Future Point Defense Options

SWM wrote:

SharkHunter wrote:Was reading another thread dealing with time dilation, and a somewhat obvious problem occurred to me in terms of long range missile interception without FTL, I think...

Let's say you have an attack missile coming at your ships at a high percentage of C. Your CM goes out at high G's to intercept, but... the combined closing speed at some point becomes faster than C. That seems to preclude "seeing" an oncoming attack missile at all, unless the CM's seekers can also pick up gravitic "wave energy" off of the shipkiller's wedge, correct? and I think the CM's available telemetry size is too small for that.

Am I missing something, or does this preclude extended range missile interceptions without an ACM or Mycroft/KHII based solution?

This is a common question about Relativity. It turns out that if you apply all of the Lorentz equations correctly, you never get the situation you are worried about. From the perspective of the counter-missile, the velocity of the oncoming attack missile is less than the speed of light. The Lorentz equations can be combined together to create an equation for this: if Frame A measures the velocity of Frames B and C, the equation will tell you the velocity of Frame B from the perspective of Frame C. It is called the Relativistic velocity addition formula, or composition law for velocities:
s = (v + u)/(1 + (vu/c^2))
where v and u are the velocities of Frame B and C as seen in Frame A, and s is the velocity of Frame B as seen in Frame C (or the velocity of Frame C as seen by Frame B).

But objects can appear to be going faster than light. E.g. if a missile is coming toward you at 0.8 c, the image of it when it was n light-sec away will reach you only 0.25 sec before the image of when it was n-1 lt-sec away. Cf. 'superluminal motion'.

--snipping the math--

SharkHunter wrote:Let's say you have an attack missile coming at your ships at a high percentage of C. Your CM goes out at high G's to intercept, but... the combined closing speed at some point becomes faster than C. ...am I missing something, or does this preclude extended range missile interceptions without an ACM or Mycroft/KHII based solution?

SWM wrote:... From the perspective of the counter-missile, the velocity of the oncoming attack missile is less than the speed of light.
...

It took me quite a bit to work the math out, but once I did it became easier to visualize with the idea of frames. It also explains why "tail chasing shipkillers" are not as successful in their attacks, such as Haven's at First Hancock or Solon, Tourville running away from the RMN at Sidemore, etc. and why the Mark-23E guided shipkillers are such a copperplated -itch to stop as they are updating faster than the op force CMs can get signal.

Examples being, if an MDM reaches .7C chasing "you" but you're running at .3C, the overtake is only at .4C. Meanwhile, your own CM's are getting their intercept readings from the attackers missiles which is "bringing the arrow to your calculator shield" in terms of signal but requiring a longer actual interception period.

The ACM screws with the balances that existed in the offensive vs. defenses equation because no the difference due to the FTL link will almost always be quick enough to generate "impossible to intercept vectors" for a majority of the attacking missiles. Then the RMN tosses in the just recently updated Dragon's Teeth and Dazzlers just to make it totally unfair.

--snipping, re math that adds up to higher than C--

Bill Woods wrote:But objects can appear to be going faster than light. E.g. if a missile is coming toward you at 0.8 c, the image of it when it was n light-sec away will reach you only 0.25 sec before the image of when it was n-1 lt-sec away. Cf. 'superluminal motion'.

...which also gives you a rate of closure and therefore the speed / accel for the CMs or shipkillers from the OpForce.

Which also gave me the "oh duh, answer answer" to how HMS Madrigal [all the way back in HotQ] knew that "those are modern missiles!" so quickly", even just with gravitic detection and light speed sensor links. All they had to do is calculate the differential between their own speed, C, and the "expected time of appearance in position Y" relative to a calculated 'point X' in space.

Bill Woods wrote:

SWM wrote:This is a common question about Relativity. It turns out that if you apply all of the Lorentz equations correctly, you never get the situation you are worried about. From the perspective of the counter-missile, the velocity of the oncoming attack missile is less than the speed of light. The Lorentz equations can be combined together to create an equation for this: if Frame A measures the velocity of Frames B and C, the equation will tell you the velocity of Frame B from the perspective of Frame C. It is called the Relativistic velocity addition formula, or composition law for velocities:
s = (v + u)/(1 + (vu/c^2))
where v and u are the velocities of Frame B and C as seen in Frame A, and s is the velocity of Frame B as seen in Frame C (or the velocity of Frame C as seen by Frame B).

But objects can appear to be going faster than light. E.g. if a missile is coming toward you at 0.8 c, the image of it when it was n light-sec away will reach you only 0.25 sec before the image of when it was n-1 lt-sec away. Cf. 'superluminal motion'.

That is true, and you have a good point--the counter-missile will observe this effect while tracking the targeted missile. But it will still be able to see the missile the entire time that it is approaching. This effect will not change the amount of time that the counter-missile has available to track the missile. The apparent superluminal motion does not change the ability of the counter-missile to target the missile (though the time dilation does).