How Does a Comet's Journey Through Space Connect to Relativity?

[enceladus_]

I am wondering about the journey of a comet:

1. Let's say this comet is located in the Kuiper Belt. From my understanding it is inert. Trying to tie in my limited Relativity understanding, could I say that it is in free float? From my understanding, it is getting its movement orders from the spacetime where it is located.

2. What exactly makes them get pulled towards the sun? It seems random.

3. Again, trying to tie in my limited Relativity understanding after some event, our comet will start heading for the sun. Could I say that it is now receiving its movement orders from the Sun? I also understand that Jupiter can come into play during this time, due to its gravity.

4. If our Comet passes the Sun, what is next? Where does it get its marching orders from? Also, do we know the curvature of spacetime in our Solar System?

Sorry if these concepts are not at all relevant, just trying to tie together some of the things I am reading now.

Many thanks for all wisdom.

 

[Simon Bridge]

I am wondering about the journey of a comet:

1. Let's say this comet is located in the Kuiper Belt. From my understanding it is inert. Trying to tie in my limited Relativity understanding, could I say that it is in free float? From my understanding, it is getting its movement orders from the spacetime where it is located.

Yep - GR is a local model for gravitation - so it is the local curvature that informs the motion.
All bodies under gravity alone are in "free fall" - don't know what you mean by "free float".

2. What exactly makes them get pulled towards the sun? It seems random.

Gravity.
OK, you know that ... so you will need to be more explicit with your question.

3. Again, trying to tie in my limited Relativity understanding after some event, our comet will start heading for the sun. Could I say that it is now receiving its movement orders from the Sun? I also understand that Jupiter can come into play during this time, due to its gravity.

It gets it's "movement orders" as it were from the local space-time. The Sun happens to be a major player in determining what this is, so is Jupiter.

4. If our Comet passes the Sun, what is next? Where does it get its marching orders from? Also, do we know the curvature of spacetime in our Solar System?

What do you mean by "passes the Sun"?
We know a lot about the curvature of space-time in the Solar System - we have, or have had, spacecraft investigating pretty much every major body int he solar system using this knowledge. We've also had over a century keeping track of masses as they move about out there.

 

[enceladus_]

Yep - GR is a local model for gravitation - so it is the local curvature that informs the motion.
All bodies under gravity alone are in "free fall" - don't know what you mean by "free float".

This book I am reading refers to free fall as free float. The author seems to think its a better term.

Gravity.
OK, you know that ... so you will need to be more explicit with your question.

I should have phrased this better. How does a comet go from getting its movement orders telling it to do nothing, to getting them from the Sun?

What do you mean by "passes the Sun"?
We know a lot about the curvature of space-time in the Solar System - we have, or have had, spacecraft investigating pretty much every major body int he solar system using this knowledge. We've also had over a century keeping track of masses as they move about out there.

It seems that most comets end up hitting the sun directly. However, some of them are able to survive passing the Sun and go past it. Do these comets continue in orbit around the Sun?

As for the curvature, when heading towards to Sun, it must be positive, correct?

Many thanks Simon.

 

[Janus]

This book I am reading refers to free fall as free float. The author seems to think its a better term.


I should have phrased this better. How does a comet go from getting its movement orders telling it to do nothing, to getting them from the Sun?

Even out in the Kuiper belt it gets its "movement orders" from the Sun. Objects in the Kuiper belt orbit the Sun due to the Sun's gravity. When it falls in toward the Sun it has shifted to a new orbit. (it still is in free fall) As to what causes this shift, it is due to the cometary body making a close pass with some other body and that body's gravity nudging it into the new orbit.

It seems that most comets end up hitting the sun directly. However, some of them are able to survive passing the Sun and go past it. Do these comets continue in orbit around the Sun?

It depends. Some comets are periodic, they have closed orbits and return regularly (our at least until it evaporates completely, and even then we are left with a meteoroid belt.) Sometimes however the body will be traveling at greater than escape velocity. In which case, it will whip once around the Sun and then exit the Solar System entirely.

Many thanks Simon.

 

[enceladus_]

That makes a lot of sense. Many thanks.

 

[Simon Bridge]

This book I am reading refers to free fall as free float. The author seems to think its a better term.

Which book would that be?

I think this deserves a bit more examination...
It's a term of dubious value. In physics, a floating object is something whose buoyancy is equal or greater than it's weight and sort-of implies some balance of opposing forces... and the intuitive image would be of the object doing nothing much.

If you google "free float" you will be hard pressed to find the author's use of the term - I think the dominant use comes from the world of finance, referring to shares. The first use that google finds for me, in connection with gravity and comets, is this thread.

The effect of gravity on an object is commonly called "falling" - when it happens to you, you don't say "I floated to the ground", you say "I fell to the ground" right? So the term "free fall" makes a tighter connection to our intuitive understanding of gravity.

Occasionally it is useful to use another term though. We may say that two bodies falling towards each other under gravity are "gravitating bodies". We also need a slight modification to our intuitive understanding of falling to include that two gravitating bodies fall towards each other (the intuition is usually that the smaller body falls toward the larger) and that objects orbiting their common center of mass are still falling towards each other. (A small object is said to orbit a larger one if the common center of mass is very close to the center of mass of the larger one.)

I should have phrased this better. How does a comet go from getting its movement orders telling it to do nothing, to getting them from the Sun?

What Janus said - kuipier belt objects are not "doing nothing".

It seems that most comets end up hitting the sun directly. However, some of them are able to survive passing the Sun and go past it. Do these comets continue in orbit around the Sun?

So, by "passing the Sun" you are (the book is?) referring to a close approach to the Sun? I don't think I can add to what Janus said. Objects in freefall towards the Sun may strike it, come close to it and then move away to cycle back again (elliptical orbit), or escape (hyperbolic orbit). Note: planetary orbits are ellipses so the Earth can be equally said to "survive passing the Sun" every year - same with Neptune.

As for the curvature, when heading towards to Sun, it must be positive, correct?

You can calculate the curvature yourself via the Einstein equations. It is not normally thought of as depending on the direction of travel.
http://www.relativity.li/en/epstein2/read/h0_en/h1_en/

The Sun and the Comet attract each other, if that's what you mean.
It's good that you are attempting to learn more about the concepts in that book :)

 

[enceladus_]

Which book would that be?

Its "A Journey into Gravity and Spacetime,' by John Archibald Wheeler. It was $0.01 on Amazon so I decided to pick it up. I've attached some pages where he talks about free float. He seems to like using fruity terms for things...he coins the term momenergy in the book as well.

What Janus said - kuipier belt objects are not "doing nothing".

That is clear to me now. I was being lazy in my description of them.

So, by "passing the Sun" you are (the book is?) referring to a close approach to the Sun? I don't think I can add to what Janus said. Objects in freefall towards the Sun may strike it, come close to it and then move away to cycle back again (elliptical orbit), or escape (hyperbolic orbit). Note: planetary orbits are ellipses so the Earth can be equally said to "survive passing the Sun" every year - same with Neptune.

Well, the Earth does not pass the Sun to the extent where it can get incinerated like a Comet.

You can calculate the curvature yourself via the Einstein equations. It is not normally thought of as depending on the direction of travel.
http://www.relativity.li/en/epstein2/read/h0_en/h1_en/

The Sun and the Comet attract each other, if that's what you mean.
It's good that you are attempting to learn more about the concepts in that book :)

My book describes the curvature of spacetime in a similar manner to a heavy person standing on a trampoline. The persons mass creates a positive curvature near him and a negative curvature outside of the depression he creates. For this reason, I assumed that spacetime must be positively curved as you move towards to Sun.

 

[Simon Bridge]

Its "A Journey into Gravity and Spacetime,' by John Archibald Wheeler. It was $0.01 on Amazon so I decided to pick it up.

A yes...
http://www.goodreads.com/book/show/1405966.A_Journey_Into_Gravity_And_Spacetime
... Wheeler tries too hard in this book.

I've attached some pages where he talks about free float. He seems to like using fruity terms for things...he coins the term momenergy in the book as well.

<cringe>
Yeah - he is trying to use evocative terms to describe things which are, let's face it, tricky to imagine.

Well, the Earth does not pass the Sun to the extent where it can get incinerated like a Comet.

Of course - though a comet that "passes" the Sun presumably does not get close enough to be incinerated either... which is what we are talking about. A comet may pass at any distance and survive. Haley's comet gets as close as 0.6AU from the Sun - farther out than Mercury - for example.

All comets that have a tail get close enough to boil away though. That's what makes the tail.

My book describes the curvature of spacetime in a similar manner to a heavy person standing on a trampoline. The persons mass creates a positive curvature near him and a negative curvature outside of the depression he creates. For this reason, I assumed that spacetime must be positively curved as you move towards to Sun.

That sounds problematical beyond the usual problems with the rubber-sheet analogy. Have you looked at a trampoline? The center of curvature is below the mat everywhere when someone is standing in the middle. Where does it curve the other way? At most the trampoline becomes flat.

Also see:
https://www.physicsforums.com/showthread.php?t=286926

 

[enceladus_]

Haha, I am a little more than 1/2 through it, and I have to agree with you. He does try too hard and his creation of new terms borders on indulgent. Get what you pay for I guess.

That sounds problematical beyond the usual problems with the rubber-sheet analogy. Have you looked at a trampoline? The center of curvature is below the mat everywhere when someone is standing in the middle. Where does it curve the other way? At most the trampoline becomes flat.

You're right. On second thought, that analogy does become problematic...

 

[Simon Bridge]

Well it's accessible.
Treat it as a fun read :)