Earth's velocity is measured don't be measuring "Momentangeschwindigkeit" as far as I know these methods - but I will check my informations.

You are applying theories which I do know well too. These theories are including instantaneous velocities. But I don't apply these theories here - my second-by-second calculations are calculations of a chain of vectors. As you know you yourself have got a result very similar to mine when you did your own calculations of my Step Two. I detected that I have to correct may calculations a little bit and our results may be closer to each other after I did all the corrections. So there is no reason now to suspect the concept to be wrong seen from the results. And I ever said that approximation is included.



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EDIT: Just this moment I read the two of the links you list and I still cannot agree to you. They simply say what I have said. It's the dimensionality that seems to cause problems.

The english link says that in the example of instantaneous velocity the speedometer shows 90 km/h that moment the car is accelerated up to that speed.

But that moment isn't one hour long - this instantenous speed in the terminology of the link you listed could be kept for an hour but it doesn't need to. The speedometer of the car only can indicate km/h and no km/s or km/min or km/5 min or the like. The dimensionality of a moment is different to the dimensionality of km/h. If I wouldn't take that into account I would get a very big mistake.

The 90 km/h are just a tangent touching a curve that shows the distance gone after a certain amount of time - the tangent shows the distance gone if the instantaneous velocity would have been kept for one hour but it has been kept only for that short moment that is represented by the point of touch between the tangent and the curve showing the distance gone. To combine such different dimensionalities caused me the error by which I got a spiral long before I first discussed at this message board.

So the dimensionalities should be made equal which means to indicate not 90 km/h but 90/3600 km/s = 0.025 km/s if the indicated speed is kept for one second or 0,001 km/0.025s if the speed is kept for 0.025 s. In this case the error would be so small that a very good approximation will be got. If there were an error at all - we could do some mathematicall infinitesimal calculations in this example perhaps (but I don't want to). In my calculations the dimensionalities are equal - Earth's velocity is given as km/s and I am calculating one second by one second.


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Post    Posted on: Tue Jan 11, 2005 3:45 pm
Ekkehard Augustin wrote:
I had a look into the book that says the orbital velocity of Earth to be 29.8 km/s. This velocity I am using in my initial calculations. The book doesn't call these 29.8 km/s "Momentangeschwindigkeit" - it's calling it "mittlere Bahngeschwindigkeit”.

We are, or should be, talking about “Momentangeschwindigkeit”. That book probably never uses the term “Momentangeschwindigkeit”. You can use either “Momentangeschwindigkeit” or "mittlere Bahngeschwindigkeit" as your STARTING velocity. And the result of your first calculation must be considered as the “Momentangeschwindigkeit” for the next calculation. Each new calculation must use the result of the previous calculation as the “Momentangeschwindigkeit” for it’s starting value.

You have never really said how you will compute any values after the first second. All you have done is describe how you break the "mittlere Bahngeschwindigkeit" into what you consider a more proper "Momentangeschwindigkeit" and another vector.

And everything you say about solar system formation has no relationship to our discussion, stop mentioning it! That is a process that takes millions of years and throws large amounts of material out of the solar system. It is also not well understood because we can’t watch it occur. It took place too long ago and even if we were there, all the orbits would SEEM stable because they take millions of years to change. Even today there is dust falling into the Sun AND being blown out of the solar system. It is a VERY complex process, using gravity, magnetic fields, light pressure, solar wind, tidal friction, and who knows what else. It takes millions of years to make noticeable changes and means NOTHING as related to space craft navigation.

(EDIT)I have made changes to orbit.xls that will allow you to enter velocity changes at every point in the calculation. Keep in mind that my time intervals are about 1.8 days long, so you need to enter the total velocity change in 1.8 days in each case. And since I use a coordinate system centered on the Sun and not rotating, you will need to calculate the X and Y components yourself before entering them.
http://home.austin.rr.com/campbelp/orbit.xls
(LATER EDIT) I have removed the changes. Orbit.xls again shows a circular orbit. To see the behavior described here, enter DeltaVx=-5 on line 2 and +5.7 on line 67.

(ANOTHER EDIT) I have entered DeltaVx = -5 km/s at the line 2 to enter a Hohmann transfer orbit. I have also entered DeltaVx = +5.7 at line 67 to show the second thrust event entering the lower circular orbit. (LATER EDIT) I have removed the changes. Orbit.xls again shows a circular orbit. To see the behavior described here, enter the numbers as described above. (END LATER EDIT) What you see is a true and accurate representation of physical reality. The path is not a spiral. It is half an ellipse tangent to a circle at the point of the second thrust. You can edit line 67 to change the second thrust back to 0 and you will see the orbit come back to a full ellipse. To get to the sun you need a larger thrust at line 2. And the result will be a half ellipse tangent to a very small circle the same size as the Sun, but the simulation will break down because 1.8 day intervals are too long that close to the Sun. You can also experiment with thrust in different directions. You can then try thrusting directly at the Sun by changing the first DeltaV from an X to a Y velocity. You will see that doing so requires an even larger DeltaV to get to the same distance from the Sun before the ellipse starts curving back up away from the Sun.


Last edited by campbelp2002 on Tue Jan 18, 2005 9:04 pm, edited 3 times in total.



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Post    Posted on: Thu Jan 13, 2005 8:13 am
Peter,

how I will and have been calculating values after the first second is quite obvious and I remember having explained it a little bit at least: I increase the vertical component and calculate the resulting velocity new out of the vertical component increased now and the tangential component left unchanged. I do that by trigonometrics - the resulting vector is the hypothenusis, the vertical vector and the tangential vector are the kathetises. I choosed to use the vertical vector as ankathetis, the tangential vector as counterkathetis, calculated the tangens, got by arcustangens the angle between hypothenusis and ankathetis, took the cosinus of the result, divided 1 by the cosinus and multiplied the new result by the ankathetis. This I am repeating many many times.

The book surely doesn't be talking about the "Momentangeschwindigkeit" - along an ellipse the "Momentangeschwindigkeit" is changing permanently as I already said.

Your "must" requires justification - please give this justification.

The result of my first calculation is the velocity after acceleration during one second - it is the resulting velocity which would be the integral of acceleration + initial velocity if velocity would be a continuos phenomenon in nature. Really it's not an integral but a sum.

This result after the first second no longer has anything to do with Earth's orbit - it only is a very very small fraction of the course of the vehicle which is resulting from the vectors the vehicle has inherited from Earth and the increase of one of these vectors. The increase has been caused by the space elevator. So the discussion about instantaneous velocity no longer does make any sense - I agreed to doing the discussion only because I used Earth's "Bahngeschwindigkeit" to get the starting vectors.

What may be and what I'm thinking about very seriously is that the velocity at the end of one second seems not to be the velocity during that second. This seems to be indicated too by the fact that the vertical vector I got by my initial calculations is only the half of the acceleration of Earth by the gravitation of sun. But please not - I'm still thinking about this seriously.

What I said about the formation of the solar system has fundamental relationship to our discussion - in this formation process impulses and velocities were involved still present in the solar system and especially the movement of Earth along its orbit around sun. These impulses and velocities are independent of sun's gravity because they really were there before sun has been formed. They are causing the tangential vector that the vehicle has inherited from Earth - but they didn't force Earth into an orbit. This does sun's gravity only. Because of this the independent tangential vector is as real as the gravitational vertical vector - to this you seem to disagree. It means that the vector of Earth along its orbit isn't the tangential vector but the result of the tangential vector and the vertical vector. (tenth repetition? twentieth repetition?) And it all can be watched and is under observation at exoplanets and distant stars surrounded by disks of dusts. All the movements that formed the system more than 4.6 billion years ago are still at work and affecting the movements of vehicles, rocks and planets.



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Post    Posted on: Thu Jan 13, 2005 1:48 pm
You must use the instantaneous velocity because that is the only real physical velocity. The average velocity over even the smallest time is just a mathematical fiction.

Have you looked at orbit.xls since I made the changes? What do you think?

Orbit.xls is numerically integrating the orbit using Euler’s method. Here is a German document describing Euler’s method:
http://www.uni-stuttgart.de/bio/adamek/ ... NuMe05.pdf

Ekkehard Augustin wrote:
… the tangential component left unchanged.

You can’t just leave the tangential component unchanged. We already agreed that the tangential component is along the ellipse and not along imaginary yellow circles in this diagram.
Image
Vectors along the imaginary yellow circles will not change due to the Sun’s gravity, but the Sun’s gravity DOES change the real black vectors tangent to the ellipse, except for the instantaneous vectors exactly at perihelion and aphelion.
(EDIT) Clarification: The Sun's gravity will change the direction but not magnitude of the vectors along the yellow circles.


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Post    Posted on: Thu Jan 13, 2005 2:46 pm
Peter,

as far as I remeber we didn't agree that the tangential component is along the ellipse... - unless I'm misunderstanding you due to not being a native English-speaker.

What's along the ellipse is the vector that is resulting if the vector that is tangent to the ellipse and the vector that is pointing towards the sun are calculated to each other.

I never have used a vector going along your yellow circles.

Your argumentation concerning that I "must" use the instantaneous velocity is invalid because all values available to me are non-instantaneous velocities - One second I don't consider to be instantaneous. The methods to measure Earth's velocity that I know don't deliver instantaneous velocities and the values in my books don't be instantaneous velocities - so all I have are average velocities that are averages for one second. And it's a fact that the vertical velocity of Earth towards sun I got by my initial calculations is extremely clsoe to the half of Earth's acceleration by sun's gravity. As I said earlier - I have to think about this and I will do it when I find time for it. I have very much to do at the moment.



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Post    Posted on: Thu Jan 13, 2005 3:22 pm
Image
I have added a magenta vector to this diagram. Does the magenta vector look like your idea of the “tangential” velocity? It is nearly the same as the black vector. For a shorter time interval it would be even closer. Now see that is NOT perpendicular to the green vector pointing at the Sun. Therefore the “tangential” velocity DOES change due to Sun’s gravity. If you don’t allow it to change in your calculations you will get the wrong result.


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