But maybe it's zipping too fast there to be easily shot down?
A satellite in LEO already has a speed of about 8 km/s. The highest speed of a satellite in a highly elliptical orbit is 11 km/s. It you can shoot a satellite at 8 km/s, you probably can also shoot it at 11 km/s.
The problem is, of course, that the perigee of a satellite in a highly elliptical orbit can be over a different part of the planet than your SAM battery.
It you can shoot a satellite at 8 km/s, you probably can also shoot it at 11 km/s.
Assuming all else is equal (same altitude, same targeting capability, same flight characteristics), an interceptor for an 11 km/s target needs about 89% more kinetic energy than an interceptor for an 8 km/s target. Realistically, between the rocket equation and atmospheric effects, the faster interceptor would likely need to be far larger still. You're probably talking about a 2.5 to 3 times bigger missile. While a country that could develop one could likely develop the other if they so chose, it doesn't seem like a safe assumption that a country with one has the other.
I dont think that it is correct to assume your interceptor needs to match velocity. Any speed will do if you can intercept it on approach instead of chase it down.
I'm not assuming the interceptor needs to match velocity. There is some point you detect the target x1, and some range for your missile from your position x0 to an interception point x2. Your interceptor needs to get from x0 to x2 by the time the time the target gets from x1 to x2. If your target is travelling 37.5% faster, you have 27.2% less time to get to the interception point, which means that you need to fly 37.5% faster, which requires 89% more kinetic energy, regardless of what the baseline speed required was. Alternatively you need to detect things from further away or fire from a closer distance, both of which pose their own issues.
That's not quite correct, is it? Consider shooting at a bird. A falcon travels twice as fast as a pigeon, but you don't need a bullet that is twice as fast to shot the falcon. You simply adjust the lead distance when you shoot at the falcon. In your argument you assume that you need to cover some distance in the same amount of time, but you don't need to. You simply lead the target a bit more. As for detection time, well, it is basically a guarantee that whoever is considering shooting at a space plane, has the tracking capabilities to know its position at all times. If they don't, they probably can find some reddit where people do that out in the open.
In this scenario increasing lead distance is equivalent to detecting and firing earlier (ie increasing distance between x1 and x2), which again has serious technical issues. Yes you can hit a falcon with the same bullet, but it's harder to hit. And the big difference in these scenarios is that the bullet is moving much faster than either the pigeon or the falcon, which means you can always buy more time for the falcon to get to the interception point by taking a less efficient path, whereas for the satellite interception where your interceptor is slower than the target, there is some optimal path (basically straight up from right below perigee) that sets a hard limit on how long it takes to get to any interception point.
If your interception point is say 500 km straight up from your launch point, just to get there you need a rocket that rapidly accelerates to over 3 km/s, and it takes a little over 5 minutes to get to the interception point. To hit an 8 km/s target, you need to fire when it is 2500 km away, to hit an 11 km/s target you need to fire when it is 3500 km away. If to score a hit you need to be within 10 meters of the target at interception, then you need to know the position and velocity of the 8 km/s target to within 4 ppm, you need to know it with an accuracy within less than 3 ppm. And note, if you are shooting from 15 km up in a fighter jet, the 8 km/s target is within your radar horizon, the 11 km/s target is not. Not to say that you couldn't build a system with target sharing and more precise tracking, but it would be a different system than the one you need for the less challenging use case.
Now it's not a strictly either or thing. You could use a missile with intermediate speed and fire it less early. There's a whole continuum of solutions, but it will always be harder to hit the faster moving target. And of course you have real world things to consider like if the target has any maneuverability or countermeasures and how much variation in conditions you can afford. Generally you are already using the best targeting system you can get and are already in the most advantageous position you can be in, so the knob you can turn is "how big of a missile do I need to get the performance I require?"
Agreed, it all depends on the use case. If you are trying to hit an evading target, you have to be faster. If you are trying to deny the ship from a destination, you don't.
If the ship's current position is 200 miles from its destination and you are 400 miles from its destination, you need to go faster than it to deny the ship from its destination. Conversely, if you are 40 miles from its destination, you can go much slower, though if you go too slow you still won't make it. You have to get to a point ahead of it before it gets there, and the faster its moving, the less time you have available to get to any particular point.
Dealing with evasion is a whole other matter. A stationary iceberg can hit a ship that tries to evade if it does so too late. Conversely simple error in your knowledge of a ship's position and velocity can cause it to be miles away from where you expect it later in the journey.
Like the parent says, you already know where it is. I'm struggling to understand the case where you are further from the destination than the x37B, with an orbit 60,000km from earth.
Like the parent says, you already know where it is.
The parent is incorrect. You know approximately where it is. If your approximation is off by some amount, you miss. How good of an approximation you have is determined by your detection equipment. How good of an approximation you need is determined by the speed. For the same detection equipment, hitting the faster moving thing is harder.
I'm struggling to understand the case where you are further from the destination than the x37B, with an orbit 60,000km from earth.
Well yeah, that's because the x37B interception scenario is the second case, where you are much closer to the destination but going much slower.
I thought the fundamental hypothesis under discussion here was that the x37 has the orbit to move quickly and avoid interception. It being the second case seems to rule against that hypothesis being true
That is the hypothesis here, and the second case in no way rules against it.
Again to clarify, no one here is arguing that to intercept a target you have to be moving faster than the target. The argument is you have to be moving faster than the minimum speed required to hit a slower target.
In math terms, you have two targets with velocites V1 and V2. To intercept there is some minimum velocity for each, v1 and v2. This is the best case scenario, you are perfectly in position, you can launch at the earliest possible time. v1 < V1 and v2 < V2 are both true. But since V1 < V2, v1 < v2 is also true. An interceptor that can achieve v1 doesn't necessarily have the capability to achieve v2.
I don't think that is quite right. You can hit a satellite with a suborbital projectile. The kinetic energy of the satellite is enough on its own if you hit it.
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A satellite in LEO already has a speed of about 8 km/s. The highest speed of a satellite in a highly elliptical orbit is 11 km/s. It you can shoot a satellite at 8 km/s, you probably can also shoot it at 11 km/s.
The problem is, of course, that the perigee of a satellite in a highly elliptical orbit can be over a different part of the planet than your SAM battery.
Assuming all else is equal (same altitude, same targeting capability, same flight characteristics), an interceptor for an 11 km/s target needs about 89% more kinetic energy than an interceptor for an 8 km/s target. Realistically, between the rocket equation and atmospheric effects, the faster interceptor would likely need to be far larger still. You're probably talking about a 2.5 to 3 times bigger missile. While a country that could develop one could likely develop the other if they so chose, it doesn't seem like a safe assumption that a country with one has the other.
I dont think that it is correct to assume your interceptor needs to match velocity. Any speed will do if you can intercept it on approach instead of chase it down.
I'm not assuming the interceptor needs to match velocity. There is some point you detect the target x1, and some range for your missile from your position x0 to an interception point x2. Your interceptor needs to get from x0 to x2 by the time the time the target gets from x1 to x2. If your target is travelling 37.5% faster, you have 27.2% less time to get to the interception point, which means that you need to fly 37.5% faster, which requires 89% more kinetic energy, regardless of what the baseline speed required was. Alternatively you need to detect things from further away or fire from a closer distance, both of which pose their own issues.
That's not quite correct, is it? Consider shooting at a bird. A falcon travels twice as fast as a pigeon, but you don't need a bullet that is twice as fast to shot the falcon. You simply adjust the lead distance when you shoot at the falcon. In your argument you assume that you need to cover some distance in the same amount of time, but you don't need to. You simply lead the target a bit more. As for detection time, well, it is basically a guarantee that whoever is considering shooting at a space plane, has the tracking capabilities to know its position at all times. If they don't, they probably can find some reddit where people do that out in the open.
In this scenario increasing lead distance is equivalent to detecting and firing earlier (ie increasing distance between x1 and x2), which again has serious technical issues. Yes you can hit a falcon with the same bullet, but it's harder to hit. And the big difference in these scenarios is that the bullet is moving much faster than either the pigeon or the falcon, which means you can always buy more time for the falcon to get to the interception point by taking a less efficient path, whereas for the satellite interception where your interceptor is slower than the target, there is some optimal path (basically straight up from right below perigee) that sets a hard limit on how long it takes to get to any interception point.
If your interception point is say 500 km straight up from your launch point, just to get there you need a rocket that rapidly accelerates to over 3 km/s, and it takes a little over 5 minutes to get to the interception point. To hit an 8 km/s target, you need to fire when it is 2500 km away, to hit an 11 km/s target you need to fire when it is 3500 km away. If to score a hit you need to be within 10 meters of the target at interception, then you need to know the position and velocity of the 8 km/s target to within 4 ppm, you need to know it with an accuracy within less than 3 ppm. And note, if you are shooting from 15 km up in a fighter jet, the 8 km/s target is within your radar horizon, the 11 km/s target is not. Not to say that you couldn't build a system with target sharing and more precise tracking, but it would be a different system than the one you need for the less challenging use case.
Now it's not a strictly either or thing. You could use a missile with intermediate speed and fire it less early. There's a whole continuum of solutions, but it will always be harder to hit the faster moving target. And of course you have real world things to consider like if the target has any maneuverability or countermeasures and how much variation in conditions you can afford. Generally you are already using the best targeting system you can get and are already in the most advantageous position you can be in, so the knob you can turn is "how big of a missile do I need to get the performance I require?"
Agreed, it all depends on the use case. If you are trying to hit an evading target, you have to be faster. If you are trying to deny the ship from a destination, you don't.
If the ship's current position is 200 miles from its destination and you are 400 miles from its destination, you need to go faster than it to deny the ship from its destination. Conversely, if you are 40 miles from its destination, you can go much slower, though if you go too slow you still won't make it. You have to get to a point ahead of it before it gets there, and the faster its moving, the less time you have available to get to any particular point.
Dealing with evasion is a whole other matter. A stationary iceberg can hit a ship that tries to evade if it does so too late. Conversely simple error in your knowledge of a ship's position and velocity can cause it to be miles away from where you expect it later in the journey.
Like the parent says, you already know where it is. I'm struggling to understand the case where you are further from the destination than the x37B, with an orbit 60,000km from earth.
The parent is incorrect. You know approximately where it is. If your approximation is off by some amount, you miss. How good of an approximation you have is determined by your detection equipment. How good of an approximation you need is determined by the speed. For the same detection equipment, hitting the faster moving thing is harder.
Well yeah, that's because the x37B interception scenario is the second case, where you are much closer to the destination but going much slower.
I thought the fundamental hypothesis under discussion here was that the x37 has the orbit to move quickly and avoid interception. It being the second case seems to rule against that hypothesis being true
That is the hypothesis here, and the second case in no way rules against it.
Again to clarify, no one here is arguing that to intercept a target you have to be moving faster than the target. The argument is you have to be moving faster than the minimum speed required to hit a slower target.
In math terms, you have two targets with velocites V1 and V2. To intercept there is some minimum velocity for each, v1 and v2. This is the best case scenario, you are perfectly in position, you can launch at the earliest possible time. v1 < V1 and v2 < V2 are both true. But since V1 < V2, v1 < v2 is also true. An interceptor that can achieve v1 doesn't necessarily have the capability to achieve v2.
I don't think that is quite right. You can hit a satellite with a suborbital projectile. The kinetic energy of the satellite is enough on its own if you hit it.
It's not about energy required to destroy it, it's about speed required to get to it.