Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: ukmicky on 13/10/2006 23:03:05
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Question please if i may if anyone knowS.
How far away from the gravitational influence of the earth would the moon have to drift for it to stop orbiting the earth and become a planet orbiting the sun.
Yours
Michael
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quote:
Originally posted by ukmicky
Question please if i may if anyone knowS.
How far away from the gravitational influence of the earth would the moon have to drift for it to stop orbiting the earth and become a planet orbiting the sun.
I don't know and the computations are not very easy. To make them even in an approximate way, however, there is need to know in which orbit you want the moon: in the same earth orbit or another one?
I am assuming you could take the moon and position it in the orbit you want with the required speed.
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we'll find out once the moon gets far enough away.
problem is that there are no clear cut methods to solve three-body gravitation without numerical simulations.
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Would it not be at the distance of one of the Lagrange point between the Earth and the Sun?
Since the Lagrange points are supposed to be points where the gravitational pull of two objects balance out, then would it not make sense to assume that one side of one the Lagrange point would have one body pulling the moon, while on the other side, the other body might pull the moon.
Then again, I would imagine there are also possible orbits where both bodies are orbited (e.g. a figure of 8 is the path followed by the moon, or alternatively an asymmetric elliptical orbit where the Earth forms one foci and the Sun the other).
George
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http://en.wikipedia.org/wiki/3753_Cruithne
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3753 Cruithne is an asteroid in orbit around the Sun. Due to its unusual orbit relative to that of the Earth, it is sometimes incorrectly described as Earth's second moon.
Cruithne is approximately 5 km in diameter, and its closest approach to Earth is approximately 30 times the separation between Earth and the Moon (12 Gm or million kilometres). Although Cruithne's orbit is not thought to be stable over the long term, calculations by Wiegart and Innanen showed that it has likely been in sync with Earth's orbit for a long time. There is no danger of a collision with Earth for millions of years, if ever. Cruithne is not visible to the naked eye at any point in its orbit.
Cruithne is in a normal elliptic orbit around the Sun. However, because its period of revolution around the Sun is almost exactly equal to that of the Earth, they appear to "follow" each other in their paths around the Sun. Cruithne's distance from the Sun and orbital speed vary a lot more than the Earth's, so from our point of view Cruithne actually follows a kidney bean-shaped horseshoe orbit ahead of the earth, taking slightly less than one year to complete a circuit of the "bean". Because it takes slightly less than a year, the Earth "falls behind" the bean a little more each year, and so from our point of view, the circuit is not quite closed, but rather like a spiral loop that moves slowly away from the Earth.
After many years, the Earth has fallen behind far enough that Cruithne is now actually "catching up" on the Earth from "behind". When it eventually does catch up, Cruithne will make a series of annual close approaches to the Earth, and gravitationally exchange orbital energy with Earth; this will alter Cruithne's orbit by a little over half a million kilometres (whilst Earth's orbit is altered by about 1.3 centimetres) so that its period of revolution around the Sun is now slightly more than a year. The kidney bean now starts to migrate away from the Earth again in the opposite direction — instead of the Earth "falling behind" the bean, the Earth is now "pulling away from" the bean. The next such series of close approaches will be centred around the year 2292 — in July of that year, Cruithne will approach Earth to about 12.5 million km.
After 380 to 390 years or so, the kidney-bean-shaped orbit approaches Earth again from the other side, and the Earth, once more, alters the orbit of Cruithne so that its period of revolution around the Sun is again slightly less than a year (this last happened with a series of close approaches centred on 1902, and will next happen with a series centred on 2676). The pattern then repeats itself.
George
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Another someone has just introduced me to Lagrange points. The points are positions at which the influence of gravity from two large bodies act equally on a third to hold it still. There are five points that are subject to those unusual conditions. The first 3 positions are kind of fussy and its difficult for objects held there to remain in place. The position of L1 is intuitive. L2 and L3 are less so, but I'll buy it.
When I'm looking at something new like this, I can almost hear a gear clunk onto place just before I understand. I'm totally baffled by the oddball location of L4 and L5.
(https://www.thenakedscientists.com/forum/proxy.php?request=http%3A%2F%2Fi16.photobucket.com%2Falbums%2Fb11%2Fjysk%2FLagrangepoints1.jpg&hash=b9066e879c056aca64cc08c6a01acee7)
L4 and L5 seem not to belong. It turns out, they are the most stable of the five positions. They hold two substantial asteroid clusters about 60 degrees behind and ahead of Jupiter.
Is there someone on this forum (or maybe another someone) who understands the logic of L4 and L5, and can describe the mechanism to me?
I’ve been developing a model entirely dependent on gravity and have struggled with a 30 degree offset anomaly that I can not explain. I’m anxious to understand the logic of L4 and L5.
Mike
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To understand the logic of those points it's not very easy because you have to draw all force vectors included the centrifugal force due to the motion of the object in the orbit at that point.
When you have drawn all these vectors, you displace the object a little and you draw again all vectors. You will see that the resultant force vector changes very little (less than the change in position) and this makes the object in a state of equilibrium at those points, which is stable only for points L4 and L5. It means that displacing the object a little, the resultant force makes it come back to its original position.
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Until recently there was only one general stable solution to the problem three bodies interacting gravitationally. That is when the three randomly sized bodies were orbiting in circles around their common centre of mass arranged at the vertices of an equilateral triangle L4 and l5 reperesent these points for the earth sun system. small deviations from the ideal position will cause the bodies to perform "orbits" around the ideal position that will remain stable.
The terrible truth is that almost every condition of more than two bodies interacting gravitiationally is potentially unstable and eventually one or more of the bodies will collide or be ejected from the system. There are some configurations, like our solar system, where there are long periods of metastability in multi body interactions but eventually they are likely to fall apart when an extreme event occurs.
You can try this out on a really interesting java applet that I wil try to find that shows another stable three body solution that has been found recently.
cant find the applet I was thinkig about but this looks quite good
http://astro.u-strasbg.fr/~koppen/body/ThreeBodyHelp.html
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