At What Rate Of Constant Acceleration Is Earth No Longer A Threat?

[Spacescifi]

 

So for this scifi scenario, you have a 1000 ton spaceship capable of 2g constant acceleration while fully loaded.

No propellant required for the sake of discussion.

You are in LEO. Several Earth nations decide they do not like you and launch 500g acceleration missiles (burn time is a few seconds at best so they are more or less like suborbital bullets).

I suspect that 2g is more than enough to escape the onslaught after you detect the launch, while taunting them via broadcast as you break orbit.

Let's also assume you are orbiting over the Pacific ocean about to fly over China.

Question: What is the lowest constant acceleration rate of g where Earth based forces could not reliably hit you in orbit?

It is interesting though, since as common as constant acceleration is in scifi, if you take that up against modern technology it becomes clear to see that we probably could not even reliably hit them in orbit. Lasers work sure, but people know that lasers are not all that good at hitting distant space targets unless the lens is huge due to beam spread.

 

What do you think? Is constant acceleration of 1g or 2g so much that Earth could never hit them from the ground with current technology?

If so.... this seals all those war of the worlds scifi stories. Since assuming they have good thrust constant acceleration, they will always have the highest 'ground' and we will NEVER hit them unless we build a giant laser lens or they are foolish enough to land. When they could do orbital bombardment all day until they run out of ammo instead.

They won't even need scifi shields.

What do you think?

 

 

Edited May 26, 2020 by Spacescifi

[Xavven]

Undoubtedly you could build a missile that would hit a craft only capable of pulling 2 G as long as it had a way to steer in the upper atmosphere and space. Surface to air missiles in real life that are designed to shoot down aircraft are multi-stage and use the atmosphere to steer. Many of them today can pull 30 G, and they have to maneuver hard in order to intercept a maneuvering target. A defending aircraft attempts to fool the seeker with decoys (chaff and flares), attempts to break lock by flying in the doppler notch of the illuminating aircraft or missile (by flying 90 degrees from the direction of the emitter) and attempts to defeat the missile kinematically by forcing the missile to make the greatest amount of turning to make an intercept, depleting its energy, and the greatest distance, basically making it run out of airspeed until it can't maneuver or reach the aircraft any longer. Generally, the closer the range to the target when the missile is launched, the greater the chance of successful intercept despite the target maneuvering at, say, 9 G, and even turning to run at Mach 1.4.

If these missiles in your sci-fi scenario have no way to steer at all, then yeah, sure, 2 G of maneuvering would defeat anything since the time of flight would be so long, there's no way you could predict where the target would move to by the time the missile gets there. But nobody builds missiles like that. They are meant to steer to their target, not act like dumb bullets. Any nation attempting to intercept such a space craft would need to build a missile that could turn harder and fly faster than it.

Edited May 26, 2020 by Xavven

[Spacescifi]

12 minutes ago, Xavven said:

Undoubtedly you could build a missile that would hit a craft only capable of pulling 2 G as long as it had a way to steer in the upper atmosphere and space. Surface to air missiles in real life that are designed to shoot down aircraft are multi-stage and use the atmosphere to steer. Many of them today can pull 30 G, and they have to maneuver hard in order to intercept a maneuvering target. A defending aircraft attempts to fool the seeker with decoys (chaff and flares), attempts to break lock by flying in the doppler notch of the illuminating aircraft or missile (by flying 90 degrees from the direction of the emitter) and attempts to defeat the missile kinematically by forcing the missile to make the greatest amount of turning to make an intercept, depleting its energy, and the greatest distance, basically making it run out of airspeed until it can't maneuver or reach the aircraft any longer. Generally, the closer the range to the target when the missile is launched, the greater the chance of successful intercept despite the target maneuvering at, say, 9 G, and even turning to run at Mach 1.4.

If these missiles in your sci-fi scenario have no way to steer at all, then yeah, sure, 2 G of maneuvering would defeat anything since the time of flight would be so long, there's no way you could predict where the target would move to by the time the missile gets there. But nobody builds missiles like that. They are meant to steer to their target, not act like dumb bullets. Any nation attempting to intercept such a space craft would need to build a missile that could turn harder and fly faster than it.

 

Cold war.  Called sprint missiles. Designed to take out an ICBM during launch. Likely did have staging, but I doubt the final stage was anywhere near as thrusty as the first.

Granted you are right. 

So it is possible to hit a 2g target trying to escape orbit.

You would have to stage the missile with the most thrustiest solid and chemical propellant known to man though. Since the ship in question is trying to literally break orbit into deep space the moment it detects the launch.

The best way to pull off tge launch is high altitutude aircraft launching the missiles, to shorten the distance to the target.

Edited May 26, 2020 by Spacescifi

[magnemoe]

2 hours ago, Spacescifi said:

Cold war.  Called sprint missiles. Designed to take out an ICBM during launch. Likely did have staging, but I doubt the final stage was anywhere near as thrusty as the first.

Granted you are right. 

So it is possible to hit a 2g target trying to escape orbit.

You would have to stage the missile with the most thrustiest solid and chemical propellant known to man though. Since the ship in question is trying to literally break orbit into deep space the moment it detects the launch.

The best way to pull off tge launch is high altitutude aircraft launching the missiles, to shorten the distance to the target.

sprint was nuclear armed, however ICBM warheads might have some cold gas trusters to fine tune its trajectory by a couple of m/s. 
Same is true for stuff like standard missile with its kinetic warhead who is far more agile but also have very limited dV as its for fine tuning only.  

An missile you use against an spaceship would need an high trust warhead / upper stage who would let it counter the random burns of the spaceship. 
In short you launch the missile into an suborbital trajectory, then it comes close to the ship it start an second burn to intercept. 
An ICBM could work here if you used upper stage for this. 

I assume this is how you would use missiles in space anyway. an initial burn to get an rough intercept, then an second burn then close. 
 

[Nuke]

usual anti satellite weapons use the target's own momentum to do the damage as they are often launched on suborbital trajectories. a couple gs of acceleration would get you to escape velocity pretty fast, but probably not fast enough to avoid the intercept of one of these munitions provided the were launched around the time the target started its burn. however these weapons are for targets in static orbits with very little thrust for collision avoidance and might not have the deltav to compensate for evasive maneuvers from the target. of course if you shotgun the asat warheads, like send up a bunch of them to increase the size of the skill zone, or perhaps have them detonate into submunitions to cover even more area. even something the size of an airsoft pellet could be quite devastating to a target at orbital velocity. even then its kind of iffy. if these asat weapons are in fact capable of more delta-v (effectively anti-torch ship missiles) then the target might not have a chance as we certainly have engines that can beat 2g, however now were talking a massive rocket that might be too large to be air launchable. if launched from a fixed ground base it might be plausable to burn in such a way that you simply never come into its firing arc.

Edited May 26, 2020 by Nuke

[Spacescifi]

16 minutes ago, Nuke said:

usual anti satellite weapons use the target's own momentum to do the damage as they are often launched on suborbital trajectories. a couple gs of acceleration would get you to escape velocity pretty fast, but probably not fast enough to avoid the intercept of one of these munitions provided the were launched around the time the target started its burn. however these weapons are for targets in static orbits with very little thrust for collision avoidance and might not have the deltav to compensate for evasive maneuvers from the target. of course if you shotgun the asat warheads, like send up a bunch of them to increase the size of the skill zone, or perhaps have them detonate into submunitions to cover even more area. even something the size of an airsoft pellet could be quite devastating to a target at orbital velocity. even then its kind of iffy. if these asat weapons are in fact capable of more delta-v (effectively anti-torch ship missiles) then the target might not have a chance as we certainly have engines that can beat 2g, however now were talking a massive rocket that might be too large to be air launchable. 

 

Interesting. So it turns out that if you have a spaceship and notice sateites around a planet in low planetary orbit, that area if you decide to enter it is a potential kill zone. It's hardly safe. Even more so if you don't have unlimited fictional acceleration of a few g.

So a common sense commander would think twice before doing so, perhaps sending a probe to low planet orbit first. If they blow that up (the planet) then they automatically go on the hostile no fly list.

I know scifi depends on scifi shields to save them but I digress. Realistically high power lasers or a project Excalibut that actually worked everytime would be an optimal albeit expensive solution.  Since lasers create lots of waste heat and project Excalibur weapons are far from simple to build. They are complex devices.

Edited May 26, 2020 by Spacescifi

[Nuke]

15 minutes ago, Spacescifi said:

 

Interesting. So it turns out that if you have a spaceship and notice sateites around a planet in low planetary orbit, that area if you decide to enter it is a potential kill zone. It's hardly safe. Even more so if you don't have unlimited fictional acceleration of a few g.

So a common sense commander would think twice before doing so, perhaps sending a probe to low planet orbit first. If they blow that up (the planet) then they automatically go on the hostile no fly list.

I know scifi depends on scifi shields to save them but I digress. Realistically high power lasers or a project Excalibut that actually worked everytime would be an optimal albeit expensive solution.  Since lasers create lots of waste heat and project Excalibur weapons are far from simple to build. They are complex devices.

i think common sense would dictate not approaching a planet with space launch capabilities. satellites are a good indication that the possess anti-sat capability. you might also want to look for evidence of nuclear weapons testing.  if you dont see either of these things you might have found a target ripe for invasion or at least something safe to approach. 

it wouldn't be too hard to stick some passive surveillance hardware on a small piece of natural space debris and send it on a flyby, and then either have it do a tight beam broadcast or go pick it up to return its findings. if someone on the ground saw the thing they would just see space debris. we see that all the time and its never out of the ordinary. that way you can get intel without risking detection.

 

[kerbiloid]

4 hours ago, Spacescifi said:

sprint missiles. Designed to take out an ICBM during launch.

During launch they could take out only US ICBM.

They were to intercept the RV, like others.

Edited May 26, 2020 by kerbiloid

[magnemoe]

1 hour ago, Spacescifi said:

Interesting. So it turns out that if you have a spaceship and notice sateites around a planet in low planetary orbit, that area if you decide to enter it is a potential kill zone. It's hardly safe. Even more so if you don't have unlimited fictional acceleration of a few g.

So a common sense commander would think twice before doing so, perhaps sending a probe to low planet orbit first. If they blow that up (the planet) then they automatically go on the hostile no fly list.

I know scifi depends on scifi shields to save them but I digress. Realistically high power lasers or a project Excalibut that actually worked everytime would be an optimal albeit expensive solution.  Since lasers create lots of waste heat and project Excalibur weapons are far from simple to build. They are complex devices.

You could use lasers for defense, couple of hundred KW should take out something who maneuver to intercept fast. 

An nuke pumped x-ray laser on the other hand would be more like an anti spaceship weapon. Very dangerous as it have an laser level range so you could just put some in orbit like mines. 
Also nice as missile warheads since you do not need to get close. Again dangerous as you can always make this warhead very hard to spot. 
In this case having high trust is nice 

[farmerben]

A suborbital projectile is somehow propelled toward a target in Leo (~125 km altitude) at 500g.  It closes this distance in less than 7 seconds, but lets go with 7s if we are not taking the shortest path.  

The target maneuvering at 2g can alter its position relative to expected position by about 1/2 a kilometer.  

The missile needs about 0.4s or 6% of its total to anticipate and respond to the most basic evasive maneuver.

Assuming the missile has finite propulsion, then the target will be much safer at long range.  If infinite propellant, not so much.  But the time the evasion can waste certainly increases with more range.  

Which evasive maneuvers are the most effective?  If you were the pilot of the target spacecraft what would you do?

 

I'm going to use maximum rotational thrusters in the plane perpendicular to the distance vector of the incoming projectile, and fire the main engines with maximum possible thrust at first.  Then introduce some randomness the closer the projectile comes.  So halfway to impact I might choose numbers between 90%-100% of maximum possible primary thrust, without significantly changing my direction of angular acceleration.  Only in the final second or so would I do something like fire retrorockets.  

Is it reasonable to spin a 1000 ton man shipped in half a second?   If the ship can do less than one spin, I would not change the direction of angular acceleration at all.  If it can do multiple spins from rest in that period of time, then it probably is a good idea to wobble.  

A zig zag maneuver covers more distance than a spin maneuver, so for a very large spacecraft its advantages increase.  But for the generic case I think a spiral with just a bit of randomness is better.  What do you think?

 

 

Edited May 26, 2020 by farmerben

[sevenperforce]

12 hours ago, Spacescifi said:

Called sprint missiles. Designed to take out an ICBM during launch. Likely did have staging, but I doubt the final stage was anywhere near as thrusty as the first.

Two stage. First stage hit 100 gees. Second stage was at least 16 gees.

[Xavven]

2 hours ago, farmerben said:

 

Which evasive maneuvers are the most effective?  If you were the pilot of the target spacecraft what would you do?

Assuming you're in space, then use your attitude thrusters to put the incoming projectile at your 3 o'clock or 9 o'clock and then fire your main engine. 2 G of thrust would move you out of the way of a ballistic (i.e. non-maneuvering) projectile. You would want to continue changing your direction to dodge follow-up shots, but if the time of flight is 7 seconds, they have little hope of hitting you with ballistic ordnance.

If this is a missile that steers to intercept you, then depending on how that missile was designed and how close you were when it was launched, 2 G could either be enough or definitely not enough. Humans have already developed missiles that can reach up into space, intercept targets maneuvering very hard, and even intercept other incoming missiles. Frankly, 2 G is fairly tame acceleration to contend with.

[sevenperforce]

@Spacescifi -- I understand that you are writing some scifi and you often come to the forum with questions. That's a really great thing; I have written some scifi and fantasy and I have done the exact same thing. It's a lot of fun and it's a great way to bounce ideas around. I know I enjoy tackling some of the tough hard-science questions. 

That being said, I confess I do not particularly enjoy discussing these questions in a constant trickle of new threads, each one for a new question. It's harder and harder to navigate the forums and find other threads when there are two or three new threads created every week or two about the same overall types of questions. 

Obviously I am not a mod or anything -- this is just a suggestion -- but have you thought about creating one master thread and sticking to it? It could be something like "Rocket science for science fiction" and you could post new questions there as you work through your fiction. It would even be something that other people could use if they were writing, or if they were wanting to discuss rocket science problems in common fiction. 

Just a thought.

[kerbiloid]

A solution. Moderators could add a dedicated subforum "Sci-fi with Spacescifi".

[Nuke]

6 hours ago, farmerben said:

A suborbital projectile is somehow propelled toward a target in Leo (~125 km altitude) at 500g.  It closes this distance in less than 7 seconds, but lets go with 7s if we are not taking the shortest path.  

The target maneuvering at 2g can alter its position relative to expected position by about 1/2 a kilometer.  

The missile needs about 0.4s or 6% of its total to anticipate and respond to the most basic evasive maneuver.

Assuming the missile has finite propulsion, then the target will be much safer at long range.  If infinite propellant, not so much.  But the time the evasion can waste certainly increases with more range.  

Which evasive maneuvers are the most effective?  If you were the pilot of the target spacecraft what would you do?

 

I'm going to use maximum rotational thrusters in the plane perpendicular to the distance vector of the incoming projectile, and fire the main engines with maximum possible thrust at first.  Then introduce some randomness the closer the projectile comes.  So halfway to impact I might choose numbers between 90%-100% of maximum possible primary thrust, without significantly changing my direction of angular acceleration.  Only in the final second or so would I do something like fire retrorockets.  

Is it reasonable to spin a 1000 ton man shipped in half a second?   If the ship can do less than one spin, I would not change the direction of angular acceleration at all.  If it can do multiple spins from rest in that period of time, then it probably is a good idea to wobble.  

A zig zag maneuver covers more distance than a spin maneuver, so for a very large spacecraft its advantages increase.  But for the generic case I think a spiral with just a bit of randomness is better.  What do you think?

 

 

randomize all the things, your main focus is to maximize the error between where the missile wants to be and where you actually are. pumping the throttle is a good idea. of course the more things changing and the higher the variations of the rates of that change the more error you produce. if your main engine is gimballed and you're not exceeding your design tolerances for your craft, and your aren't splattering the crew (blacking out is acceptable if this is all computer controlled), rapid changes in orientation will help add more error. of course if that missile has infinite fuel then you will just end up doing this forever (this is why the expanse has pdcs as the missiles are so fast and manuverable and long range that if they miss they can turn around and make another attempt).  but for a missile that has one shot at hitting you, it might work. maneuvers might also be chosen to waste the missile's delta-v budget if that is a known quantity. in this case maximum thrust burns would be best.

31 minutes ago, kerbiloid said:

A solution. Moderators could add a dedicated subforum "Sci-fi with Spacescifi".

i kind of like the daily hypotheticals. if it helps him write better scifi then its worth it, and if not its still an effective mental exercise. and its better he asks us than a bunch of science illiterates. 

Edited May 26, 2020 by Nuke

[sevenperforce]

31 minutes ago, kerbiloid said:

A solution. Moderators could add a dedicated subforum "Sci-fi with Spacescifi".

That's a little unkind. I'm not trying to pile on @Spacescifi.

5 minutes ago, Nuke said:

i kind of like the daily hypotheticals. if it helps him write better scifi then its worth it, and if not its still an effective mental exercise. and its better he asks us than a bunch of science illiterates. 

I like them too. That's why I comment. I've commented on most of these threads; answering cool hypotheticals is something I enjoy.

I just think having them all in one place would be a better way of doing it.

[Spacescifi]

7 hours ago, farmerben said:

A suborbital projectile is somehow propelled toward a target in Leo (~125 km altitude) at 500g.  It closes this distance in less than 7 seconds, but lets go with 7s if we are not taking the shortest path.  

The target maneuvering at 2g can alter its position relative to expected position by about 1/2 a kilometer.  

The missile needs about 0.4s or 6% of its total to anticipate and respond to the most basic evasive maneuver.

Assuming the missile has finite propulsion, then the target will be much safer at long range.  If infinite propellant, not so much.  But the time the evasion can waste certainly increases with more range.  

Which evasive maneuvers are the most effective?  If you were the pilot of the target spacecraft what would you do?

 

I'm going to use maximum rotational thrusters in the plane perpendicular to the distance vector of the incoming projectile, and fire the main engines with maximum possible thrust at first.  Then introduce some randomness the closer the projectile comes.  So halfway to impact I might choose numbers between 90%-100% of maximum possible primary thrust, without significantly changing my direction of angular acceleration.  Only in the final second or so would I do something like fire retrorockets.  

Is it reasonable to spin a 1000 ton man shipped in half a second?   If the ship can do less than one spin, I would not change the direction of angular acceleration at all.  If it can do multiple spins from rest in that period of time, then it probably is a good idea to wobble.  

A zig zag maneuver covers more distance than a spin maneuver, so for a very large spacecraft its advantages increase.  But for the generic case I think a spiral with just a bit of randomness is better.  What do you think?

 

 

 

Hmm... I am the pilot? That's... unfortunate. We are probably going to die, but we will definitely go out fighting for our lives.

If I was captain though this whole situation may be different. Because:

1. We should have an officer watching at ALL TIMES for any suspicious signs of activity on Earth. If you see several air forces of various nations taking off simulataneously that's a huge red flag flag right there. And if they are flying toward a spot we can calculate that could easily hit us from via launching, that is our cue to hit max thrust and leave orbit. Granted, if it's underground ICBM's that WILL take me by surprise, but that still gives greater aler time than aircraft launched missiles will.

2. If my ship is not equpped to deal with hostile weapons fire via interception (I actually have missiles or lasers), I won't even visit a potentially hostile planet.

Back to the setting though:

What would I do?

Depends on what my ship can do. If it is only the main engines that can do 2g indefinitely, then turning really fast with RCS which is usually weaker than main engines is noy going to happen. At best I tell the captain to do an emergency dump of ALL cargo so our TWR increases so that now we are going beyond 2g since we are less mass. If we survive, I am reporting my captain to his superiors for being irresponsible.

If my ship is so fictional that even the RCS has indefinite 2g thrust then I still dump cargo, only this time I start jinking side to side as I accelerate away.

 

5 hours ago, sevenperforce said:

Two stage. First stage hit 100 gees. Second stage was at least 16 gees.

 

Definitely sounds more escapable than 500g launches.

With Tlthis I actually probably have a good 30 seconds before impact or a succesful evasion... maybe more.

Edited May 26, 2020 by Spacescifi

[natsirt721]

The biggest thing that I have picked up from reading sci-fi is that, it doesn't really matter so much if something is 'possible', what matters is how the author justifies it. Justification can range from the hairy and explicit (e.g. that bit in The Martian where the author discusses the nature of the failure of the first Iris launch) to totally implicit (relying on the reader's comprehension of the word the author has created) - as usual, the best works lie somewhere between the two extremes. Often times, the technical details aren't particularly relevant, after-all this is science fiction, and that gives the author quite a bit of leeway as to how they craft the world the story takes places in.

What does matter is internal consistency. This is where the true art of the trade is shown; by crafting a believable setting, telling a story, not breaking any important laws of physics^[1], and having the reader come out the other side smiling. That is the real mark of a successful work of science fiction, not whether some scenario is physically possible.

As the author, you should try to decide what the outcome is ahead of time to meet the needs of the narrative, then craft the world to result in that scenario, not the other way around. I don't mean bore the reader with technical details about the ship and the missiles (although bridge-crew dialog is a great way to drop hard numbers into a story without force-feeding them through narration), but I think if you go at this from the other side you'll have a more fruitful experience. So back to the original question:

On 5/25/2020 at 8:51 PM, Spacescifi said:

Question: What is the lowest constant acceleration rate of g where Earth based forces could not reliably hit you in orbit?

Pretty much any combination of ship acceleration and missile performance can result in anything from the total vaporization of the ship to the UN shaking its fist as you zoom off to your next destination unscathed. In this case, you should pick what you want to happen first, and craft the performance of the ship and missiles to result in that scenario.

I'm assuming you want the ship to escape in this scenario, and also that the ship is going to be a somewhat important part of the story going forward. Start with the class of the ship. Is is a military grade cutter, capable of pulling 8 gees but can't go past the moon? Is it a dilapidated cargo freighter from the last century, barely able to pull two unladen? Once you know the performance of the ship, choose the performance of the missile. If you want them to get away easily, a few dozen dumbfires at 500 gee might make for a good hair-raiser. If you need some battle damage, proximity warheads (high-explosive frag or nukes) could batter the hull a bit, or perhaps result in a propellant leak. If you need a mission kill, a lucky hit to the engine or reactor might force an emergency shutdown. Any or all of these are valid scenarios given different combinations of ship and missile performance, but if you make that 70 year old cargo ship dodge a barrage of state-of-the-art ASAT missiles, you better tell me how that happened.  As a reader, thats the kind of thing that will bother me - I could care less about the exact acceleration and guidance capabilities of the missile and the ship, as long as the outcome is believable. Maybe the pilot is Rain-Man. Maybe the ship has an experimental AI-controlled EW suite that confused the missiles' guidance. Maybe you jettison your cargo to act as a decoy. Maybe the astromilitary's missiles are designed for low-maneuverability targets. Any of these are good answers, but it is up to you to pick one that makes sense within the bounds of your setting.

[1] FTL is ok sometimes, but if you're working strictly inside the solar system I would recommend against. Trying to deal with breaking causality can be a real nightmare if you aren't read up on your special relativity. Above all, avoid breaking conservation of momentum (i.e. reactionless drives) - or be prepared to deal with a world where every spacecraft is potentially a life-exterminating WMD.

Edited May 31, 2020 by natsirt721

[YNM]

It depends on whether each side knows or not the trajectory of the other side. I think the numbers isn't all that important - we have ASAT missiles that works with barely the 500 g hypothetical performance.

It also depends whether the kill vehicles is is orbit or not, and whether it has rendezvous to you slowly or not - much easier to evade a fast - moving (relative) one if you know where it was going (and it can't do anything anymore either) than one where it's just ready and was pretty much parked next to you.

[KerikBalm]

X=0.5a*t^2. You've specified acceleration of roughly 5 km/s/s. I will take a t of 3 seconds (a few seconds). so the distance they travel before running out of fuel is 22.5 km. Their final velocity is 15 km/s.

Lets take LEO to be 200km. you have over 14.83 seconds to avoid the missile, 11.83 after it stops accerating. At 1 g, in 10 seconds, you can move your ship 500 meters from where it would have been if you didn't accelerate. In 11.83 seconds, that is 700 meters.

If your ship is more than 1400 meters long, this is not enough (assuming the missile is aimed at the center of the ship). At 2 G's, its 1.4 km you can dodge. But do they have proximity fuses? What is the blast radius? If the blast radius is 1.4km, they get you even at 2G.

Do they have 4 seconds, 5 seconds, several seconds of fuel? Due to the t^2 term, one additional second of 500g acceleration changes a lot. Final velocity at 4 seconds of burn is 20km/s, it travels 40km while accelerating, and to intersect your orbit, needs to travel another 160km, or 8 seconds. At one G, you can move just 320 meters.

Any movement you do before the missile stops accelerating is essentially irrelevant, given that it is accelerating 250 to 500x faster, and will easily compensate for your altered trajectory. If the missile assumes that you will keep accelerating at 1 (or 2) g, you shut off engines, and it misses by the same amount as if it assumed you wouldn't accelerate, and then you engaged engines.

Going from LEO to higher orbits would change things a lot.

Edited June 3, 2020 by KerikBalm

[magnemoe]

1 hour ago, KerikBalm said:

X=0.5a*t^2. You've specified acceleration of roughly 5 km/s/s. I will take a t of 3 seconds (a few seconds). so the distance they travel before running out of fuel is 22.5 km. Their final velocity is 15 km/s.

Lets take LEO to be 200km. you have over 14.83 seconds to avoid the missile, 11.83 after it stops accerating. At 1 g, in 10 seconds, you can move your ship 500 meters from where it would have been if you didn't accelerate. In 11.83 seconds, that is 700 meters.

If your ship is more than 1400 meters long, this is not enough (assuming the missile is aimed at the center of the ship). At 2 G's, its 1.4 km you can dodge. But do they have proximity fuses? What is the blast radius? If the blast radius is 1.4km, they get you even at 2G.

Do they have 4 seconds, 5 seconds, several seconds of fuel? Due to the t^2 term, one additional second of 500g acceleration changes a lot. Final velocity at 4 seconds of burn is 20km/s, it travels 40km while accelerating, and to intersect your orbit, needs to travel another 160km, or 8 seconds. At one G, you can move just 320 meters.

Any movement you do before the missile stops accelerating is essentially irrelevant, given that it is accelerating 250 to 500x faster, and will easily compensate for your altered trajectory. If the missile assumes that you will keep accelerating at 1 (or 2) g, you shut off engines, and it misses by the same amount as if it assumed you wouldn't accelerate, and then you engaged engines.

Going from LEO to higher orbits would change things a lot.

If you are smart then you launch the missile you don't do one very hard burn and then cruise, and you don't need 500 g acceleration, even 50 g is kind of overkill but can be nice during intercept 
You launch for an expected intercept, then cruise and do an second burn to intercept, better do multiple correction burns to counter the ship burns this is cheaper in dV but as you say if the ship stops burns and missile assumed you would continue burning it will also have to do new corrections. 

Current ABM or anti satellite weapons have very limited dV for course correction. Something going after an scifi spaceship don't have that luxury and probably have an upper stage for intercept. 
One problem for the missile is that it will probably have lower isp then the ship as the missile is smaller and much cheaper this assuming same tech level. 
You could easy have an setting where you have good fusion engines but they are far to large and expensive to put on an missile unless the missile was pretty much an robotic ship with point defense weapons advanced targeting systems and might even some armor.  

While the fighter planes in space is pretty unrealistic or having very limited use, think custom inspector or cop car in orbit simply as space operations tend to last a long time and you don't want to spend weeks in an seat.
Something like an missile boat warship is more realistic. 

An manned ship with an 3-7 crew an good fusion engine, plenty of fuel and plenty of large missiles. 
Now using an radical over expanded nerva engine you could make the missiles pretty stealthy, the ship itself would not be but it would pass way outside the moon during the run crew would guide the missiles.

[KerikBalm]

Well, what I said assumes the missile launches from directly underneath the orbit of the ship. If the missile launches from Florida, and the orbit of the ship doesn't take it to a higher lattitude than Costa Rica, the distance to intercept is much greater, and the time is much greater.

I was also assuming a single burn, like some ridiculously high performance SRB... Or the way many AAMs work. However, many AAMs have a 2nd pulse as they near the target.

If you had 4 seconds of 5km/s2 acceleration, and burned for 3, then at the very last second, you can still change where you are going to hit by 2.5km.

Of course, doing it earlier can make a bigger difference, but then the ship has more time.

If the missile can throttle back or has an arbitrarily high number of restarts and arbitrarily short burns, it can put itself on an intercept course with a 2 second burn, and match the ships 1G maneuvers for the next 500 seconds... which is more than enough time to hit.

A ship moving at 2G brings this down to 250 seconds.

Basically, if your ground track goes over the missile, the missile can get you in leo, even more so if it can throttle/pulse its propulsion.

But even 8 seconds is plenty of time for a CIWS laser to neutralize it...

So maybe you want to have it burn all at once and go for a kinetic impact... That sort of missile won't be easily defeated by an active defense system... A maneuvering one, or one with a warhead would be more vulnerable.

[Spacescifi]

7 hours ago, KerikBalm said:

X=0.5a*t^2. You've specified acceleration of roughly 5 km/s/s. I will take a t of 3 seconds (a few seconds). so the distance they travel before running out of fuel is 22.5 km. Their final velocity is 15 km/s.

Lets take LEO to be 200km. you have over 14.83 seconds to avoid the missile, 11.83 after it stops accerating. At 1 g, in 10 seconds, you can move your ship 500 meters from where it would have been if you didn't accelerate. In 11.83 seconds, that is 700 meters.

If your ship is more than 1400 meters long, this is not enough (assuming the missile is aimed at the center of the ship). At 2 G's, its 1.4 km you can dodge. But do they have proximity fuses? What is the blast radius? If the blast radius is 1.4km, they get you even at 2G.

Do they have 4 seconds, 5 seconds, several seconds of fuel? Due to the t^2 term, one additional second of 500g acceleration changes a lot. Final velocity at 4 seconds of burn is 20km/s, it travels 40km while accelerating, and to intersect your orbit, needs to travel another 160km, or 8 seconds. At one G, you can move just 320 meters.

Any movement you do before the missile stops accelerating is essentially irrelevant, given that it is accelerating 250 to 500x faster, and will easily compensate for your altered trajectory. If the missile assumes that you will keep accelerating at 1 (or 2) g, you shut off engines, and it misses by the same amount as if it assumed you wouldn't accelerate, and then you engaged engines.

Going from LEO to higher orbits would change things a lot.

Well it is sad, but the only way to not surely die in LEO via human weaponry would require the scifi ship to have 500g nuclear tipped missiles of it's own.

Let's round the number it has off to 50, and as these are scifi missiles (not the human ones), let's say they are only a meter long each.

So... while in orbit of Earth the ship keeps it's missile turrets (ten total) aimed at Earth. Which is enough to make Earth feel threatened enough to launch, which is very ironic since this is also the only surefire way I can think of to stop an Earth missile strike.

When Earth launches swarms of missiles the ship launches counter missiles.

It does not even bother trying to evade, as the 500g counter missiles quickly penetrate the atmosphere and detonate close enough to the launched missiles that either an EMP takes them out or the air blast wave does.
 
Should work no? I am trying to not to die here lol!

If the scifi ship DOES escape the Captain will muse to himself, "Can't even orbit a planet without getting shot at. The galaxy we live in nowadays."

 

EDIT: If I wanted to make this horrifically unfair I would only need to upgrade each scifi missile with a kilogram of antimatter each.

 

Epic blast wave in atmosphere. Should take out many missiles at launch.

 

EDIT: Wikipedia states Sprint missiles had a 100g first stage solid propellant. Missile looked like a conical spike, and the air resistance was so great the rocket glowed white during launch.

So 500g is highly unlikely. Missile would not survive it.

Let's calc all the missiles, counter missiles included, with 100g.

Edited June 3, 2020 by Spacescifi

[KerikBalm]

https://what-if.xkcd.com/58/

As XKCD said, space isn't like this:

 it is like this:

Low orbit is like... really really close to Earth.

Close enough that you don't need to worry just about missiles, but also about high energy lasers if humans decided to build them... and there's no escaping those.

You seem to be assuming some high tech humans, a sprint missile had a dV of about 5 km/sec, yet your first mention of earth lanched missiles was giving 3-4 times that dV with 5x the TWR (which also meant some pretty robust heat protection for the missile).

Why would you get so provacatively close, what possible reason do you have?

Also, if you take some time, you can survey the Earth from much higher up, and identify probably missile silos (granted, some ICBM silos are rather hard to distinguish, since they are mostly underground), and take an orbit that avoids them.

Also, decreasing the acceleration of the missile doesn't change much, its still much higher than that of the ship. What you need to compare is how much dV the missile has, vs how much dV the ship can generate in the time it takes the missile to intercept. If your lower the missile TWR but keep dV the same, not much has changed. If you lower TWR and keep burn time the same, a lot can change.

But lets do the math, 4 second total burn at 100g, 3 second burn to intercept, then 100 seconds of matching a 1G acceleration. Acceleration is now 1 km/s

Velocity after the initial burn (minus gravity losses, which would be 1%, and unknown aero losses) would be 3 km/s. Distance covered during those 3 seconds is 4.5 km. If the orbit is about 200 km, then after the burn, it still needs to go another 195 km, which takes 65 seconds. Your missile can hit. If the ship is going at 2Gs, then the missile with this burn profile has 50 seconds of "chase", and expends its dV 15 seconds before intercept. 15 seconds at 2 G = a miss by 2.25 km. If it was 2second initial burn, and then the remainder for a "chase", the  velocity is 2 km/sec, and it has another 2km/sec in reserve for chase. It thus takes 100 seconds to reach 200km, and has 100 seconds of chasing a 2G maneuvering ship... but... previously I was ignoring the effect of gravity... with the 500g missile getting a final velocity of 20km/ sec, time to intercept was so short, and velocity was so high, that gravity would not substantially slow the missile.

In this case, in 100 seconds, gravity slows the missile from 2km/sec, to 1km/sec, so in 100 seconds it actually only reaches about 150 km, not 200km, In another 50 seconds, it's slowed to 0.5 km/sec, and hasn't even reached 190km... a ship accelerating at 2 G would avoid this missile.

If we go back to the 500G missile... and we assume the missile is launched from KSC (28.6 degrees north), and the ship is orbiting at the equator, then the missile has to travel not 200km, but over 3,000 km. A 20 km/sec intercept still takes 150 seconds,  during which time a ship accelerating at 2 Gs can change its velocity by 3 km/sec. A 15 km/sec intercept speec + 1km/s dV for chase has an intercept time of 200 seconds, during which a 1 G ship can change its velocity by 2km/s, easily outmatching the 1km/sec reserve of the missile.

So if you know where to point your missile defense missiles, you should also know where you can simply avoid passing over.

Flying right over a missile silo puts you really really really close to it. Why would you do that? A semi synchronous orbit of Earth is 20,200 km... orbital time of 12 hours. Medium Earth orbit... at these distances, those missiles are easily avoided. Heck, even a 2000km high orbit would make it easy to avoid these missiles.

Again, why why why would you put your ship within 200km (even worse if you're talking about just above the karman line at 100km) of a potentially hostile force?

 

 

[kerbiloid]

16 minutes ago, KerikBalm said:

Low orbit is like... really really close to Earth.

(Thoughtfully looks at the mountain at the horizon. It's as far from here as the space border.)