Can You Determine the Center of Mass Distance Using Instantaneous Orbital Data?

[JANm]

Try again, Jan. You cannot deduce the semi-major axis from the acceleration and velocity.

Hello D H
You did a lot of homework. I will adjust my next writings to this profound way of defining. Indeed there was trouble with acceleration and semimajor axis and perhaps others. I will read this thread more profoundly some other time...

If you say try again and then say that what I have to try is impossible that does not sound inviting. I say now for the third time.

In the case that velocity and acceleration are given on the umbilical points of the curve a more indefinite stage appears than in the most common stage that the velocity and acceleration are not normal to each other.

I am very bothered by the fact that the threadgiver does not give a general example at this moment of discussion. I am discussioned to defeat with an example measurement would never give...

If you are in an elliptical orbit around an object and you measure velocity and acceleration than it is impossible to measure exact at the moments of the umbilical points of the curve.

Umbilical points in differential geometry are difficult. In differential geometry it is nicer to calculate on a geoid than to calculate on a bolar object. Information of curvature in different directions being different on a geoid and exact the same on a bolar object LOOSES INFORMATION.

I HAVE ADMITTED THAT THERE ARE MANY SOLUTIONS POSSIBLE if you take umbilical points. Moving in a circle is the most probable solution if given values of velocity are normal to acceleration, because moving in a circle means that velocity is ALWAYS normal to acceleration.

B4488 and DH you are teasing the differential geometrist and for the very last time I need an example where acceleration and velocity are NOT normal to each other. Then I can test the calculations (which took me very much time I must say; doesn't matter, but after all my work I want a sensible testcase...
greetings Janm

 

[belliott4488]

What's pi_p? Otherwise, this is all very nice.

You're losing me ... it looks like you're setting a = 94/15 and GM = 376 ... where do these values come from?

pi_p is the point of perihelium in the language of spring-point? Is that the right name?

If I understand you, you're referring to the argument of perigee, which is the angle in the orbital plane between the ascending node and the perigee (perifocus or periapsis in general), measured at the central body. The ascending and descending nodes are the intersections of the orbit with the x-y plane of the inertial coordinate system. (By the way, the English spellings are "apehelion" and "perihelion" for orbits about the Sun.)

If you take e =0,25 and your example v=10 km/s and acc=10 km/s^2
a is normal to v, then follows a =94/15, r_min=4,7 and GM=376.
This is perihelium and there

-GM/(2a)=v^2/2 - GM/(a(1-e) and

acc= v^2/rc - GM/(a(1-e)^2

Okay, so you have arbitrarily chosen to set e = 0.25 (as we write on my side of the Atlantic Ocean - 0,25 in Haarlem). This selects one of the infinite number of possible solutions. (e = 0 gives the circular orbit solution you selected earlier.)

So there is the example of a solution of an ellipse. I have admitted there needs to be extra information in the case that the point taken is perihelium or aphelium. So that is an exeption to the solution I still mean to have if another point on the ellipse is taken.

Greetings Janm

Okay - maybe we're now in closer agreement. You have shown that the solution is known if we assume a circular orbit, but if the orbit is general (ellipse, parabola, or hyperbola), then we would need additional information, such as a second point of the orbit, in order to find a unique solution.

 

[JANm]

(By the way, the English spellings are "apehelion" and "perihelion" for orbits about the Sun.)

Hello Belliott4488
You mean that if you have an ellipse for instance of the vulcano active moon of Jupiter Io to Jupiter YOU WOULD NOT CALL THE CLOSEST POINT OF IO TO JUPITER THE PERIHELIUM, and after it he's turned 180 degrees in whatever subsytem rotation planet curvature system you and DH work: YOU STILL WOULD NOT CALL THAT APHELIUM
Is that what I understand with discussion with you both?
I do not want to speak with you for a whole week. I am sich and tired of your pityfull only circular excample witch can only point to a circle of 10 km.

AND I AM VERY ANGRY WITH YOU THAT YOU DIDN"T ADMIT THAT
e=0, r=a=b=10km, GM=1000 is actually really a solution to the problem. Statistically the only sensible one.

A physisician is NOTHING if he can't admit that another physician is RIGHT AT ONE TINY LITTLE BIT of moment

Ih

 

[belliott4488]

JanM - I thought from your previous post that you had agreed that this problem is indeterminate, but now it seems that you have returned to your earlier position, despite all the simple reasons we have given in opposition to it (which you continue to ignore).

...
I am very bothered by the fact that the threadgiver does not give a general example at this moment of discussion. I am discussioned to defeat with an example measurement would never give...

...

B4488 and DH you are teasing the differential geometrist and for the very last time I need an example where acceleration and velocity are NOT normal to each other. Then I can test the calculations (which took me very much time I must say; doesn't matter, but after all my work I want a sensible testcase...
greetings Janm

I am surprised! You are a mathematician, no? I would not have expected that you would require a physically meaningful set of conditions for what is essentially a mathematics problem. But no matter - I believe the following should be more realistic, and the velocity and acceleration vectors are not normal to each other, as you requested. (I'm still setting the components in the z-direction to zero so that we can stay in the x-y plane; I trust you will not object). Here is the new problem:

velocity v = 0 km/sec i + 10 km/sec j
acceleration a = -0.6 km/sec² i - 0.1 km/sec² j

I'm pretty sure that's a more physically realistic example. It is close to values I might use in my daily work.

So, given the new velocity vector and acceleration vector, do you still claim to be able to tell us how far this vehicle is from the central body?

 

[belliott4488]

Hello Belliott4488
You mean that if you have an ellipse for instance of the vulcano active moon of Jupiter Io to Jupiter YOU WOULD NOT CALL THE CLOSEST POINT OF IO TO JUPITER THE PERIHELIUM, and after it he's turned 180 degrees in whatever subsytem rotation planet curvature system you and DH work: YOU STILL WOULD NOT CALL THAT APHELIUM

No, I would not - the correct words in English are "aphelion" and "perihelion", which refer only to orbits around the Sun (Greek \alpha\pi o (apo) for "away" and \eta\epsilon\lambda\iota o\sigma (helios) for "Sun". For Earth orbit you have apogee and perigee (Geos = Earth), for the Moon, aposelene and periselene, etc. I don't know the words for Jupiter-centered orbits off-hand, but the general terms are apoapsis and periapsis (or apofocus and perifocus, as DH has explained).

Is that what I understand with discussion with you both?
I do not want to speak with you for a whole week. I am sich and tired of your pityfull only circular excample witch can only point to a circle of 10 km.

Actually, the 10 km circle was your solution. As DH and I both told you, there are an infinite number of elliptical orbits with the given velocity and acceleration, including ones that will have semimajor axes of thousand of kilometers, if that's what you want. Just let GM increase without bound, and you get ever-larger distances to the central body for the same acceleration. Of course, if you place anybody at such a point and give it the velocity I stated, it must enter some kind of orbit - it must go somewhere, mustn't it?

AND I AM VERY ANGRY WITH YOU THAT YOU DIDN"T ADMIT THAT
e=0, r=a=b=10km, GM=1000 is actually really a solution to the problem. Statistically the only sensible one.

Of course we admitted that your solution is valid - we simply denied that it was the only solution.

Now you are speaking of statistics? Is this how you solve problems in Physics? You consider the infinite set possible solutions of an indeterminate problem and then apply probability to pick one solution? Wow. I would simply call the problem "indeterminate" and leave it at that.

A physisician is NOTHING if he can't admit that another physician is RIGHT AT ONE TINY LITTLE BIT of moment

Ih

Well, in English a "physician" is a medical doctor; the scientists are called "physicists", but I assume you are trying to insult me and not your medical care-giver.

But I am relieved to hear that I am more than "nothing" since I have noted many times when you were correct, for example, your circular solution is a correct solution to the problem given -- it is, however, only one of an infinite number of perfectly physically correct solutions.

You, on the other hand, seem never to have considered the possibility that you might be wrong in your reasoning. Instead of responding to a number clear objections that both DH and I have raised, you simply ignore those objections and present another incorrect argument - or you diverge onto an unrelated subject in which you can refer to a lot of impressive mathematics that has no bearing on the current problem.

You don't seem to be at all interested in learning how to improve your understanding of the subjects we've brought up, so if you want to end this exchange here, that's fine with me. Until you are interested in seeing where you have gone wrong (and you are definitely wrong - you have made mistakes for which I would have given my first-year Physics students very poor marks), then this conversation is really a waste of all of our time.

 

[D H]

Hello Belliott4488
You mean that if you have an ellipse for instance of the vulcano active moon of Jupiter Io to Jupiter YOU WOULD NOT CALL THE CLOSEST POINT OF IO TO JUPITER THE PERIHELIUM,

I have not criticized you regarding your abuse of terminology because you don't know the terminology. But since you asked -- I absolutely would not call the closest point of Io to Jupiter the perihelium point. Perihelion (apparently perihelium in German) means closest to the Sun, and the Sun only. If I were talking about the closest point on Io's orbit about Jupiter to Jupiter I would either use the correct specific term (perijove) or one of the correct generic terms (perifocus or periapsis).

AND I AM VERY ANGRY WITH YOU THAT YOU DIDN"T ADMIT THAT
e=0, r=a=b=10km, GM=1000 is actually really a solution to the problem.

Neither of us said r=10 km is not a solution to the problem. In fact, just the opposite:

That is one of an infinite number of solutions. You do not know which is the case.

That solution is not unique.