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.
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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.