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So, imagine a 22th-23th century human space-faring civilization which has settled several colonies on asteroids and moons (not too different from our own Moon, for the sake of comparison).

Suppose that there is the need to define the position for a "last line of defense" around the colony itself, in case of enemy starship attack / bombing (let's say, internal rebellions, conflicts between colonies, conflicts between colonies and Mother Earth).

My idea was to define the Bell-Kann Edge (from the fictional two guys who theorised it in my story):

The Bell-Kann Edge is defined as the distance from the colony which prevents spacecrafts deployed from surface from intercepting incoming enemies before they can gain air (space) supremacy. The enemy ships are considered moving at full velocity, while the defending ships are considered unmanned and parked at the instant the Edge is reached by the invading force.

I'll try to explain it better:

when a number of enemy starships overcome the Bell-Kann edge, they are actually able to destroy spaceports and landed starships before they could effectively take off to retaliate.

Provided that colonies like that would have not a thick atmosphere, we can think about it like everything is in vacuum (so, no atmospheric friction and so on). Also, consider that AA defenses are not taken into account since the Bell-Kann Edge is considered to be a worst-case-scenario definition.

Obviously, there are several hypothesis this definition is based on (knowledge of the maximum velocity of the enemy spacecrafts, minimum time needed to deploy a spacecraft from land, efficiency of enemy weapons, and so on), leading to an evolving definition of the Edge during the war...

So, it comes the question:

  • Is there a way to smoothly define this concept in order to rely on a smaller number of parameters?
  • If not, how could it be improved?
  • Considering this definition reliable, it would make sense to locate a permanent line of defense in proximity of the Bell-Kann Edge, so that landed spacecrafts could have time to take off while the preliminary troops try to contain the enemy?

I am looking for scientific / pseudo-scientific answers with some touches of military strategy :)

Bonus question:

  • How can this definition be extended to planets with Earth-like atmosphere?

I hope this is not too broad or off-topic :D If so, I will try to squeeze it to the bones ;)

Edit: the definition has been updated following @Mike Nichols's comment, in order to be more precise. As regards @Frostfyre's comment, if expanded in a complete answer I could think about accepting it :D

Edit 2: after having read this answer, this answer and this answer, I think I have found a better way to define it in a reasonable manner:

The Bell-Kann Edge is defined as the distance from the colony which prevents spacecrafts deployed from surface from intercepting incoming enemies before they can gain air (space) supremacy. The enemy ships are considered moving at full velocity, while the defending ships are considered unmanned and parked at the instant the Edge is reached by the invading force. This definition can be applied only in case of direct spacecraft attack from an enemy and doesn't take into account long-range bombing.

So, with this adjustment the definition becomes valid only in case of direct engagement (that is, scenario number 3 in @Mike Nichols's answer), since - as @Kolaru stated - space bombing would have no actual limitation (safe for "damage control"). And, yes, it would have some political/military implications as @Cort Ammon stated.

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    $\begingroup$ The Bell-Kann Edge is planetary orbit, unless you want us to ignore the possibility of orbital bombardment. $\endgroup$ – Frostfyre Aug 28 '15 at 13:13
  • $\begingroup$ I'd say the Edge will change based on the speed and armaments of the enemy, as well as the speed and armaments of your parked ships. Just find out how long it takes for your ships to take off, and compare it to how long it takes the enemy to get within firing range. $\endgroup$ – DaaaahWhoosh Aug 28 '15 at 13:19
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    $\begingroup$ Something to consider is that your "edge" will be different depending on the velocity of the enemy ship. I don't mean the "speed" of the ship or how fast it is. What I mean is how fast it is going. A ship parked just outside the "edge" will take longer to reach its target than a ship far outside the edge that is already moving towards the target at a significant speed. So your edge isn't a one size fits all distance but should be some function of distance and relative velocity. $\endgroup$ – Mike Nichols Aug 28 '15 at 13:56
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    $\begingroup$ Isn't the Bell-Kann Edge the first line of defense? Or a very serious middle line? Everything beyond the BKE is offense. The last line will be on the ground around whatever resources are important enough that the invaders would not want to destroy them from orbit. $\endgroup$ – DeveloperWeeks Aug 28 '15 at 16:00
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    $\begingroup$ For example, if I can force a planet to waste its fuel by repeatedly hopping over the Bell-Kann line, then retreating, then either the definition was poor, or the actions associated with the line were not sufficiently wise. $\endgroup$ – Cort Ammon Aug 28 '15 at 20:48
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As Kolaru has pointed out there is no maximum engagement range in space, especially against stationary targets. If one asteroid base wanted to destroy another one they could simply launch missiles, accelerate projectiles, or fire lasers from their own base in order to destroy the enemy base's retaliatory capabilities. There are 3 possible outcomes to such an offensive action based on the technology available to the defenders. Which one you choose will result in very different outcomes on how war is conducted in your universe.

  1. The base under attack is unable to detect the incoming attack before it is destroyed. In this scenario every base has first-strike capability. This is not a stable scenario. Any perceived threat will escalate to a full attack because each base will recognize that unless it destroys all other bases with offensive capabilities it will be destroyed by one of them. Essentially, strike first or someone else will. This situation is unlikely to develop as once one base develops offensive capabilities it can impose its will on the other bases and prevent their own weapon development. But even if multiple bases developed long range strike capability around the same time they would not coexist for long, unconditional war would be inevitable.

  2. The base under attack is able to detect incoming attacks in time to launch counter-attacks, but is unable to effectively defend from the incoming attack. This scenario is analogous to modern nuclear warfare in which the deterrent to attacks is mutually assured destruction. Warships could exist in this universe as a means of extending counter-attack capabilities, but all-out war is very unlikely to occur in this scenario. The only winning move is not to play.

  3. The base under attack is able to detect incoming attacks in time to defend against them. This could be through the use of active counter-measures like point-defense This is the most interesting scenario as long-range attacks are no longer effective. This means that for one force to effectively damage another they need to get in close so the defenders don’t have enough time to react to incoming attacks. Therefore they need to use ships. In this scenario a very meaningful “edge” would be the distance at which fire from an enemy ship could no longer be reliably defeated by active counter-measures. If enemy ships entered within this envelope they would essentially have first-strike capability and could knock out defensive military installations before those installations could react, winning the battle handily. This distance would be the point at which the time on target of the offensive armament is equal to the time it takes light to travel that same distance plus the time it takes the defensive systems to react. Getting back to the original question’s concept of “air superiority”, it seems to me that if defensive ships can launch unmolested then they will be capable of mounting some defense. The entire force could be launched and could muster near the surface and under the umbrella of the defensive systems. This means a fleet exerting air superiority on a defensive force must be able to target ships as they launch, while they are outnumbered and restrained in their ability to maneuver. But if an enemy fleet can hit ships as they are launched then surely they are also capable of destroying those launch facilities and any other military targets on the surface. Therefore the “edge” would still be the point at which no sane space-based resistance could be attempted.

I hope this line of reasoning makes sense. It may not be exactly what you are looking for, but I found your question very interesting and I wanted to share my thoughts.

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  • $\begingroup$ Upvote! The third point summarizes exactly what I wanted to convey with my question :D The third scenario is really the most interesting and actually make totally sense in my mind! Man, there are too many good answers, it will be a pain to choose one! :D $\endgroup$ – Andrea Jens Aug 29 '15 at 12:57
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The line would be very effective for a civilization which has unbeatable star ships, and just has to get them off the ground.

If I may take your wartime defintion, and strip it down to a comparable information theory definition:

The Bell-Kann Edge is an edge defined by an information oracle (such as radar) and a defensive capability (the star ships). It is the line at which, if the oracle announces an attack, the defensive capability has just enough time to engage in a specified capacity.

The only time the Edge is useful is if you are unaware of anyone approaching the line. If you are aware, you should be maneuvering your troops to defend. Also, the line is defined to just be the point where they cannot gain supremacy. However, such a line is not actually a line, its more of a probability. There's a % probability of gaining superiority, or losing it, unless your star ships are so unbeatable that you're 100% certain to defeat them if you launch.

In reality, nobody cares about the point where there is a 0% chance, unless you have weapons-of-last-resort to use after the starships fail. One usually cares about a much higher percentage, like 50% or 90%.

However, it could also be thought of as part of a Playing Possum tactic. If you are playing possum, you do care about the point where you actually cannot defend yourself any more. At that point, you have to start showing activity on the ground to scramble fighters. This could be effective if dealing with groups like the Reavers from Firefly, where being quiet is one way to get them to go away.

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  • $\begingroup$ This is the best answer until now IMHO. I have only one remark: Bell-Kann Edge would be useful even if you are aware of the enemy approach: if your troops get overwhelmed at Bell-Kann Edge, you have to quickly reorganize what's left of your army taking into account that the enemy could gain air supremacy :D $\endgroup$ – Andrea Jens Aug 28 '15 at 22:17
  • $\begingroup$ My experience with warfare is that in 99% of the cases, you don't want to have to rely on your model being accurate. The enemy will always surprise you. Accordingly, any general overseeing a battle that is approaching the Bell-Kann Edge should have already begin reorganizing to be ready for the possibility that air supremacy could be lost. However, you do bring up a point. Such a line would be valuable in a political situation where the citizenry is intentionally not allowed to know how the war is going. Mobilizing ground troops would reveal the state of the war, so the generals... $\endgroup$ – Cort Ammon Aug 28 '15 at 22:51
  • $\begingroup$ ... might choose to delay mobilizing ground troops until the last possible moment. I could see this occurring in a situation where a General would rather risk losing their entire planet instead of risking political fallout of mobilizing troops. $\endgroup$ – Cort Ammon Aug 28 '15 at 22:52
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There is two main scenarios in my opinion :

  1. The attackers bombard the planet from outside the radar range of the defender.

If you are far away (order of "light day" for example), you can just accelerate your missiles near the speed of light (providing they carry enough fuel) and by calculating beforehand their trajectory, make them hit they targets. Due to the speed of the projectiles, they will most probably be hard to intercept. If the planet in question orbits around a star, you can even hide the missiles behind the star (this is actually a fear scientists have about meteorits : if they come from behind the sun, we will not be able to detect them in advance, due to the radiations of the sun "shadowing" everything behind it).

In the case the Bell-Kahn Edge is infinity. If you plan your attack long enough in advance, you can virtually hit any point of universe from anywhere (well, there is other things to take in account if you would really want it from anywhere, like universe expansion or unpredictability of planets orbits on very long scale).

  1. The attackers come very fast and then stop near the planet to bombard it.

In this case (more interessant regarding your question), the Bell-Kahn Edge will be define by the capacity of the attacker to deccelerate. Once again I assume that if you are patient enough and have enough fuel, you can reach near the speed of light, by being shadowing by a star, you can totally surprise the defenders.

But then you have to stop to avoid both crashing into the planet (you don't care if you are a missile, YOLO) or being unable to stay in the planet's orbit. So you have to deccelerate.

Lets make some assumption to make a fancy physics calculation. Assume the attackers' vessels are manned, then the maximum acceleration their crew can whistand is about $10 g$ which is about $100 m/s^2$. Assume they come from behind the nearest star, which is at about $150 \cdot 10^6 km$ away (distance sun-earth). Assume finally that the attacker must have a velocity of 0 to attack.

If you make the (non relativistic) calculation you find that the maximum speed of the attacker (if subject to a constant decceleration of $10 g$ which would kill most human) is $5.5 \cdot 10^6 m/s$ or about $1.8\%$ of the speed of light.

Then you have your maximum velocity. Note that the journey from the star to the planet would, in this case, take $5.5 \cdot 10^4 s$ or about 15h30.

Knowing the fastest way to approach the planet, you can know deduce where you should place the Bell-Kahn Edge.

To answer your third question, in fact it would not only make sense to station defences at the Bell-Kahn edge, but it would make sense to station all your defences there, since you will need less time to deploy your troups from there and you will probably be able to hit the planet quite fast as well if needed.

EDIT

In the case of very long range bombing, the question arised to know if it is possible without anhiliating the target. Here is a bit of information to judge it ($c$ stands for the speed of light, HB stands for the energy of the Hiroshima Bomb (63 TJ)). I assumed that mass does not transform into energy upon impact, since I do not know how to estimate the amount of mass transformed.

  • Projectile speed : $0.5 c$ ; energy by kg of mass : $1.39$ PJ $= 21.9$ HB
  • Projectile speed : $0.6 c$ ; energy by kg of mass : $2.25$ PJ $= 35.8$ HB
  • Projectile speed : $0.7 c$ ; energy by kg of mass : $3.60$ PJ $= 54.8$ HB
  • Projectile speed : $0.8 c$ ; energy by kg of mass : $6.0$ PJ $= 94.9$ HB
  • Projectile speed : $0.9 c$ ; energy by kg of mass : $11.65$ PJ $= 186.1$ HB
  • Projectile speed : $0.95 c$ ; energy by kg of mass : $19.82$ PJ $= 313.9$ HB

So yes, using very fast projectiles, you can totally ravage a planet, and most probably any space craft on its trajectory.

But since you can use very small projectile (an apple weighting $100$ g at $0.5 c$ is still more than $2$ HB), they may be undetectable and target specific strategic areas without blowing up the whole planet.

But anyway, Ihave no definitive answer on wether such bombardment is feasible without destroying the planet, that becomes, in my opinion and for my knowledge, too technical.

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  • $\begingroup$ Well, the infinite-range bombing is a tactic I have never considered :D Seriously, when you take off atmosphere, friction and so on, things become really weird and interesting at the same time ;) By the way, have you considered that in case 2, ships has even to be maneuvered (I suppose straight line trajectories are not so good in a space filled by debris and small chunks of matter ;) )? At millions of m/s, a single wandering rock could severely damage the hulls, so - maybe - numbers could be refined a bit. BTW, you have an upvote for the ideas exposed :D $\endgroup$ – Andrea Jens Aug 28 '15 at 15:26
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    $\begingroup$ Very good answer; I only want to point that the first option could make it very difficult fo the attacker to do anything other than planetary anhilation (any sizeable object moving at a significant fraction of c has lots of mass and energy). So, that would be a strategic retraint forbidding your attacker to perform that kind of attack if his objective is to conquer your planet. $\endgroup$ – SJuan76 Aug 28 '15 at 17:24
  • $\begingroup$ @SJuan76 You can always choose a smaller projectile though. $\endgroup$ – 2012rcampion Aug 28 '15 at 17:29
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    $\begingroup$ @2012rcampion which would also be easier to deflect due to the smaller mass (maybe not preventing impact with the planet, but avoiding the destruction of the critical power plant/military factory/astroshipyard/etc.) Everything has pros and cons. $\endgroup$ – SJuan76 Aug 28 '15 at 17:34
  • $\begingroup$ @SJuan76 and this is exactly one of the reasons why I couldn't think of long-range bombing as a viable attack solution :D $\endgroup$ – Andrea Jens Aug 28 '15 at 22:14
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Well the first issue in figuring out this limit is knowing the reaction time of your defenses. If it takes 5 minutes from warning to armed response then you need to make sure your 'warning' gives a minimum of a 5 minute response time.

Then you need to know the max speed any attack force can come at you. Once you know how fast they can attack, and the speed at which your people/sensors can identify and notify home base of the incoming ships/projectiles, you can calculate how far out these outposts need to be in order to warn in enough time to have a viable response.

Space is big. Very big and when things are moving fast, there is no 'last line' of defense, but a minimum warning distance for a reasonable reaction time. You need sensors/outposts that can 'see' what is out there and where it is headed and identify destinations accurately. If a ship is traveling @ 50-100K miles/hr you need to see it coming a LONG way away. At 100K mph you need to spot the ship 8500 miles away to give a 5 minute warning. a small asteroid would have an internal 'surface area' of 1,446,264,375,000 sq. mi. to 'watch' at that distance. The Earth would have a MUCH larger area to monitor.

So ultimately the 'last line of defense' is knowledge. Knowing where everything is and where it is going within a large sphere around the possible target.

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  • $\begingroup$ The idea was more finding a uniform way to define this concept. This would make sentences like "they have overcome Bell-Kann Edge" be translated as we are screwed... but, yes: Bell-Kann Edge would be a sort of a minimum warning distance for a reasonable reaction time - not a bad definition :D You have my upvote, but I'll wait for some more answers before marking it as accepted ;) $\endgroup$ – Andrea Jens Aug 28 '15 at 14:59
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For most practical purposes, the various defense zones would probably collapse into a one light minute zone where the sensors can make accurate observation of the incoming craft, and a one light second zone where your weapons can effectively engage.

This is actually freakishly huge compared to the typical SF movie or TV show where the weapons might as well be muzzle loading cannon due to the short ranges depicted; a massive laser weapon with a one light second range means targets could be effectively engaged at almost the distance from the Earth to the Moon (note a laser that powerful would actually be able to burn deep lines on the Moon itself, since the beam is still dangerous beyond one light second). One light second is a rather arbitrary distance selected because most incoming spacecraft, weapons or even debris isn't going to move very far in the second between lining up on the target and the beam reaching the target. The gunnery officer or AI will also be able to see the effect one second later, and make appropriate corrections or shift to a new target at that time.

Countering with a missile is going to be difficult, consider that it took New Horizon about 9 hours to fly past the Moon after launch, and this is the fastest spacecraft yet built. That is a lot of seconds for the gunnery officer to use when carving incoming spacecraft into finer and finer slivers.

In the Atomic Rockets website, the mechanics of such a Ravening Beam of Death (RBoD) are discussed in the Space Warfare section, a Free Electron Laser (FEL) can generate a beam at x-ray frequencies capable of vaporizing metal, ceramic or carbon fibre in milliseconds at one light second range, but the electron beam accelerator would be one kilometre in diameter. Rocketpunk Manifesto has a multitude of posts devoted to space warfare, and the only counter for a RBoD is to flood the sky with tens of thousands of tiny kinetic energy projectiles, a saturation attack where the number of targets is far more than the beam can effectively destroy before they impact. The name these were given was "Soda Cans of Death" (SCoD) based on the calculated size.

So space warfare isn't a linear exercise. Pickets of long range sensors will be able to see incoming spacecraft from huge distances (the Space Shuttle's main engine could theoretically be detected if the SSME was fired near Neptune, and even the small manoeuvre thrusters could be seen from as far away as the Asteroid belt from Earth), the real limiting distance is based on how fast the weapons or ships travel, since they can be engaged at the speed of light. The only weapon which has no effective counter that I know of would be a missile coming in at relativistic velocity. When you see it, you are seeing its position in the past, so intercepting it will be almost impossible with any known technology.

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