Universal Gravitation and orbit

[Gabby Jay]

This question may be a simple one, but the answer will have lots of implications that I'll follow up on. I'm trying to steer clear of all the jargin though since for the most part it's pretty useless. Say there is an object B orbiting an object A of the same size. What happens when an object C of the same size as A and B is introduced? Assume for now that objects A and C are stationary.

 

[Mentz114]

Not a lot will happen. The stability of the system will be disturbed and the orbiting body will probably fly off into space and be followed by C. It depends crucially on the physical parameters of the system. In other words the spatial position and velocities of the three bodies.

You can use Lagrange's equations to solve this. Just write down the lagrangian and do a bit of differentiation and you get some ODE's which might be numerically solvable.

Sorry about the 'jargin' but you can't do physics without it.

 

[Gabby Jay]

Alright, but the only object with a velocity is object B. Say the distance between A and B is x and between A and C is 2x. It makes sense that when object C is introduced object B will be released out of orbit in some direction, which is determined by the point at which object C is introduced in relation to B. However, would objects A and C stay stationary, be drawn together, or go in different directions or is this also merely a matter of spatial relations of C and B when C is introduced? Is it possible for any of those scenarios to happen?

I guess one of my bigger questions is that it seems extremely implausable that an object will go into orbit considering all of the matter around it, assuming that the universe is finite. If I understand it correctly, an object needs to be traveling at a velocity that is perfect in relation to the distance between the two objects and also the masses of each object. Why wouldn't the surrounding matter always throw off the course of an orbiting object taking into account that these conditions must be so perfect?

 

[ZapperZ]

You may want to consider your premise of "... an object B orbiting an object A of the same size.."

If by "same size" you mean having the same mass, then you might want to look up the definition of "center of mass" and why using that knowledge, your original premise is faulty.

Zz.

 

[Mentz114]

Yes, it is unlikely that one body will capture another in orbit, unless one is very much massier than the other.
Most of the matter that we can see or detect in the cosmos is in orbit around something, or falling towards something. Our galaxy has 7 or 8 much smaller ones whizzing around it, for instance, while the whole caboodle including some nearby galaxies is falling towards something we can't see but must have a lot of mass.

Astronomers use the wobbles in predicted paths to infer the presence of unseen masses, on a daily basis.

A curious but undeniable fact also, is that if we did not possesses exactly 3 spatial degress of freedom, stable orbits would be impossible.

Make you think, doesn't it ?

 

[Gabby Jay]

Yeah definitely, it all makes me think. I've always had a strong interest in the universe, but since I hardly have any background in physics I really have to rack my brain when I can't seem to come up with answers. So I appreciate the help, even though these are simple questions!

I'll be sure to have more to come...