# Motion in space due to space-time curvature

1. Oct 30, 2008

### cosmogrl

Why do things orbiting, i.e. free-falling, around earth float away from each other? Why don't they both free fall toward earth together? I remeber hearing once that if you let go of 2 objects while 'floating' in space they both go away from you and away from each other. Is this due to curving space-time from each of the masses?

2. Oct 31, 2008

### Mentz114

You've been misinformed. Please say where you heard this. Gravity causes masses to move towards each other, not away from each other.

Two objects falling radially towards the earth will get closer because their paths converge, not necessarily because they attract each other.

3. Oct 31, 2008

### Staff: Mentor

Hi cosmogrl, welcome to PF,

Yes, please say where you heard this. My guess is that they are talking about the fact that different orbits have different orbital velocities, so an object in a slightly higher orbit with a slower orbital velocity will "fall behind" and an object in a slightly lower orbit with a faster orbital velocity will "speed ahead". But without further details it is hard to say what they were refering to.

4. Oct 31, 2008

### cosmogrl

Well, I mean astronauts in outer space float away from the shuttle and everything floats away from them. I don't mean planets orbiting around the sun. I guess I think that if the astronaut is detached from the shuttle s/he will float away from it, but I don't understand why. I knwo they are both in free-fall around earth, so why don't they move together.

5. Oct 31, 2008

### Jonathan Scott

Everything floats away because the slightest contact with normally imparts some outwards momentum and once things are moving apart in space, they continue moving apart because there is no friction (except that if they are in orbit, there is also a superimposed elliptical motion due to the different orbits). The gravitational attraction between objects even the size of the Shuttle is negligible. Before the Shuttle, in the Skylab days, they discovered the "jack in the box" effect, which is that anything which is put in a box or cupboard but isn't actually held in will tend to pop out when it is opened in zero gravity.

6. Nov 2, 2008

### Naty1

I'm thinking cosmogrl is right on!!

Seems to me the force of attraction between the earth and and a mass is F = GmM/r^2. (1)

The gravitational attraction between two objects is miniscule in comparsion with that of the earth acting on each object. So when two objects of different mass are floating together...they will be subject to slightly different attractive force from earth...and should tend to drift apart....radially (Likely the difference in masses swamps any miniscule change in "G" due to their different distances of center of gravity from earth.)

And if one is further distant, the fractional change in F is twice the fractional change in r. (This has top be derived, not obvious without math)

I'm less sure about the following:

If the orbital velocites of two objects of different mass, held together, are initially the same, from mv = MV aren't their orbital momentums different since v = V at the start??? so this seems like they would move apart along the orbital direction....

and I seem to remember

F=mv^2/r.. (2) for centripetal force.... or is this gravitational attraction (1) in disguise?? Anyway it looks like an indication, again, of radial separation.

I've think I've forgotten more than I knew!!!

7. Nov 2, 2008

### cosmogrl

Thanks everyone, so if I understand correctly, both objects in space are being radially pulled toward earth, but because they have slightly different velocities, they are in different free-fall orbits around earth. It appears then, from the reference point of one of the objects in space, that they are moving away from each other? And, because they are at different distances from earth, they will feel different force of gravity? If so, then I think I understand now. Thanks everyone.

8. Nov 2, 2008

### Naty1

You posted:

I think you meant "masses" since the initial velocities are the same...until release as separate objects subject to free fall...

9. Nov 2, 2008

### Jonathan Scott

I hope not. Velocities is what it's all about. The slightest contact pressure between two objects in zero gravity (unless they are sticky or fixed together in some way) tends to push them apart. Locally over a period of a few minutes, they just keep going because locally free fall is like any other inertial frame. However, over the period of a whole orbit, the slight difference in the orbit typically causes one to move around the other.

10. Nov 2, 2008

### cosmogrl

Yep, I meant velocities. they are in different velocities which translates to different orbits, which means they move away from each other.

11. Nov 2, 2008

### HallsofIvy

Staff Emeritus
No, it doesn't. If two objects, in different orbits, are close together then they will come back together after completing their orbits. Yes, since they are not on the same orbit they will start moving away from each other but then they will move back together again.

12. Nov 2, 2008

### DaveC426913

If they're in orbit then this radial force won't manifest. It manifests if they fall, since they're falling toward a common point.

But in the ideal case of two objects orbiting next to each other, they will neither drift apart nor together.

However, if they are far enough apart that their differing altitudes are a significant factor (and it doesn't have to be more than a few feet), then they will drift apart (because they're in different orbits). They will however approach each other again as their orbit progresses.

13. Nov 3, 2008

### Naty1

So if two initially adjacent objects centers of gravity are at slightly different distances from earth, their v=wr velocities are slightly different so they move apart. ok.

But if their center's of gravity are at the same distance from earth, then their velocities are equal, and they will tend to stay together....also ok.

And there is no radial change in distance because all objects experience the same acceleration due to gravity....

(my prior post about radial gravitational forces was wrong...because all massess accelerate the same radially....and so too mv =Mv is ok, but they don't separate as same v's don't move them apart even though they do have different momenta. Nice try, but no prize; it HAS been too long!!!)

14. Nov 3, 2008

### Jonathan Scott

If objects in orbit separate slowly in a radial direction, they will have similar energy and similar orbit times, so they will pass each other again (or collide) after half an orbit, and continue to oscillate past each other from then on. If however they separate in a tangential direction along the orbit, this will maximize the difference in energy, so they will miss each other by an increasing amount after each orbit. Note that the one which separates BACKWARDS will get round its orbit a little more quickly because it will drop lower, so it will end up in front of the other one.

15. Jun 13, 2010

### phy_freak

"every massive particle in the universe attracts every other massive particle with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between them." that was Newton's law of universal gravitation. so what heard was actually wrong.

see: http://en.wikipedia.org/wiki/Newton's_law_of_universal_gravitation