I just finished reading a Sci Fi novel. I won’t say which one to avoid spoilers, though anyone reading it will probably figure it out…
Anyway. Let’s say you are in orbit around earth, and let’s say it’s a stable orbit, sufficiently high enough to avoid atmospheric drag.
Now let’s say you are on a spacewalk and have (say) 6  12 mini satellite / science experiments with you. You “launch” these satellite / science experiments by simply tossing them in different directions from your current position.
Is this enough to prevent them from having collisions in the near future?
What if you took one in either hand and tossed them 180 degrees apart at the same time? Would these be likely to collide in the near future? And would it matter if you tossed them side and side, front and back, or up and down?
How hard would you have to toss them to prevent collisions in the future?
I would say that if you give each one an impulse of random direction and magnitude at a random time, then the probability of a collision between any two of those satellites within your lifetime would be extremely low. Especially true if these satellites are extremely small compared to their orbital radius (obviously this is true if you’re in earth orbit and these are handheld, handlaunched satellites).
If you tossed one left and one right at the same time with the same velocity (relative to you), you’ve placed them both in elliptical orbits that intersect at the point where you launched them; I would expect them to collide back at that launch point after having completed a single orbit.
If you tossed one up and one down at the same time with the same velocity (relative to you), the result is less clear to me. You’ve put them both on elliptical orbits that intersect at the launch point, but one is headed for its apogee, and the other is headed for its perigee. I don’t know whether the two would have the same orbital period, but if they did, then you’d expect them to collide again after having completed a single orbit.
By definition a stable orbit is one in which a small peturbation (of which the extra momentum imparted to the minisats by tossing them would be a perfect example) will not increase signifcantly. So you would expect the minisats to remain relatively close to each other, but on the other hand you wouldn’t necessarily expect them to collide either because there’s nothing bringing them together.
Yeah, I think collisions are very unlikely  especially since (if I read the same book as the OP), she tosses the satellites out sequentially; each one of them is going to intersect the original orbit at some point, but no two of them should intersect the original orbit at the same point.
The orbits will intersect, and the satellites will reach that intersection point. The question is just whether they’ll reach it at the same time. They were at the intersection point at the same time once, when they were deployed… but their deployment probably put them into orbits with slightly different periods, so it won’t be at the same time the next time they come around. Eventually, they will, but this will probably take a fairly long time.
On a related note, there are very small satellites called cubesats, each one a cube 10 cm on a side and usually built by college students or other amateurs, which are launched several at a time and deployed out of something that resembles a Pez dispenser by a spring that pushes them out of the end. Being so small, of course, reduces the chance of collision, and they’re generally also not expected to last all that long anyway.
That said, however, it is possible for these cubesats to collide. At least two of them have gotten stuck together by magnets intended for attitude control. Both survived.
You could get at least three of them to not collide. Throw one in the direction of your orbit. It’s orbit will graze your orbit, but otherwise be outside it. If you could throw one of these mini satellites twenty feet in the air when standing on Earth, the satellite’s orbit would be about twenty feet higher than yours, at its peak*.
After half an orbit, throw a second one opposite the direction of your orbit. That one will be lower than your orbit, grazing it when the other satellite is at it’s highest relative to your orbit. It’s low point should be twenty feet lower than your orbit*.
After an additional quarter orbit, throw one perpendicular to your orbit. It will cross your orbit twice, and both times, the orbits of the other two satellites will be some distance from yours, around 14 feet* I’d guess. That’s all I can visualize in my head, but I wouldn’t be surprised if you could fit more nonintersecting orbits in there.
I’m assuming here that the satellite’s masses are small enough relative to yours that I can neglect your recoil.
ETA: * I think. I wouldn’t be surprised if there’s a factor of 2 in there somehow.
If you can consistently throw them at say 40 mph (which is not that fast), then throw them all in the same direction, waiting about 30 seconds between tosses. If I did my math right, they’ll be about 1760 feet apart from each other for the foreseeable future.
(5280ft*40mph)/3600 is 58 2/3 feet per second (I hope), times 30 seconds is 1760 feet.
Isn’t that in an idealised scenario though? In reality, aren’t their different paths going to expose them to enough variables (minor variations in the number of gas particles they interact with, bumps in the Earth’s gravity, etc) to make a near miss more likely?
I seem to remember ISS spacewalkers purposefully “throwing away” external balky equipment after a repair/swap out was complete. But I can’t find any mention of that on Google…
It was a 1400 lb tank of ammonia they let loose in 2007. It burnt up a year or so later. But that’s very unusual for trash to be deliberately released. Generally they want to avoid adding to the junk in low Earth orbit.
If you are spacewalking on a tether that places you 20’ above your vessel (which is in a nearly circular orbit) and you throw the satellite downrange with force, you will be placing it into an elliptical orbit, at periapsis (perigee), because a circular orbit that is higher means the body moves slower (you are adding your vector of moment to the object you are throwing, while also reducing your own momentum in doing so). If you throw one downrange and one uprange, the one you throw uprange will be at apoapsis while the one you throw downrange will be at periapsis of their respective elliptical orbits, so the net orbits of each will not have the same period: they might never cross paths again, unless you do some really good math and aim well.
No, they may well collide. The “tossing” is insignificant, the satellites are in the same orbit …basically at the same place since they were launched at the time. The perturbations will make them wobble around in their orbit and collide pretty quick.
OK, no, that’s way off. Throwing the ball straight up on Earth gives it kinetic energy M * Vthrow^2. When it hits its peak, all that kinetic energy will be turned into potential energy.
Throwing the ball in the direction of orbit will give in kinetic energy of M*(Vorbit+Vthrow)^2, compared to what it had before, MVorbit^2. So its energy goes up by about 2MVorbitVthrow. This is much larger than MVthrow^2, and the peak orbit difference will also be much larger, by a factor on the order of 2Vorbit/Vthrow, which is something like 1000.
Also, when it’s at its peak, it won’t be travelling at Vorbit, but more like Vorbit  Vthrow, giving an additional factor of 2 I was wondering about in my ETA. So maybe 2000 * 20 feet, or about 8 miles. That gives a lot of space to work with.
I think your best bet for nonintersecting orbits of N small satellites would be to throw them at about the same speed equallyspaced in angle, covering a range of in the direction of your orbit to opposite the direction of your orbit, and equally spaced in time over 1/2 of an orbit. So with 5 satellites, as you go through your orbit around the Earth, throw them in the directions shown below. They all still intersect the original orbit, but at different points in the original orbit, and the orbits don’t intersect each other.
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^

Earth >

v
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Here, they have an up/down component, but you could use a left/right component instead.