You Might Be a Platonist If ...

[J_B_]

Planets, of course.

Indeed. What information were you given about these planets in order to answer the question at hand?

 

[essentialsaltes]

Indeed. What information were you given about these planets in order to answer the question at hand?

Orbital radius (or semimajor axis) and period?

 

[J_B_]

Orbital radius (or semimajor axis) and period?

Would that be sufficient information for the most advanced research project by experts in cosmology studying the orbits of those planets? Say, for example, to study the precession of Mercury?

 

[essentialsaltes]

Is your thread suitable for the most advanced research project by experts in cosmology?
Are we ever going to get to the relevance of the "perfect, rigid sphere" in your question?

 

[J_B_]

Is your thread suitable for the most advanced research project by experts in cosmology?

No.

Are we ever going to get to the relevance of the "perfect, rigid sphere" in your question?

The relevance is to see how you answer the question. That's all.

Are you going to answer my question? Was the information provided in your freshman physics class sufficient for the most advanced research project by experts in cosmology studying the orbits of those planets?

 

[public hermit]

Ahhhhh!!!


Man, I was so hoping this thread was about Plato and Platonism. Sorry I don't have anything to contribute, except my sincere disappointment, lol.

 

[J_B_]

Ahhhhh!!!


Man, I was so hoping this thread was about Plato and Platonism. Sorry I don't have anything to contribute, except my sincere disappointment, lol.

It could have gone that direction, but it's too late to turn the ship now. I understand your disappointment.

 

[Speedwell]

I never said there was. I asked you to assume. When studying Kepler's laws in your introductory physics class, what type of object was specified for examples, homework, etc.?

It was generally assumed that the forces involved acted on the center of mass of the object--a reasonable assumption if the object is approximately rigid and spherical.

 

[J_B_]

It was generally assumed that the forces involved acted on the center of mass of the object--a reasonable assumption if the object is approximately rigid and spherical.

Agreed it is a reasonable assumption. Said assumption essentially equates to assuming a perfect, rigid sphere ... among other possibilities. So, same question to you as that posted in #23.

 

[essentialsaltes]

Are you going to answer my question? Was the information provided in your freshman physics class sufficient for the most advanced research project by experts in cosmology studying the orbits of those planets?

If they were answering the same question, i.e. "What does Kepler's Law predict in this situation?" then yes. That's probably as much orbital mechanics as cosmologists know, anyhow.

 

[J_B_]

If they were answering the same question, i.e. "What does Kepler's Law predict in this situation?" then yes. That's probably as much orbital mechanics as cosmologists know, anyhow.

Never mind.

 

[public hermit]

It could have gone that direction, but it's too late to turn the ship now. I understand your disappointment.

I'll take a shot, even though this is way outside anything I have an inkling about.

I'm assuming these are the only two objects in the universe. Does there need to be another force (besides B) in order for A to have an elliptical orbit? Maybe that's too Aristotelian? Perhaps because A will always want to go in a straight line its orbit will be elliptical simply on account of B? I don't know. I think I'll choose "I don't know."

 

[FrumiousBandersnatch]

I should like to take credit for that, but I don't think it was me. I don't want to plagiarise credit.

Oops, you're right! I've confused you with Yttrium... apologies both - I'll correct it.

 

[sjastro]

I'll take a shot, even though this is way outside anything I have an inkling about.

I'm assuming these are the only two objects in the universe. Does there need to be another force (besides B) in order for A to have an elliptical orbit? Maybe that's too Aristotelian? Perhaps because A will always want to go in a straight line its orbit will be elliptical simply on account of B? I don't know. I think I'll choose "I don't know."

All you need are two bodies for an elliptical orbit.
This is known as a Keplerian orbit.
Newton derived the equation for the two body problem.

u=1/r where r is the radius of the orbit.
θ is the angle subtended.
m is the mass of the orbiting body
l is a constant.
f(1/u) is the force law which Newton suggested was an inverse square law.

The general solution is the equation of a conic section;
r = p/(1 + ecosθ)
The terms p and e contain l and m; e is the eccentricity.

The solution predicts for 2 closed orbit types and 2 open orbit types;
(1) Circular (unstable) where e = 0
(2) Ellipse where e = 1
(3) Parabola where e <1
(4) Hyperbola where e > 1

The two body problem is one of the very rare examples of harmony between pure mathematics and science.
When a third body or more is added to the mix, perturbation theory is required where there is a deviation to the above equation.
Unfortunately the solutions to the new perturbed equations cannot be solved directly.
Furthermore the orbits eventually become chaotic, unpredictable and unstable with time.

This is where the pure mathematicians were told to step aside by the applied mathematicians and their partners in crime the physicists.
In order to obtain workable solutions they had to slice and dice Newton’s original differential equation much admired by pure mathematicians and produce numerical approximations based on algorithms like this example.

And this is one of the more elementary algorithms used in celestial mechanics.

 

[public hermit]

All you need are two bodies for an elliptical orbit.
This is known as a Keplerian orbit.
Newton derived the equation for the two body problem.

u=1/r where r is the radius of the orbit.
θ is the angle subtended.
m is the mass of the orbiting body
l is a constant.
f(1/u) is the force law which Newton suggested was an inverse square law.

The general solution is the equation of a conic section;
r = p/(1 + ecosθ)
The terms p and e contain l and m; e is the eccentricity.

The solution predicts for 2 closed orbit types and 2 open orbit types;
(1) Circular (unstable) where e = 0
(2) Ellipse where e = 1
(3) Parabola where e <1
(4) Hyperbola where e > 1

The two body problem is one of the very rare examples of harmony between pure mathematics and science.
When a third body or more is added to the mix, perturbation theory is required where there is a deviation to the above equation.
Unfortunately the solutions to the new perturbed equations cannot be solved directly.
Furthermore the orbits eventually become chaotic, unpredictable and unstable with time.

This is where the pure mathematicians were told to step aside by the applied mathematicians and their partners in crime the physicists.
In order to obtain workable solutions they had to slice and dice Newton’s original differential equation much admired by pure mathematicians and produce numerical approximations based on algorithms like this example.

And this is one of the more elementary algorithms used in celestial mechanics.

Yes.

 

[sjastro]

A Keplerian orbit based on Newton's equation; perfectly predictable.

The three body problem based on the algorithm in post #34.
Subject to the data input, orbits eventually become chaotic and a planet is ejected.
Our solar system will become chaotic and possibly cease to exist in the (very) distant future.
Stability of the Solar System - Wikipedia

​

 

[durangodawood]

In answering the poll, assume perfect, rigid sphere A is orbiting perfect, rigid sphere B and that no other objects affect the motion of sphere A.

Then, pick your poison.

It seems like the question is sort of Platonist up front, so the answer would naturally be Platonistical.

But if one is made of feathers, then that changes everything.

 

[durangodawood]

A) The orbit IS an ellipse

Is there a difference between "IS an ellipse" and "is an ellipse" that I should be aware of?

Not being a wise ass. I just get the sense that, to quote a famous president, it depends on what the definition of "is" is.