Let me see if I can. Before we go to space, let's try something on the ground. Imagine pitching a ball horizontally. What do you expect if you pitch it too slow? The ball will curve more towards the ground and meet it early, won't it? (In other words, it doesn't go very far and doesn't stay airborne for long). Going from ground to space, this action remains the same. You need to 'lower an orbit'? Reduce its forward velocity. It will curve more towards the planet and reach closer to the ground.
However, there is a bit more detail involved here. Why doesn't the satellite just fall to the Earth? (Please excuse me and disregard this part if you know this already. I'm trying to maintain conceptual continuity.) So, when something is flying horizontally (no aerodynamic forces), we know that its trajectory will curve towards the Earth due to the pull of gravity. If the ground (on Earth) curves as fast as, or even faster than the trajectory's curve, the object will never get an opportunity to even reach the ground. This is 'orbiting'.
Now assume that the satellite is initially in a circular orbit. The gravitational force acting on the satellite at any point in the orbit is perpendicular to the satellite's velocity vector and tangential to the orbit. The satellite will maintain a constant speed at this point, since its velocity and the force are always perpendicular [1]. So, what happens when we reduce the satellite's forward velocity? Just as we've seen with the ball, the satellite's trajectory (orbit) starts to curve more towards Earth. Now a subtle, but important change occurs. The velocity and the gravitational pull are no longer perpendicular! They start to align! And when that happens, the speed MUST increase. So, the satellite is now losing altitude and speeding up simultaneously [2]. At some point, the satellite will pick up enough speed again to 'straighten its curve' and avoid falling to the ground. In effect, the satellite had to compensate for the lost velocity in order to remain in orbit, and it did so by exchanging some of its altitude (gravitational potential energy) for velocity (kinetic energy) [3].
So our satellite 'fell' from where we slowed it down, until it had enough velocity again to maintain orbit. At that point, the gravity and the velocity are parallel again, since it will keep falling otherwise [4]. But since it 'fell from a higher altitude', it's speed is now too high for it to remain at that altitude. The orbital curvature is a bit 'too straight' now and it starts to curve away from Earth. So now we're in the exact opposite situation of what was explained in the last paragraph. The satellite is now climbing back up again! As it happens, the satellite actually climbs back up to the point where we slowed it down! And when at that point, its velocity is exactly the same as what it was, after we had slowed it down! [5] So the satellite did the inverse of what it did earlier - it exchanged kinetic energy to get back its altitude (potential energy). The satellite is now living in cycles juggling kinetic energy and potential energy back and forth. The final effect is that the point in orbit that's diametrically opposite to where you slowed it down, is now at a lower altitude. And thus you've effectively 'reduced the orbit'!
One more detail to pin down. How do we slow down a satellite in the first place? Easy! Push the satellite in the opposite direction of its velocity [6]. This is called 'retrograde thrusting' or 'retro burn'. But that's about as easy as it gets. Remember that unlike on Earth, you don't have a surface (a wall or the ground) to lean against. Imagine pushing something heavy on an ice rink. The good news is that you can still push things on an ice rink. The only catch is that the push force will set both the item and you in motion in opposite directions [7]. And that's exactly what we do in space. We throw out mass from the satellite in the form of super-fast gaseous of plasma exhaust. The key is to throw out the mass with as much momentum as possible. But the mass is limited by how much you can carry - it's a depleting resource. So you're basically left figuring out how to throw it out with ever increasing speeds. And that's how we slow down the satellite in space - fire your thrusters!
And finally to lower an orbit entirely, instead of just one point on it, you have to do multiple firings. There are bunch of these 'orbital maneuvers'. The most common one is the Hohmann Transfer [8]. If you could understand what's given above, most orbital maneuvers including Hohmann Transfer will feel very intuitive to you.
[1] Speed is the magnitude of velocity and it remains steady in a circular orbit. However, the perpendicular force will keep bending the velocity vector, thus constantly changing its direction.
[2] This is the from-the-first-principles explanation of conservation of angular momentum. This is how the ballerina spins faster by pulling in her arms.
[3] If this sounds like a 'negative feedback' phenomenon to you, that's because it is. Feedback is a mathematical construct. Nobody ever said that a feedback mechanism must be implemented separately. Some systems have them inherently built-in.
[4] This is the lowest point of the orbit - the periapsis.
[5] Yes. There is quite a bit of hand waving here. I didn't explain why the satellite went back to its original position with the exact same speed. But that's what actually happens. It might take a lot more 'mathematical sense' to explain just using words. One thing I know is that this has something to do with the fact that the gravitational field is one of those 'conservative fields'. If you take a trip inside a conservative field, and return to the location where you started, you will be left with the exact same (kinetic) energy as you started with. You may exchange your energy during the trip, but you always regain it back when you get back to the starting point, no matter what path you took. As far as I understand, the 'conservative' part refers to the part that the energy is conserved and stored, and never lost. Unfortunately, the force field that we're most familiar with - frictional force - isn't conservative at all. If you're going on a trip, be ready to spend some energy!
[6] One matter that confuses a lot of people is why the satellite's position changed at the opposite side of the orbit, instead of the point where we applied the force. The answer is in the Newton's second law. Force changes momentum, not position - at least not directly. The direct effect of application of retro thrust is that the velocity reduces at that point. The change of position on the other side of the orbit is only a consequence of that velocity change.
[9] Every so often, someone comes along and argues that gravity is not a real force and all these explanations are wrong. If you want to deal with this in terms of relativity and space time curvature, be my guest. But for all practical purposes, the old faithful Newtonian physics works just fine, even as a special case of relativity.
[10] This should probably have been a blog post. Please don't shout at me if it annoys you. This is one of my favorite subjects and I just got carried away. I used to teach and train many students and junior professionals in these topics.
Blowing up something in the same orbit as the targets isn't an effective strategy. The explosion disperses the fragments into different orbits that intersect the original orbit only at one or two points. And even if some of those fragments find their targets, the collision velocity will be low (relatively slow).
It will be like getting hit with with shrapnels from a grenade. Depending on how they collide, the target may survive. If you think that grenade shrapnels are fast, you need to understand the 'hypervelocity impact' that happens when objects in different orbits collide, or when an interceptor hits a satellite. Hypervelocity impacts are impacts where the impactor moves faster than the speed of sound in the solid target. What that means in practice is that the debris/interceptor may have hit one end of the satellite and vaporized already, while the other end of the satellite doesn't yet feel the shock and vibration from that impact. That end doesn't yet know about the carnage that's about to hit it in a few milliseconds.
I imagine you could just send a rocket to the specific orbit and just start metering out 100s of thousands of small steel (or whatever) BBs like seeding a yard; seeding a Kessler event.
The 'expendable mass' is almost never a solid or liquid. It's the gaseous combustion exhaust or plasma exhaust from the satellite's thrusters. The advantage of gases is that they just expand and disperse fast enough to be too wispy to cause anything on impact.
However, there are a few systems that do use solid masses for obtaining a reaction force. A remarkable example is called a 'Yo-yo despinner' [1]. It was used in missions like Phoenix (Mars mission) and Dawn (Asteroid belt proto-planet mission). And yes, it does create space debris. But those space debris are probably somewhere in orbit around the sun. Nothing that those guys are going to be too worried about.
That depends on how you define risk. If it means the probability of a collision, then you'd be correct. But if a collision does happen, the consequences will be worse than being in the same orbit. Based on an oversimplified model, debris in orbit is likely to have low relative velocities with respect to an intact satellite in the same orbit, since a large deltav would change the orbit. (It's not as simple as this, but it's good enough in practice.)
This is actually what asat weapons take advantage of. They usually don't even reach orbital velocity, just like ballistic missiles (of course, there are exceptions like the golden dome monstrosity). The kill vehicle just maneuvers itself into the path of the satellite and lets the satellite plough into it at hypervelocity.
That's the Kessler Syndrome. But it's better if it happens in a lower orbit, irrespective of what assets are present there. Space will be free for exploration again in a few years since all the debris there would eventually decay and deorbit.
The article mentions a few months at 480 km. I'm a little skeptical about this figure though, because the last tracked piece from an NRO satellite that was shot down at ~250 km by SM-3 missile in operation burnt frost, lasted 20 months in space before reentry. SpaceX is probably using a statistical cutoff percentage of fragments to calculate the time. But all the pieces are dangerous uncontrolled hypervelocity projectiles. Spain lost a military communications satellite a few days ago from a collision with a tiny undetermined space debris.
It's one reason why space should be regulated (but globally / internationally), the systems in place are kinda loose and more of a gentleman's agreement insofar as I understand it. A plan for decomissioning / de-orbiting stuff should definitely be mandatory. I know there's an area for geostationary sattelites to park themselves after their lifespan, for example.
But the LEO ones like Starlink will see their orbit decay in about five years (if I'm reading things correctly) even if they run out of fuel / can no longer be controlled, according to e.g. https://space.stackexchange.com/a/59560. But it's exponential, at 600 km it takes 10 years, at 700 25 years, at 800 100 years, etc. Between 500-600 km seems to be ideal for things to naturally decay in case of issues.
But also, it won't be a hard and fast "we are confined to the earth now"; the simplest model is a "the risk of being hit by debris is now x%", more advanced is "there are debris clouds in these altitudes / inclinations so best to avoid those at these times of day".
Given that the previous world police are presently treating international law as toilet paper, how do you propose global regulation of space would work or be enforced?
Two objects colliding can send debris into different orbits. Combined kinetic energy and mass differences can send debris to many different orbits.
A golf ball hitting a bowling ball or basketball, both traveling at 30 units of speed can produce quite a fast golf ball. Not all of the debris will safely burn up.
At the speeds we're familiar with, basketballs and golf balls have elastic collisions. At orbital speeds, satellites are nearly inelastic. So fragment exit velocities lie between the two initial velocities, kv1 + (1-k)v2 for some k that depends on where each fragment came from. If they're colliding, the velocities must be somewhat different, so the weighted average speed has to be lower than orbital speed. So fragments usually don't survive many orbits.
Very well put. It also seems like there's a limit to how bad Kessler syndrome can get. The more debris there is the more collisions, but the more collisions the quicker the debris collides with itself and de-orbits.
That's what I was thinking, Kessler syndrome should be impossible for objects in LEO since all debris orbits decay rapidly (probably 99.9% enter the atmosphere and burn up in minutes, the rest in hours)
Possibly. But more likely the thrust from escaping gas will push it in a direction to either slow the orbit down or make it more eccentric and unstable.
Right, if there's something like a small hole in a pressure tank, it's very unlikely to be aligned exactly with the CG, so the tank will spin around and the net thrust will be near zero.
If a pressure tank splits in half, both halves will fly away but that's a very inefficient way of using the energy in the gas, so the added velocity will be a small fraction of the speed of sound in the gas, which is 1/6 of orbital speed for hydrogen, less for any other gas.
You can't really get much of a chemical explosion because the fuel and oxidizer both disperse very quickly in space.
Just to elaborate the correct reply given by the others, the perigee of all fragments will be less than or equal to the altitude at impact point. If that's low enough, they will all eventually decay and deorbit. Even the fragments in elongated high-eccentricity orbits will have their orbits circularized by lowering apogee (the perigee is never going to rise) due to air drag. It will eventually spiral into the atmosphere. Here is the best visualization for this phenomenon - the Gabbard plot.
You're right that all the fragments will pass roughly through the impact point in orbit. But it's not always the periapsis.
1. The normal or anti-normal delta-v imparted by the explosion/fragmentation (i.e, the velocity imparted perpendicular the plane of initial orbit) will cause the orbital plane of the fragment to change. The new orbit will intersect the old orbit at the impact point. Meanwhile, the eccentricity (the stretch of the orbit), semi-major axis (the size of the orbit) and displacement of periapsis from the impact point (the orientation of the orbit) remains the same as the initial orbit.
2. The prograde and retrograde delta-v (velocity imparted tangential to the orbit) will cause the diametrically opposite side of the orbit to rise or fall respectively. Here too, the new orbit intersects the old orbit at the point of impact. But since the impact point isn't guaranteed to be the periapsis or apoapsis, the above mentioned diametrically-opposing point also cannot be guaranteed to be an apsis.
3. The radial and anti-radial delta-v (this is in the third perpendicular axis) will cause the orbit of the fragment to either dip or rise radially at the point of impact. Again the impact point remains the same for the new orbit. So the new orbit will intersect the old orbit either from the top or the bottom. The new orbit will look like the old orbit with one side lowered and the other side raised about the impact point.
So none of three components of delta-v shifts the orbit from the impact point. You can extrapolate this to all the fragments and you'll see that they will all pass through the impact point. The highest chance of recontact exists there. However the perturbation forces do disperse the crossing point (the original impact point) to a larger volume over time.
Edit: Reading the discussion again, I get what you were trying to say. And I agree. The lowest possible altitude of the fragments in orbit (i.e the periapsis) is the same that of the impact point. So if the impact point is low enough to cause drag, the orbit will decay for sure. There is nothing that demonstrates this better than a Gabbard plot [1][2] - the best tool for understanding satellite fragmentation.
>But since the impact point isn't guaranteed to be the periapsis or apoapsis, the above mentioned diametrically-opposing point also cannot be guaranteed to be an apsis.
You're correct on the generalized case of the math here, no argument at all, but this also feels like it's getting a bit away from the specialized sub-case under discussion here: that of an existing functional LEO satellite getting hit by debris. Those aren't in wildly eccentric orbits but rather station-kept pretty circular ones (probably not perfectly of course but +/- a fraction of a percent isn't significant here). So by definition the high and low points are the same and which means we can say that the new low point of generated debris in eccentric orbits will be at worst no lower then the current orbit of the satellite (short of a second collision higher up, the probability of which is dramatically lower). All possible impact points on the path of a circular orbit are ~the same. And in turn if the satellite is at a point low enough to have significant atmospheric drag the debris will as well which is the goal.
No worries. I think I could have been more precise in my wording. :)
My comment is based on the hunch concerning physical calculations and interactions from an engineering physics degree and way to many hours in kerbal space program a decade ago.
Thanks! I figured that you had a reasonable understanding in this subject. But I still couldn't help just laying it out. I have some background too - as a professional.
How illegitimate do you have to be, if your power is so threatened by protests that you're willing to put a teen to death? Any regime that oppress criticism deserves the noose.
Sure! They all have overinflated egos that're propped up by PR shenanigans and doesn't match their demonstrated achievements. But their opinions are more likely their aspirations rather than oversimplifications.
What follows is my gut feeling from observing their public interactions. So take it with as much salt as you like. At this point I'm confused as to whether they're motivated by wealth (greed) or by the suffering they inflict while amassing it (misanthropy). If you carefully observe the interviews of the broligarchs and some others in power, you'll notice that they're genuinely happy and excited to discuss plans and activities that cause widespread misery, pain or even death. I can give you numerous examples of such instances, but this will probably seem eerily familiar to you too. Even this story is one such example.
It's as if multiple people bullied or abused them in their childhood and now they're out to prove their superiority and importance and show humanity its place. It's like a super villain revenge fantasy. I know that at least a few individuals among them does have such a dark history. But this behavioral pattern in pervasive among them.
They either lack that foresight and are completely oblivious of that limitation (the Dunning-Kruger effect), or they're lying shamelessly to manipulate the market in the hopes cashing out in the end, sort of like a pump-and-dump scheme or a pyramid scheme. Based on many of their track records I wouldn't be too surprised if both effects are at play, reinforcing each other.
However, there is a bit more detail involved here. Why doesn't the satellite just fall to the Earth? (Please excuse me and disregard this part if you know this already. I'm trying to maintain conceptual continuity.) So, when something is flying horizontally (no aerodynamic forces), we know that its trajectory will curve towards the Earth due to the pull of gravity. If the ground (on Earth) curves as fast as, or even faster than the trajectory's curve, the object will never get an opportunity to even reach the ground. This is 'orbiting'.
Now assume that the satellite is initially in a circular orbit. The gravitational force acting on the satellite at any point in the orbit is perpendicular to the satellite's velocity vector and tangential to the orbit. The satellite will maintain a constant speed at this point, since its velocity and the force are always perpendicular [1]. So, what happens when we reduce the satellite's forward velocity? Just as we've seen with the ball, the satellite's trajectory (orbit) starts to curve more towards Earth. Now a subtle, but important change occurs. The velocity and the gravitational pull are no longer perpendicular! They start to align! And when that happens, the speed MUST increase. So, the satellite is now losing altitude and speeding up simultaneously [2]. At some point, the satellite will pick up enough speed again to 'straighten its curve' and avoid falling to the ground. In effect, the satellite had to compensate for the lost velocity in order to remain in orbit, and it did so by exchanging some of its altitude (gravitational potential energy) for velocity (kinetic energy) [3].
So our satellite 'fell' from where we slowed it down, until it had enough velocity again to maintain orbit. At that point, the gravity and the velocity are parallel again, since it will keep falling otherwise [4]. But since it 'fell from a higher altitude', it's speed is now too high for it to remain at that altitude. The orbital curvature is a bit 'too straight' now and it starts to curve away from Earth. So now we're in the exact opposite situation of what was explained in the last paragraph. The satellite is now climbing back up again! As it happens, the satellite actually climbs back up to the point where we slowed it down! And when at that point, its velocity is exactly the same as what it was, after we had slowed it down! [5] So the satellite did the inverse of what it did earlier - it exchanged kinetic energy to get back its altitude (potential energy). The satellite is now living in cycles juggling kinetic energy and potential energy back and forth. The final effect is that the point in orbit that's diametrically opposite to where you slowed it down, is now at a lower altitude. And thus you've effectively 'reduced the orbit'!
One more detail to pin down. How do we slow down a satellite in the first place? Easy! Push the satellite in the opposite direction of its velocity [6]. This is called 'retrograde thrusting' or 'retro burn'. But that's about as easy as it gets. Remember that unlike on Earth, you don't have a surface (a wall or the ground) to lean against. Imagine pushing something heavy on an ice rink. The good news is that you can still push things on an ice rink. The only catch is that the push force will set both the item and you in motion in opposite directions [7]. And that's exactly what we do in space. We throw out mass from the satellite in the form of super-fast gaseous of plasma exhaust. The key is to throw out the mass with as much momentum as possible. But the mass is limited by how much you can carry - it's a depleting resource. So you're basically left figuring out how to throw it out with ever increasing speeds. And that's how we slow down the satellite in space - fire your thrusters!
And finally to lower an orbit entirely, instead of just one point on it, you have to do multiple firings. There are bunch of these 'orbital maneuvers'. The most common one is the Hohmann Transfer [8]. If you could understand what's given above, most orbital maneuvers including Hohmann Transfer will feel very intuitive to you.
[1] Speed is the magnitude of velocity and it remains steady in a circular orbit. However, the perpendicular force will keep bending the velocity vector, thus constantly changing its direction.
[2] This is the from-the-first-principles explanation of conservation of angular momentum. This is how the ballerina spins faster by pulling in her arms.
[3] If this sounds like a 'negative feedback' phenomenon to you, that's because it is. Feedback is a mathematical construct. Nobody ever said that a feedback mechanism must be implemented separately. Some systems have them inherently built-in.
[4] This is the lowest point of the orbit - the periapsis.
[5] Yes. There is quite a bit of hand waving here. I didn't explain why the satellite went back to its original position with the exact same speed. But that's what actually happens. It might take a lot more 'mathematical sense' to explain just using words. One thing I know is that this has something to do with the fact that the gravitational field is one of those 'conservative fields'. If you take a trip inside a conservative field, and return to the location where you started, you will be left with the exact same (kinetic) energy as you started with. You may exchange your energy during the trip, but you always regain it back when you get back to the starting point, no matter what path you took. As far as I understand, the 'conservative' part refers to the part that the energy is conserved and stored, and never lost. Unfortunately, the force field that we're most familiar with - frictional force - isn't conservative at all. If you're going on a trip, be ready to spend some energy!
[6] One matter that confuses a lot of people is why the satellite's position changed at the opposite side of the orbit, instead of the point where we applied the force. The answer is in the Newton's second law. Force changes momentum, not position - at least not directly. The direct effect of application of retro thrust is that the velocity reduces at that point. The change of position on the other side of the orbit is only a consequence of that velocity change.
[7] Yes, the Newton's vengeance law.
[8] https://en.wikipedia.org/wiki/Hohmann_transfer_orbit
[9] Every so often, someone comes along and argues that gravity is not a real force and all these explanations are wrong. If you want to deal with this in terms of relativity and space time curvature, be my guest. But for all practical purposes, the old faithful Newtonian physics works just fine, even as a special case of relativity.
[10] This should probably have been a blog post. Please don't shout at me if it annoys you. This is one of my favorite subjects and I just got carried away. I used to teach and train many students and junior professionals in these topics.
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