Gravity/velocity question of two bodies

Factual Questions
1

I am wondering about a situation of two identical bodies traveling the same speed on parallel trajectories at the same spot on the trajectories. They exert a gravitational attraction that will eventually have them come together. For the sake of simplicity of the question, they do not ricochet off one another, but stick together.

The bodies had to curve their course to come together. Which means they had to cover additional distance to converge than if they had continued in a straight line. But gravity pulled them together. Did that impart an increase in speed? A slight gravitational slingshot effect? Did that balance out so the now converged bodies are traveling at their original speed? Or are they going slower or faster?

This question came to me when contemplating expansion of the Universe. I started imagining all the particles blasting outwards from a common point. Then being attracted together in various clumps. What is the relation between these accumulations vis a vis speed and gravitational fields. Of course in that scenario the trajectories are not parallel. But parallel is easier for the question.

2

Yes, the mutual gravity attraction accelerates the two objects. The energy for this acceleration comes from the conversion of potential energy into kinetic energy. After the convergence, the potential energy of the two objects is lower than it was before.

3

It’s a very simple situation and easy to solve: they come together and the combined mass has the same velocity as the starting velocities of the two masses. NB two bodies sticking together is an inelastic collision, so the gravitational potential energy will be coverted to internal energy (e.g. heat) of the bodies.

Cosmic expansion though is not matter expanding from a point, it is matter that is approx. evenly distributed througout a space that is expanding itself. I don’t think this very simple situation, which needs nothing other than Newtonian physics, will give you much insight into cosmic expansion.

4

This is a common misconception, but it’s wrong.

Take a flag, and put it at a particular spot in space. Let’s also make it so that this flag never, ever moves. Now take a second flag, and put it somewhere else in space. This flag also never, ever moves.

Here’s the funny thing. The two flags move away from each other.

Now wait a minute, you say. I thought the flags never moved? The answer is, they don’t. The flags aren’t moving at all. The space in between the flags is increasing.

Weird. But that’s the way it works. You can thank some guy named Edwin Hubble for figuring this out. You might have heard of him. He got a telescope named after him.

Now, as a little thought experiment, let’s rewind our two flags in time. Going forward in time, the flags keep getting farther apart, so if we go back in time, the flags get closer together. But again, the flags aren’t moving. It’s those two points in space that are getting closer together because the space between them is shrinking.

Put a bunch of unmoving flags all over the universe. They are all moving away from each other. Go back in time, and all of the flags move towards each other, until they all squish down to a single point.

So here’s the key point. At the Big Bang, it’s not a bunch of particles blasting out. That implies that the space already existed and all the matter was squished down into a point and just blasted out into an already existing space. That’s wrong. What really happened is that all of those different points where you placed those flags, every bit of space itself, was condensed down to a point. It wasn’t matter blasting out from a point, it was space itself (along with the matter) blasting out.

After that, then you get into the clumping. And that ends up being a surprisingly complex topic, including the fact that modern scientists don’t quite agree on some simple aspects of this, such as the facts of exactly how clumpy the universe actually is.

5

While the two objects are accelerating towards each other, their speeds are indeed increasing, though not necessarily by very much. Remember, velocity is a vector. Both are still moving forward at whatever speed they originally had, and also now have a component of velocity at right angles to that, towards each other.

When they eventually collide and stick together, that component of velocity towards each other will again go to zero, but they’ll still have whatever forward velocity they had, still unchanged.

6

Thank you for the replies.

7

About the velocity added by the gravitational pull going to zero upon the bodies combining.
Wouldn’t there be an additive effect? The now single body traveling faster than the original velocity of the two? I imagine that the gravitational effect may be 90 degrees between the bodies. But not sure. But the angles of velocity may not be, depending on when they collide? Probably stating it in a clumsy way.

8

It’s simpler to evaluate your two bodies from a different reference frame that is moving along with them – even that’s not well said, because they’re only moving together if viewed from some reference frame. So choose instead a reference frame in which the average of their two positions is stationary. In that reference frame you will see each accelerate toward the other, until they collide and form a stationary object that has also been heated a little by converting their kinetic energies.

Their mutual infalling doesn’t accelerate them along what you describe as their average moving axis perpendicular to the line between them.

9

Since they are identical and are moving in parallel the acceleration is exactly 90 degrees to their “original” and eventual direction and exactly cancels out.

10

When the two bodies come together they lose gravitational potential energy, but that energy cannot add to the kientic energy of the combined mass as momentum needs to be conserved. It has to go somewhere else, such the internal energy of the combined mass.

11

ETA: got interrupted halfway through and the real physicists beat me to actually posting. Oh well, I typed it so you’re stuck looking at it. :wink:

Gotta be careful about combining “faster /slower” which is about speed with “velocity” which is about speed and direction.

@Chronos did a fine job in very few words, but maybe a little too abstract for you. The three experts just above me also did a fine job, but may lack the context for you to slot their good info in where it belongs.

Lemme try this, taking it in smaller more explicit bites.

Let’s call the direction the two bodies are traveling as North. They start out both going North at the same speed on parallel tracks some specific distance apart.

Once we let them go, gravity begins pulling them towards each other. The one to the west is pulled exactly east by the gravity of the other. And vice versa. The one to the east is pulled exactly west by the gravity of the first one.

100% of the gravity force is east/west and zero of it is north/south. So the speed in the northerly direction remains exactly the same. While meanwhile the speed of the western one moving east and of the eastern one moving west keeps increasing over time. So the longer time goes by the faster they’re going east/westward. Their total speed in a northeasterly or northwesterly direction is increasing because it’s the vector sum of the unchanging northerly speed and the increasing east- and west-bound speeds of the two bodies.

And the closer they get together, the stronger the mutual gravity gets, so they accelerate towards each other at an increasing rate. But still, 100% of this acceleration is east/west and is having zero effect on their absolutely constant speed northward.

As time goes on they keep getting closer and closer and moving faster and faster east/westward. With their still unchanging northward speed. The vector sum of those speeds, their velocity, is increasing. And is aimed more and more easterly/westerly as that component of velocity continuously gets bigger while the northerly component is unchanged.

At the moment just before they touch, the western one is moving east at some speed X. And the eastern one is moving west at the exact same speed X, just in the opposite direction. While both are also going north at the original unchanging speed.

Eventually they crunch together. And per your assumptions stick together in a single bigger lump. At that moment the easterly speed and westerly speed combine to zero. The northerly speed remains unchanged. And so the vector sum of zero east/west and the unchanged northerly speed is exactly the same as when the experiment started. Same direction (north) and same magnitude of speed. So same velocity as at the start. But a different direction and a different magnitude = speed from the moment before they collided.

What happened to the kinetic energy of their east/west motion? It was converted to heat as they smooshed and stuck together. Where did that kinetic energy come from originally? From the potential energy that was two gravitating bodies held some distance apart just before we let the experiment begin.

12

Think of two cards travelling in the same direction at 45 mph (or kph). They drift into each other, get locked together. That doesn’t make them suddenly go at 90 mph.

(Okay, maybe the drivers panic…)

13

Not sure what the issue is here - consider two bodies. They are moving at a certain velocity, parallel to each other at first. This is a system with a common center of mass. The system is moving with a constant velocity. what happens within that system, the two bodies attracting each other and colliding, does not change the location and velocity of the total system. The two bodies collide and stick? Presumably the energy that they had (potential energy) by being apart was converted by gravity into kintetic energy (they moved faster and faster toward each other) and that energy is now converted into other energy - probably heat from the collision, and they melt into one simple round ball. But the mass and velocity of the total system has not changed. Two masses of X were travelling with velocity vector Y now one mass of 2X is still travelling with velocity vector Y. What happens inside the total system stays in the system.

14

LSLGuy.

Stated in a way that let my visual mind grasp nicely. The concept I presented was very vague in many ways. I did consider the kinetic energy being converted in some way. But could not visualize it as being totally converted in ways excepting adding some velocity. When a couple of replies came in I did see that the gravity angle would always be 90 degrees in effect. But the vectors of the masses changing direction and velocity remained fuzzy in my mind.

Thank you for taking the time to detail your explanation. Now I will ponder how to frame my next question along this line of thought.

15

Just an odd offshoot question.
If oxygen and hydrogen atoms are wandering along some vectors and come together to form a water molecule. Does that molecule heat up due to the combination of vectors?

16

Good one.
A nice simplification. But I am not sure if it is clean enough to apply directly to my thoughts. The cars are not being drawn together by gravity. But It seems you do make the point.

17

My overall thought on this question is how conglomeration of mass after the big bang may cause gravitational forces to be sublimated to velocity of the masses as they coalesced. The answers I received say the velocity remains the same. No increase. But the masses come together over some distances. They combine mass and increase gravitational force. But they are on average more distant from other masses going through conglomeration. With the fall off of gravitational force over distance. Will velocity triumph over gravitational pull? All the various chunks becoming farther apart. With various localized effects being different of course. Probably answered years ago. But can’t find specific answer to my fuzzy concept.