# What if we throw two solid objects parallel in space? Do those two objects have any chance to collide with each other?

What will happen if just throw two solid objects (for example, solid footballs) parallel in outer space and those two objects are floating and going far away in the universe.

So is there any possibility in which those two football-size solid objects can collide with each other, or will they will float parallel for an infinite amount of time in the universe?

I'm considering gravity also, and I find that other stars's and planets's gravitational pull can pull them into their gravitational fields and change their direction.

But what if those two objects will never get destroyed by luck? Could those will collide each other?

• Are the objects moving at the same velocity as one another? Jan 10, 2016 at 17:58
• They will have a gravitational impact on each other, so yes.
– user21
Jan 10, 2016 at 18:35
• Ignoring small variations in the gravitational field that earnric correctly points out, I think it's possible that if the objects were small enough or far enough away that the expansion of space would be greater than the gravitational attraction between them? So they might, collide in a theoretical empty space scenario, they might not. Jan 11, 2016 at 5:05

It all depends on the direction you "throw them" and the space-time they find themselves in.

Case 1 - in a perfectly empty universe (other than your footballs) the two would eventually collide. It doesn't matter what initial velocity you give them. The only thing that matters is there separation and their mass. You can just use Newtonian gravity to compute the two footballs' acceleration toward one another -- and hence the time for them to collide.

Such an 'empty' universe as above is called a Minkowsky space-time.

If you put these footballs on a trajectory into our real universe, well we know that space-time is curved by the matter/energy (just energy density in general) that occupies it. Hence a trajectory that starts out parallel will invariably end up "not parallel". The balls will either collide or diverge depending on the geometry of the space-time they find themselves in. The "geometry of the space-time" is (again) completely dependent on the distribution of "stuff" (matter/energy) in the universe as related to the location of the footballs.

In short, the footballs will follow the geometry of the space-time they find themselves in. That geometry (in our real universe) means they will not remain on parallel paths.

• can't they be parallel but have different velocities? Jan 10, 2016 at 22:18
• In a real universe they will have different velocities because of the different space-time they encounter. If by velocity, you mean "speed": same argument -- they will eventually differ because they are on different geodesics (paths thru space-time). Jan 11, 2016 at 4:47
• I was thinking of the empty universe scenario. Parallel but opposite direction is equal speed but different velocity, and the case of same direction but different speed is also different velocity. Your argument about normalizing the frame of reference works in either case. Jan 11, 2016 at 4:58
• Parallel but different velocities it becomes an escape velocity problem. Just calculate the escape velocity which is a function of mass and distance. If we say the objects are footballs, the mass is quite low and the escape velocity would probably be millions of times slower than a snail. Escape Velocity calculator here: hyperphysics.phy-astr.gsu.edu/hbase/vesc.html Jan 11, 2016 at 5:10
• Even with different velocities (which, with only 2 objects could be modeled as a 'stationary' object and one trying to 'escape' as @userLTK mentions) they will change velocity: i.e. - slow with respect to one another. But you know this. As userLTK mentions, whether or not they stop and eventually come together is an escape velocity problem: does K + U = 0 Jan 11, 2016 at 5:19