How objects start revolving in the space

[RohitRmB]

In uniform circular motion we need velocity and centripetal acceleration.
so if a object is placed in space around the Earth then as Earth pull it down, it must fall straight way on the surface, if its given some velocity then it must fall following a spiral trajectory.
so my question is, if a large amount of debris in the vicinity of a planet is attracted by the planet, then it should fall into it directly, why it starts revolving around it?

 

[Nessdude14]

The "centripetal acceleration" you mention in the case of an orbit around a planet is caused by the gravitational pull of the planet. Everything that passes by Earth has some initial velocity, so anything that collides with the Earth will make this spiral trajectory that you mentioned, to some extent. As long as it doesn't come too close and its velocity is right, it will be able to escape Earth's pull and the only effect from Earth's gravity would be to bend the objects trajectory slightly. If the object were to pass by the Earth at exactly the right velocity and distance, it would go into permanent orbit around the earth.

 

[RohitRmB]

but if the scenario is, there is a large enough hydrogen cloud which for millions of years form a star, then the debris which is around the star is attracted by it, so it moves towards the star, so here the velocity we have is radially towards the star, so the debris must fall directly into the star.
for uniform circular motion we need velocity which is perpendicular to the centripetal force(here the gravitational pull)

 

[Jakeus314]

Don't assume that all of this hydrogen gas, or space junk is just standing still before it begins this fall.

 

[K^2]

First of all, with sole exception of falling onto a black hole, an object will never spiral down onto another. An object in gravitational field of a planet/star, can only have one of 3 possible trajectories: ellipse, parabola, or hyperbola. All conic sections. Of course, anyone of these can intersect planet/star surface, in which case, you have an impact.

With that out of the way, what you need to have orbital motion is not velocity, but rather angular momentum. Things can speed up or slow down in any direction, but angular velocity is conserved. The thing is, though, that for two objects that start very, very far apart, you can get a lot of angular momentum from very little tangential velocity, as L = r x v. If r is large enough, v can be very small. And that's your starting point. You start out with hydrogen gas and debris spread over very large distance. Just a little bit of relative movement, from pretty much whatever cause, would result in fairly large angular momentum of the system.

As gravity pulls things together, the r decreases, meaning that v has to increase for the angular momentum to stay constant. And so it does. As things start to move faster and faster, they tend to collide and interact via gravity with each other. So the things that aren't rotating with everything else will eventually end up colliding with things that are. And so you end up with large chunk of mass in the center, forming the star, a bunch of matter moving around it in fairly circular orbits, making accretion disk and, eventually, planets, and then some fraction of stuff keeps moving every which way, forming comets and other space debris.

 

[RohitRmB]

i don't get the conservation of angular momentum stuff,
even if the debris is in some kind of motion(that is not necessarily perpendicular to the centre of gravity) then when gravity attracts the debris how would it speed up?
and even if it does then it would do that without changing its direction
can u explain how does the conservation of angular momentum goes here?

 

[GarageDweller]

http://en.wikipedia.org/wiki/Effective_potential

The angular momentum L is defined as
L=p x r, the cross product between the position vector and the objects linear momentum vector.
So as long as p is non zero and not parallel to r, the trajectory will not be radial.

 

[GarageDweller]

i don't get the conservation of angular momentum stuff,
even if the debris is in some kind of motion(that is not necessarily perpendicular to the centre of gravity) then when gravity attracts the debris how would it speed up?
and even if it does then it would do that without changing its direction
can u explain how does the conservation of angular momentum goes here?

Edit: Please use proper grammar, pain to read.

 

[K^2]

i don't get the conservation of angular momentum stuff

That's unfortunate, as it's a much easier way to understand orbital motion.

For a single object, it's fairly easy to see the kinematics of it. Suppose, I have a star, and I place a comet very, very far away from it. Now, rather than placing it completely still, I give it just the tiniest nudge in perpendicular direction.

Now the comet begins to fall onto the star. Yes, right now it only picks up radial velocity, but it also drifts a little in perpendicular direction due to the initial nudge. It drifts slowly, but it has time, because it started out rather far away, so the fall is going to take a long time.

Eventually, it reaches the star. But it doesn't fall on it, because it has drifted far enough out to miss it. Now, it's moving rather rapidly, and needs to fall in the direction opposite to that of the initial nudge. It does so, picking up yet more speed, and attaining its lowest point on the side opposite to the initial placement. Now it's moving really fast in direction opposite to the initial nudge. Here it's moving way too fast for gravity to hold it, and it starts moving away. The second half of the orbit is the symmetric opposite of the first half. At the end of that half, the comet will end up at its initial position moving with velocity of initial nudge, ready to repeat all of this.

Now, look back at the lowest point in the trajectory. Here, the comet is moving really, really fast in direction perpendicular to radial. That velocity was picked up entirely due to gravity and the initial nudge we gave it. It's also higher than velocity required to settle into circular orbit. But imagine that down there it collided with something. Maybe an asteroid, or a smaller comet going in different direction. This will result in loss of velocity. A single collision probably won't settle it into a circular orbit right away, but it can bring down the aphelion (highest point in orbit around a star) quite a bit. A side effect is that the comet will be moving much faster than the initial nudge at the new aphelion.

 

[phinds]

Edit: Please use proper grammar, pain to read.

This is obviously someone who does not have English as a first language and I have to say, he speaks English WAY better than I speak whatever his native language is.

 

[GarageDweller]

i don't get the conservation of angular momentum stuff,
even if the debris is in some kind of motion(that is not necessarily perpendicular to the centre of gravity) then when gravity attracts the debris how would it speed up?
and even if it does then it would do that without changing its direction
can u explain how does the conservation of angular momentum goes here?

Well if you think about it, angular momentum is always defined about some point.
If that point is defined to be the source of the force, then the attraction force will always be parallel to the position vector, hence torque will be zero (assuming no other forces act on the body), since torque is the derivative of angular momentum, then angular momentum must be constant.

 

[voko]

An object in gravitational field of a planet/star, can only have one of 3 possible trajectories: ellipse, parabola, or hyperbola.

This is true only in Newtonian gravity and only in a very symetrical case. Mercury, for example, has been known for centuries to have an orbit different from those. What is true is that except for very massive objects, there are trajectories that stay at some finite distance from the central body infinitely.

 

[GarageDweller]

I think many more orbits are allowed in Newtonian gravity, are knot trajectories GR only?

 

[voko]

Keplerian motion (conic sections) occurs only in the idealized situation of point masses. With real gravitating bodies, their gravitational field is not symmetric, plus it changes because of the rotation of the bodies. The resultant motion can be quite complex, but it is still frequently represented as a modified Keplerian solution. This is done by making constant parameters of a Keplerian solution functions of time.

 

[RohitRmB]

Thanks K^2 and garagedweller, i understood the action of angular momentum and the comet example, but i am still confused about the formation of planets in our solar system?
books and documentaries just tell you what happened in our early solar system but they do not answer, why did that happen!

 

[RohitRmB]

This is obviously someone who does not have English as a first language and I have to say, he speaks English WAY better than I speak whatever his native language is.

thanks for understanding

 

[voko]

http://en.wikipedia.org/wiki/Formation_and_evolution_of_the_Solar_System

 

[RohitRmB]

http://en.wikipedia.org/wiki/Formation_and_evolution_of_the_Solar_System

Thanks voko, i will read the link and return to this thread if there is any further confusion in my mind or if i need any help in understanding anything written there