What is the equation of the orbits of things in space?

[MonkeyKid]

I appologize for any grammar or spelling errors. English is not my first language. I do my best.

Given 2 objects in space, is there an equation that explains that one will, naturally and without any interference other than gravity, assume an orbital movement around the other? And does the same equation (or is there another for that end) describes the precise orbit? describing things like the shape of the orbit, distance and velocity of the orbiting body at any given point of the orbit, etc

On a related subject, why are orbits so common? I'd assume (probably naively) that the most common form of gravitational interaction would be the less massive object being attracted by the more massive object in a trajectory that would lead to a collision. Why are there so many orbital behaviours in the universe, like pairs of stars, stars and their planets, planets and their satelites (including the man made ones here on Earth) and so on, instead of things just falling into other more massive things?

 

[mfb]

Given 2 objects in space, is there an equation that explains that one will, naturally and without any interference other than gravity, assume an orbital movement around the other?

They do not have to orbit each other.

There are three options for the long-term development:
- the objects fly apart forever
- the objects orbit each other forever
- the objects crash into each other after a while

In the special case of masses with a spherical symmetry, neglecting relativistic corrections and if you know the initial conditions, there is an exact solution for the motion of the particles, and it is easy to predict how they will move - including orbital parameters. This is called Kepler problem (and it is solved).

On a related subject, why are orbits so common? I'd assume (probably naively) that the most common form of gravitational interaction would be the less massive object being attracted by the more massive object in a trajectory that would lead to a collision.

Astronomical distances are huge, and objects are tiny. A small initial motion (in non-radial direction) is sufficient to avoid a collision.

"things just falling into other more massive things" happens as well - many small objects hit Earth all the time. The more massive collisions were more frequent in the early solar system, now most objects have orbits where they stay far away from each other (otherwise the collision would have happened long ago).

 

[MonkeyKid]

I got it, thank you for such a clear explanation. Most of the big bodies that were bound to collide have already collided by now. It makes perfect sense and I don't know how it didn't occur to me. It's probably because I'm still not used to see the universe as so very old as it really is, blame it on church's sunday school lol.

As to the Kepler problem, I'll check it out. I hope the mathematics are not too far ahead of my skills. Even though I'm secretly interested in things like math and physics and because of this interest I'm far ahead than what I'm taught at school, I'm still a long way from understanding calculus, non-euclidean spaces, and all those other "mythematical" creatures.

Again, thank you.