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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: Wed Aug 20, 2008 7:16 pm
I really don't want to revive this thread actually - I no way want to do that which is valid for one or two other threads also.

But I couldn't resist :D because of the spirally going discussion about the term "spiral" or "spirally:
Quote:
The researchers chose to sacrifice some detail in their simulation in order to model planetary systems from start to finish. They hope to extend their hybrid model approach so that they can eventually model planets spiraling all the way into the central star. Currently, the simulation cannot track such planets beyond a certain point.
.

Source: "Study: All Planets Are Born in Killer Environments" ( www.space.com/scienceastronomy/080807-p ... ution.html )

The article refers to
Quote:
Edward Thommes, a physicist at the University of Guelph in Ontario, Canada


Of course the environment considered and modelled is quite different to what was discussed in this thread.

Please let's keep this thread limited to such quotes and not continue the discussion experienced here.



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


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Post    Posted on: Thu Aug 21, 2008 3:10 am
Just can't let if go, huh? I know. It eats away at me too. But we are never going to find any common ground on this question, so you just have to let it go.


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Post Re:   Posted on: Wed Aug 05, 2009 2:44 pm
Yes, I wasn't considering Earth's eliptical orbit. In a perfectly circular orbit, though, as an object nears the sun, the gravity of the object on the sun increases while the acceleration of the object away from the sun doesn't. The closer an object is to another object, the more gravity there is, right?

campbelp2002 wrote:
SuperShuki wrote:
The reason that the earth isn't getting closer to the sun (i.e., that it isn't moving) is that the forces are equal. But the fact that there is a countervailing force to that of gravity (i.e. inertia) does not mean that the earth is moving in respect to the sun. Since there is no change in location, the earth does not move.
To directly answer your question, therefore: yes, if there were no other forces present, gravity would cause the two objects to come crashing together. But the lack of other objects doesn't mean that there are no other forces.

Dude, what’s your sign? I am a Leo. That means that the Sun is seen in the constellation of Leo on my birthday. If you are an Aries then the Sun is seen in the constellation of Aries on your birthday. The sun moves, as seen from the Earth, against the background of fixed stars. You are assuming that you can ignore the stars and look only at the Sun from the Earth in such a way that it seems to stand still in the sky, and that the apparent lack of motion can be assumed to be the same as a real lack of motion. This does not work for the following reason.
To make the Sun stand still in Earth's sky you need to turn the direction you are looking at just the same speed as Earth orbits the Sun, but in the opposite direction. You have in fact placed yourself in a rotating coordinate system. I am looking at the Sun-Earth system from an inertial coordinate system that is not rotating or accelerating. In my inertial coordinate system, the Sun is at the origin and the Earth moves in X and Y. (Or if you prefer polar coordinates R and Theta.) The problem with a rotating coordinate system is the virtual forces (centrifugal and coriolis) that go along with it. These forces can only be calculated from the rotation rate, so the rate that the Earth revolves around the Sun is extremely important. In addition, you are making another common but invalid simplifying assumption, that the Earth’s elliptical orbit is close enough to a perfect circle to be considered as such. From the real Earth, the Sun never stands still in the sky. It gets farther and closer as Earth moves from aphelion to perihelion. It also speeds up and slows down so that your coordinate system is rotating at a variable speed. And the only way to know that speed is to do a calculation in an inertial coordinate system.
So if you throw a rock at the Sun, it behaves just like the Earth does. It gets a little closer to the Sun, stops, moves back from the Sun, stops again, moves toward the Sun again, and so on for ever. It is a complex interplay of centrifugal force, coriolis force, and the variable rotation rate of your rotating coordinate system.
To see what will really happen if you throw a rock at the Sun, use my orbit simulator:
http://home.austin.rr.com/campbelp/orbit.html
First, click the drop button to release a “dot” from the rocket. At first the dot will be hidden behind the rocket. Consider this dot as the Earth, since the rocket starts in an orbit identical to the Earth’s orbit around the sun. Then enter 1.0g and 100.0 Sec. in the thrust controls. Turn the rocket to point at the Sun and click the Fire button. At first nothing seems to change because the rocket is still right on top of and hiding the dot. After about a quarter of an orbit the two will separate enough to see them separately. Remember, the dot represents the Earth and the rocket is the object being thrown at the Sun.

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Post Re:   Posted on: Wed Aug 05, 2009 3:53 pm
Sev wrote:
Hence the circular motion equation - mv^2/r = GM1M2/r^2
Without the velocity, they would not balance. And if there is a difference in velocity, they have to be moving.


So G changes directly with r^2. But why? What is accelerating the Earth? Where is the energy to change the speed coming from?

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Post Re: Orbital Mechanics   Posted on: Wed Aug 05, 2009 4:52 pm
you really gotta do that? start back up a year old thread?

but regardless, you're asking a "why?" question about gravity on a space forum. this is somewhat analogous to asking a "why?" question about god on a religion forum. i don't care what responses follow mine, none of them will be good or accurate.

EDIT: not entirely true, any reply that doesn't attempt to answer the question is good.

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Post Re: Orbital Mechanics   Posted on: Wed Aug 05, 2009 9:12 pm
Science doesn't delve into the supernatural. And it's really a what question. And I don't like to drop a subject when it still bugs me. And many times a why? question about God on a religion forum is appropriate. If I understand what you mean by a "why" question.

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Post Re: Re:   Posted on: Thu Aug 06, 2009 2:16 am
SuperShuki wrote:
Sev wrote:
Hence the circular motion equation - mv^2/r = GM1M2/r^2
Without the velocity, they would not balance. And if there is a difference in velocity, they have to be moving.


So G changes directly with r^2. But why? What is accelerating the Earth? Where is the energy to change the speed coming from?



Velocity is a vector, with a magnitude and a direction. The Earth is in an elliptical orbit about the Sun. As it moves along this orbit, two things are basically happening.

1: As the Earth moves from farther out to closer in, it is in effect falling, so it accelerates, or its velocity magnitude increases. As it moves back again, it is climbing like a thrown ball, so it decelerates, or its velocity magnitude decreases.

2: As the Earth follows its orbit, its direction changes, therefore its vector direction changes.

So, the Earth's velocity is actually changing in two ways constantly. Well, its not quite that simple, but I hope you get what I've said.

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Post Re: Orbital Mechanics   Posted on: Thu Aug 06, 2009 8:35 am
But what about an object that is in a perfectly circular orbit around the sun? Does it accelerate? Is a changing direction vector acceleration?

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Post Re: Orbital Mechanics   Posted on: Thu Aug 06, 2009 12:14 pm
SuperShuki wrote:
But what about an object that is in a perfectly circular orbit around the sun? Does it accelerate? Is a changing direction vector acceleration?



Acceleration is a change in the velocity vector. In a circular orbit, the direction component is changing, so, yes, there is an acceleration.

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Post Re: Orbital Mechanics   Posted on: Thu Aug 06, 2009 4:45 pm
I highly recommend taking a class in intermediate level mechanics as you will learn how to solve all sorts of nifty gravitational problems. Of particular elegance is the Hamiltonian/Eulerian method of finding an exact orbit using the calculus of variations. That's how you can exactly solve for the Lagrange points in a 3-body system (pretty sure you can't actually exactly solve any system beyond 3-body but whatever). Hard problem though, I haven't taken the time to solve it myself :(.

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