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Author Topic: Is the Coriolis Effect responsible for planetary orbits rather than collisions?  (Read 6512 times)

Offline CliffordK

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I suppose this will sound a little DENSE   [xx(]

I have never understood well why two bodies tend towards orbiting each other rather than colliding.

It would seem as if the gravity would suck them towards the center of the bodies, and cause far more collisions than one actually experiences. 

However, this evening it dawned on me...  the Coriolis Effect essentially means that your target is always moving.  So, while gravity sucks the object towards the center of mass.  The target is actually moving, for example the earth orbiting around the sun.  So, at some point the movement exceeds the ability to pull the object towards the center, and the two miss...  or start orbiting.  I suppose there would be more complex equations to demonstrate this.

Of course, in our solar system there are complex interactions between Saturn, Jupiter, Mars, Earth, Venus, and the Sun (as well as other planets)

« Last Edit: 17/01/2011 08:12:31 by CliffordK »


 

Offline JP

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I think you're on the right track, but the Coriolis effect refers to what is really straight motion appearing curved to you because you're in an accelerating reference frame.  It's an effect of your point of view, not something fundamental in the motions of planets.  If you stepped outside of the planets in our solar system and looked down, you'd see motion with no Coriolis effect in it.  It's when you look out from our point of view on the accelerating earth that you get this effect.

Anyway, things in orbit miss each other because there is some motion perpendicular to the gravity pulling them together, like you show in the drawing.
 

Offline Eric A. Taylor

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What you're describing here is not the Corollas effect, rather it has to do with falling. Take an object, something soft if you're inside (like a rolled up pair of socks) and toss it. It will trace out a curved line, called a parabola. A parabola is just an "orbit" that hit's the surface of the earth. If you throw the socks fast enough, and nothing slows them down the curve of the parabola will match the curve of the Earth and they will continue all the way around and hit you in the back of the head. I'd duck if I were you. Even though they are soft they are going really fast. Throw the socks even harder and the curve of the parabola will be less than the Earth's and they will spiral higher and higher until they escape Earth all together.

Now imagine you're the captain of a battleship. You're at the equator and the enemy is several thousand miles north at latitude 45 (Battleship guns can't fire that far, but here it makes the math easier, and I suck at math).

Though you're stationary in relation to the sea, (as is the enemy) you are moving from west to east at a little more than 1000 miles per hour. The enemy, who's also stationary in relation to the sea, is also moving west to east but he's only going 500 miles per hour. You take aim at the ship, or rather adjust your guns to hit where he is and fire. The velocity (speed and direction) of the shell is not due north even though you fired with your gun pointed at 360 degrees. Your west/east speed is still in the shell that is now headed down range, so your shell, velocity is really north/west relative to the sea. At first there is not much "west" in the velocity but as the shell moves north the sea is slowing down in the east/west direction but velocity of the shell is the same, so as seen relive to the sea it inscribes a circle.

An odd counter intuitive effect of orbital mechanics that should be mentioned. If you wish to go faster (Say to catch up with the ISS you need to hit the "breaks". By performing a burn opposite to your velocity you will drop to a lower orbit and speed up. A higher orbit will be slower.
 

Offline Soul Surfer

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Clifford K the way to describe the way two gravitating bodies approach each other and interact over and above the direct inverse square attraction is the conservation of angular momentum.  If two bodies are initially moving independently at some long distance apart (so that gravitational attraction is negligible) and then approach each other so that their mutual gravity starts to pull them together the attractive force is along the line joining their centres of gravity together.  It is however very unlikely that that their initial motions were both exactly along this line.  Their original motions can therefore be resolved into two component velocities one along the line of their motion and one perpendicular to it.  This second velocity coupled with their distance apart defines the angular momentum shared by these two attracting bodies.  the centre of motion and separation is defined by the centre of gravity of both bodies taken together.  This angular momentum defines how close the bodies will get at their closest approach.  Because as they get closer this cross track velocity increases to conserve the angular momentum, that is, when the distance has halved the cross track velocity has doubled.  If the closest approach distance is greater than the combined radii of the two bodies they will miss each other.  This is why it is extremely difficult to fall into a black hole.

With only two bodies present the resulting orbit is hyperbolic or at best parabolic and the two bodies will approach each other only once and pass on their way with their directions and velocities changed.  it requires some other effect to slow the bodies down to turn the open orbits into closed elliptical ones.  This could either be the gravity of another body or retardation caused by hitting gas and dust.
« Last Edit: 16/01/2011 22:38:00 by Soul Surfer »
 

Offline CliffordK

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Thanks for the responses.

Obviously nothing in space is not moving...  so everything begins with an approach vector, or any two bodies have different vectors.

The question on whether it is the coriolis effect or something else...  One of the most common descriptions of the coriolis effect is when rotating on a merry-go-round, apparently it is difficult to throw a ball the the person across from oneself as it always appears to be a curveball...  but would be better described as being a ball thrown at, say the slide across from oneself, except one's partner rotates so that they are no longer in front of the slide (I haven't actually tried this).

In this case, the gravity actually does curve the approach vector towards the object...  but would tend to bring it around behind the object.

This is unlike playing ball on a train at a constant velocity where everything has a constant forward momentum.

This interaction around a single central body would also force everything to orbit essentially in a plane, and thus would require all planar galaxies to have a relative movement in their own plane.

It would also force any binary galaxies to also exist in a single plane.

Thus, you could also conclude that a paper such as this one has a huge miscalculation somewhere (or they are describing a very young system).

http://www.redorbit.com/images/gallery/galaxies/paired_galaxies_ngc7332_type_s0_on_the_right_with_its/112/133/index.html

As far as running into a black hole.
That would actually be an interesting problem.
Assuming the black hole is tooling through space in more or less a straight line.  Then you could likely approach it from either straight ahead, or straight behind which would be relatively velocity independent.  Otherwise, one could define a number of approach vectors that would lead to the same two points which would be velocity dependent (of course, using the term "point" loosely as it would not regress into a single point).

And...  a "super-massive" black hole would tend to collect clutter around it which would eventually block any direct approaches.
 

Offline JP

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The question on whether it is the coriolis effect or something else...  One of the most common descriptions of the coriolis effect is when rotating on a merry-go-round, apparently it is difficult to throw a ball the the person across from oneself as it always appears to be a curveball...  but would be better described as being a ball thrown at, say the slide across from oneself, except one's partner rotates so that they are no longer in front of the slide (I haven't actually tried this).

In this case, the gravity actually does curve the approach vector towards the object...  but would tend to bring it around behind the object.

You're right about the physics, but the curving of the paths is not due to the Coriolis effect in the case of gravity.  Coriolis is the apparent curving of a path due to the fact that you're accelerating.  The ball you throw from the merry go round isn't a curve ball, but it appears to be from your point of view since you're rotating (a constant centripetal acceleration).

In the case of gravity, the path is physically curved due to gravity.  It's not an apparent curvature due to your motion, so it's not the Coriolis effect. 

One way you could check this is to ask a stationary (non-accelerating) observer to look at both situations.  In the case of the merry-go-round, they'll tell you the ball flies in a straight line, indicating that the curve you see is due to the Coriolis effect.  If you sent a probe out into space and had it stop accelerating, it would still see the orbiting objects moving along curved paths, indicating that it's a real force, not the Coriolis effect.
« Last Edit: 17/01/2011 05:38:54 by JP »
 

Offline Soul Surfer

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You just do not seem to be reading or trying to understand what I have said above!  I have described precisely how two gravitating bodies approach each other and interact. 

You also just do not seem to appreciate the velocities and relative velocities of things flying around in space.  consider this a "typical" velocity of any small body moving through space near a planet star or in a galaxy is the velocity of a circular orbit around the centre of that planet star or galaxy  this is around 5 miles per second for things reasonably close to the earth  18 miles per second for the earth's orbit round the sun and 220 miles per second for the sun's orbit round the galaxy. On a statistical basis typical encounter velocities are very unlikely to be slow.  the typical encounter velocity of a spacecraft with another small particle of space debris in orbit around the earth is faster than a rifle bullet!  It takes a very great deal of care and precision for one spacecraft to approach another at low speed

Bearing this in mind and noting that these velocities are in approximately random directions.  If our sun was replaced by a black hole of the same mass it would be about one mile across and if an object at the position of the earths orbit was heading towards it it would be going at a velocity around 18-36 miles per second.  if this velocity was not directed precisely at the 1 mile diameter object it would miss and orbit around or go away.  The resolved velocity across the path that would prevent the object hitting the black hole is very considerably less than one inch per second at the distance of the earth's orbit.
 

Offline Eric A. Taylor

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Thanks for the responses.

Obviously nothing in space is not moving...  so everything begins with an approach vector, or any two bodies have different vectors.

The question on whether it is the coriolis effect or something else...  One of the most common descriptions of the coriolis effect is when rotating on a merry-go-round, apparently it is difficult to throw a ball the the person across from oneself as it always appears to be a curveball...  but would be better described as being a ball thrown at, say the slide across from oneself, except one's partner rotates so that they are no longer in front of the slide (I haven't actually tried this).

In this case, the gravity actually does curve the approach vector towards the object...  but would tend to bring it around behind the object.

This is unlike playing ball on a train at a constant velocity where everything has a constant forward momentum.

This interaction around a single central body would also force everything to orbit essentially in a plane, and thus would require all planar galaxies to have a relative movement in their own plane.

It would also force any binary galaxies to also exist in a single plane.

Thus, you could also conclude that a paper such as this one has a huge miscalculation somewhere (or they are describing a very young system).

http://www.redorbit.com/images/gallery/galaxies/paired_galaxies_ngc7332_type_s0_on_the_right_with_its/112/133/index.html

As far as running into a black hole.
That would actually be an interesting problem.
Assuming the black hole is tooling through space in more or less a straight line.  Then you could likely approach it from either straight ahead, or straight behind which would be relatively velocity independent.  Otherwise, one could define a number of approach vectors that would lead to the same two points which would be velocity dependent (of course, using the term "point" loosely as it would not regress into a single point).

And...  a "super-massive" black hole would tend to collect clutter around it which would eventually block any direct approaches.

To say nothing in space is stationary is a bit wrong. There is no such thing as "absolute space". For movement to have meaning you need a reference point, some kind of benchmark to compare your speed to.

Imagine space as containing only one thing, you. In such a place there is nothing you are moving towards or away from, thus motion has no meaning. So when we say a car is moving at 80 MPH the reference is the road (or Earth). But how fast is it moving relative to the sun? or the Milky Way, or Andromeda.
 

Offline Soul Surfer

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CliffordK  your understanding of how multiple gravitating bodies interact is basically flawed.  There is absolutely no tendency for isolated groups of bodies to interacting ONLY BY GRAVITY to form a plane.  it is only by non linear interactions i.e. collisions between these bodies that the planar configuration slowly gets established because for colliding bodies this minimises the number of collisions.  This can be seen easily in the spherical symmetry of globular clusters and large elliptical galaxies.  The stars almost never collide and interact only gravitationally and so as they have angular momenta in all sorts of different directions from when they were formed and interact only gravitationally the objects are spherical even though they are very ancient and have had plenty of time to stabilise.
 

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