# How Does Orbital Warfare Work?

Let's say in the near future(so no fusion drives or anything exotic like that, VASIMR engines are the "best" engines placed on ships, not on expendable weapons), two space ships, armed with missiles, are orbiting so that they are opposite sides of the planet. If they are both suddenly ordered to fire missiles(torpedos, idk what they would be called in space), how would the missiles burn their motors or engines to hit the other spaceship in as short of a time as possible?

I would assume the missiles can't just accelerate faster directly forwards, given that they would gain delta V and rising up in orbit?(from basic physics, I don't know anything about orbital mechanics).

• Low orbit or high orbit? What is performance of the engines of the missiles, that is, what delta v are they capable of? Are the engines restartable? Mar 22 at 0:19
• @VogonPoet: The question explicitly says near future with no exotic drives. The constraints matter very heavily. Basically, the question ask about real-world realistic targetting solutions. Mar 22 at 10:16
• @AlexP read closely. VASIMR is the best engines ships have (but not expansible weapons). No matter. “Shortest” has a single mathematical solution unless we are in ridiculous orbits like a lunar distance. 1. You MUST increase altitude. 2. You MUST use a vector that subtracts rather than adds the other ship’s vector from the solution for $t$ (no chase solution will be faster, or more efficient if that mattered). The missile must close distance in the opposite vector of the target. You will be shooting behind you. Mar 22 at 10:32
• @VogonPoet I have to stand with AlexP, in that physics is quite important; If your missile lacks the fuel and power to reach the target because of its design or the environment, then the answer is "infinite". Mar 22 at 11:12
• Isn't blowing up ships in orbit kind of a bad idea? The debris will be a hazard to all space traffic. You would think there'd be some law to prevent this. If this happens enough it may cause an impassable layer of debris. See: en.wikipedia.org/wiki/…
– aiwl
Mar 22 at 14:33

## A BRIEF SUMMARY (Visit the TOUGH SF & ATOMIC ROCKET websites far more information on realistic space warfare.)

Since both ships are capable of performing orbital maneuvers the first priority would be to get 'eyes' on the enemy ship. This could be done from the surface of the Earth by ground stations or even ships and aircraft but a lot would depend on whether or not both sides have managed to establish world wide tracking networks.

The other and more conventional alternative would be from 'above' i.e. via a chain of surveillance satellites placed in high Earth orbits where they can monitor and track orbital changes by the hostile ship. Since VASIMR drives are hot 'burn' maneuvers will be obvious. The satellites can then simply relay targeting data to your ship in real time.

The problem is of course you now have multiple potential targets to deal with i.e. both the enemies ship and their satellites. Since your ship is in orbit and has a nuclear reactor on board to power the VASIMR drive it should have the surplus power needed to run a laser weapon for destroying/crippling/blinding satellites and there's no atmosphere to distort the beam. But still you can only hit the ones that are above the ships 'horizon' i.e. not hidden by the Earth's circumference. This is the 'fast' part of the war. Fast identification of targets and fast destruction. Next comes the 'slow' bit.

The enemy of course can do the same but while you still have real time tracking data you can launch kill vehicles. These would be chemical rockets (with high thrust to mass) that are basically sensors with a small fragmentation charge and shrapnel package attached. Assuming you have an good/approximate lock on the target you fire a 'spread' of rockets 'up' i.e. into higher orders tangentially from your own orbit. As they go higher they can see further over the horizon while simultaneously traveling closer to that part of the opposite hemisphere where the enemy vessel is or was last located.

Eventually a couple (possibly more) of your rockets will detect the enemy ship and depending on the course and altitude changes it has made will hopefully be in position to adjust course & intercept. Note: You have launched lots of small rockets not a few large ones. But THIS STILL WILL TAKE HOURS. During this time you have the chance to send course corrections to your missiles (assuming your still getting tracking data) and start evasive maneuvers yourself.

The enemy will detect some if not all of your kill vehicles as they come over the horizon and attempt to knock them out with their laser. How easy that is depends on how much else is going on. You can stealth them (a little) however by using radar absorbent materials and cryogenic cooling - but not for long. There is also now a lot of junk flying around in all sorts of weird trajectories thanks to exploding satellites so that might help.

As they approach the target (which is more or less ducking and weaving i.e. firing its engine to change orbital path and altitude) your surviving kill vehicles will estimate intercept 'cones'. These are points in space where the enemy might be given its velocity and the ability to maneuver. (The kill vehicle is the 'tip' of the cone. The maximum distance the enemy ship is likely to be away from the missile forms the base.) Regardless the kill vehicles detonate their shaped charge warheads and send clouds of dense, high velocity armor piecing shrapnel onward into the space where they predict the ship will be at the time of impact. Many will miss, but some will hit. Importantly even if parts of the ship armored things like the cooling system and other vital systems can't be.

The enemy ship is damaged/crippled if not destroyed outright and can no longer function. Given only the simplest repairs can be accomplished in space the ship will almost certainly have to be abandoned by any surviving crew members. A short time later your ship is also destroyed by the enemy's kill vehicles and the war is over. Lots of incredibly expensive 'junk' then starts falling from the skies down to Earth including satellites that have nothing to do with the war. (Their owners are pissed off.)

• Could you include a link to the "TOUGH SF & ATOMIC ROCKET websites"? Sounds fascinating.
– Tom
Mar 22 at 1:17
• Sure thing. Be prepared to learn more than you thought possible about the physics and technology of space warfare. 1) toughsf.blogspot.com 2) projectrho.com/public_html/rocket And let us know what you think.
– Mon
Mar 22 at 1:28
• +1 just for the atomic rocket recommendation. That page is a must for every SciFi writer or serious fan.
– Tom
Mar 22 at 20:21
• be warned: projectrho is a tv-tropes-level time wasting threat Mar 23 at 21:11
• Mon, I think Yorik just means that if you go to the projectrho website you are liable to end up spending a lot of time there, at the expense of other things you should be doing. ;) Mar 26 at 2:45

There are some options that I can think of —

Orbital velocity is about 10 km/s. The world is about 40,000 km in circumference. ISS orbits the whole thing in about 92 minutes.

SO, one option would be to launch a high parabolic AGAINST your direction of motion. The missile has no orbital velocity, but you’ve offset for that with more altitude. The warhead is coming nearly straight down on the target 46 minutes later. This would work great for very low altitudes.

Another option would be to go low. Still burning against your direction of orbit, but trying to go into a counter-orbit. You’d need a continuous roughly 2 gee burn (if I’m doing the math right) and you’d hit your target in about 23 minutes. You could probably shave a few more minutes off the time by going faster than 10 km/s on the other end (hyperbolic trajectory into the target).

A third option would be to get defensive : maybe you know the other ship has probably been commanded to attack you as well, or maybe it’s just good doctrine — increase your ship inclination to go into an almost polar orbit; spoiling the firing solution in the first two suggestions. Wait until your enemy comes into view, and direct fire.

• I would love it if you could share the math you did. But I won't insist: your tactical thinking seems clear enough.
– Tom
Mar 22 at 1:16
• Actually I'm quite sure the circumference of the Earth is about 40 000km Mar 22 at 14:47
• This is either a very significantly simplified description (to the point that the descriptions seem wrong/lacking consideration for important factors), not really seeming to take into account actual orbital dynamics, or assuming such a high delta-v expenditure and/or high thrust values as to be well into science-fantasy for something happening in the "near future". Mar 22 at 15:42
• This actually contains my answer with math (beyond just 'X'), and maybe I didn't catch it. Steal my cool graphic if you want, I think I will delete my answer. Mar 22 at 15:54
• @RBarryYoung a modern rail gun can contribute about 2 km/s to the velocity changes (which isn’t a bad start), but might be hard on the rest of the launch vehicle. Basically, this solution proposes a missile about as 1.5 x 2 as big as would be required to get the same payload into its current pre-launch position. Mar 23 at 18:31

Short answer: they wouldn't fight. They're in the wrong place, and they can't get to the right place quickly enough to be useful.

If they are in approximately the same orbit, that the orbit is circular, and on opposite sides of the planet, what they almost certainly won't do is fire missiles straight away. If their orbits are different enough (say, one is in a polar orbit and the other an equatorial orbit) it might not even be possible to hit their opponent with a missile without doing some substantial manoevers first.

As you've observed, simply firing a missile will not necessarily have the effect people might expect. Shooting it prograde (in the direction of the ship's travel) will raise the apogee of the missile's orbit (the highest point) High orbits have lower orbital velocities, which means that the missile will appear to shoot away from you, rise up from the planet and then drop away behind you.

Shooting it retrograde (against the direction of the ship's travel) will lower the perigee (lowest point) of the missile's orbit. Lower orbits have higher orbital velocities, which means the missile will drop behind you, fall towards the planet and then overtake you.

If you fire a missile to retrograde and it has enough delta-V to inject itself into a retrograde orbit (so the same perigee and apogee but an inclination that's 180 degrees away from the ship's) then it would shoot away from the firing ship very quickly, and rapidly approach the target. Unfortunately, orbital speeds tend to be very high... 7.6km/s for the ISS, which means you'd need a rocket with 15.2 km/s delta-V in order to shoot backwards. You can't really use an ion drive or vasimr to do this because their thrusts tend to be much too low (so the missile would crash into the atmosphere before getting back up to orbital speed), and you can't use a chemical rocket to do this because its specific impulse is too low and you'd need a Saturn-V-sized missile to hold enough fuel.

Now, the firing ship could change its orbit... it could drop down into a fast orbit with the aim of catching up with its opponent, or it could rise into a higher orbit so its opponent would catch up with it. At the same time, your opponent will be doing the exact same sorts of things, and the odds are good that both ships would be observed by their opponent's ground stations and observation satellites so they'd be trying to jockey for position.

Eventually they'd want to be able to get close enough to their opponents such that they could fire a missile that would have sufficient delta-V to intercept them. This could take some time... the synodic period of two objects with orbital periods $$P_1$$ and $$P_2$$ is $$1 \over {1/P_1 - 1/P_2}$$. Something like the ISS has a period of about 90 minutes, so another object with a period of 270 minutes would "meet" it every 135 minutes or so. That means at least an hour's wait and perhaps more before you'd be able to see your opponent, and you'd still need a powerful missile that would take quite some time to cross the intervening space to be able to usefully intercept the target.

So, potentially hours of waiting, jockeying for position trying to get a first strike without being overly exposed (and higher orbits have less background clutter, remember).

Who's got the time for that?

No, what would really happen is that you'd get a bunch of ASAT missile launches from the surface. A suborbital rocket isn't unreasonably complex or expensive to make, certainly a lot simpler than a nuclear powered VASIMR-driven space warship. They'd pop up and drop a load of crud... maybe just dumb fragments, maybe smart interceptors like an exoatmospheric kill vehicle. They wouldn't be travelling at orbital speeds, and the enemy would coming trucking into them at many kilometres per second and get blown to bits, probably hours before the warship could do anything useful at all.

Boring, but that's space warfare for you. Debris goes round and round, everyone dies.

As a point of reference, it takes a rocket with about 8.6km/s delta-V to reach low orbit from Earth's surface. Here's an example of a small rocket with this capability:

The Satellite Launch Vehicle was an Indian project from the late 70s, and could put 40 kilos into a low Earth orbit. It was about 22m long, 1m wide, and weighed about 17 tonnes.

If you want a "missile" that can make dramatic orbital changes, or cross several thousand kilometres of space in relatively short order, that is the kind of size and weight of weapon that you'll be needing.

Have a think about how big the launching warship will need to be, and how many of these rockets it can carry. And have a think about whether or not launching them from Earth makes more economic and military sense.

A few other answers have included suggestions with dramatic orbital changes, such as transitioning from an equatorial orbit to a polar orbit. Such an action is very expensive in terms of delta-V... for a spacecraft in a circular orbit at ISS altitude it would be ~10.7km/s (more than getting into that orbit from the surface!) and rather impractical for a chemically fuelled rocket.

Happily your warships have VASIMR engines, so they have delta-V to spare. Unfortunately, high-efficiency engines are marked by having very low thrusts. A VASIMR capable of driving a ship with a centigee of thrust (yep, one hundredth of a standard gravity) would be a phenominally powerful thing, and require a substantial nuclear reactor, heatsink array, technological advances, etc etc.

A 10.7km/s manoever with such an engine would take >1800 minutes to complete... that's nearly 20 ISS-orbit-equivalents. An even more outrageously powerful VASIMR which could manage a whole tenth of a gravity still takes >180 minutes, giving plenty of opportunity for ground-based interceptors to reduce you to a navigational hazard for future generations to enjoy.

Prompt manoevering requires high thrust. Electric rockets can't provide that at your tech level. Chemical rockets don't have high Isp. You need high Isp to make dramatic orbital changes.

Your warships can't make dramatic manoevers. If you want high thrust, high-Isp engines, you need Project Orion.

I don't know anything about orbital mechanics

I can only recommend picking up the KSP and Children of a Dead Earth videogames - those are a great way of learning orbital mechanics, as demonstrated in XKCD.

how would the missiles burn their motors or engines to hit the other spaceship in as short of a time as possible?

So what you're describing is an orbital intercept maneouver. The fastest way involves an infinite amount of thrust and ΔV, so constraints are gonna be important here.

You've set the scene as near-future, so I'm making the following assumptions:

• Low(ish), coplanar, circular earth orbit
• Chemical engines for the missiles, which implies:
• High thrust, thus theoretical instantaneous maneouvers
• Limited ΔV (i.e. limited "fuel"), thus limited burn time

An efficient low-ΔV intercept maneouver is for the missile to burn prograde (that is, "forward") in order to raise its orbital period (the time it takes to make an orbit) by a factor of 1.5x, and... wait.

Note how the relative angle of the green ship and green projectile at the time of launch are the same - that's the prograde maneouver.

If you want to lower the intercept time, then you'll have to spend more ΔV and change the angle of your burn towards radial (i.e. "out"). The intercept in the following diagram would spend more ΔV and intercept in about 1.1 orbits:

Note how the relative angle of the green ship and green projectile at the time of launch is changing "outwards" - that's the radial component.

Increasing the ΔV budget more, intercept time of ~0.9 orbits:

Increasing the ΔV budget even more, to reduce the time to about ~0.5 orbits, turns the intercept orbit into a quasi-vertical; the projectile would burn at a ~45-degree angle relative to radial ("up and left" in the image), to cancel out the forward ("down") velocity and impair outwards ("left") velocity:

We can keep going until the extreme case: the projectile cancels out its forward orbital velocity and turns into a reverse orbit, lowering the perigee in order to skim the atmosphere. Intercept time would be ~0.2 orbits:

The absolute limit on the fastest maneouver is how much the perigee of the retrograde can be lowered without forcing the projectile into an atmospheric reentry.

Now, keep in mind: the maneouver to take depends heavily on your ΔV budget. A low-ΔV prograde maneouver can take... maybe 1000 m/s, whereas the fast retrograde skim-the-athmosphere-in-reverse-orbit would take maybe 22000 m/s.

Why is this important? Because the fuel mass increases exponentially relative to the ΔV and payload mass. So you can choose between having one projectile capable of the retrograde skim maneouver, or a few hundred projectiles capable of the slow 1.5 orbits prograde maneouver, or one projectile with a hundred times the payload. Yes, the order of magnitudes is hundreds

This highlights the tactical concerns of choosing the projectiles payloads. Whereas the fastest intercept is possible, it might mean having a projectile with a payload too small to make a difference (or too easy to avoid with an evasive maneouver). I would argue that the optimal solution is a projectile capable of the slow-ish ~1.2 orbits intercept, carrying a shrapnel payload - a kilometer-wide cloud of ball bearings traveling at ~500m/s relative to the target would be hard to avoid, cause damage to the target, and burn in atmospherical reentry.

(Please bear in mind that my diagrams and numbers are back-of-the-envelope quality; if you want more accurate numbers and orbits, play KSP with RSS and MechJeb's maneouver planner. If you want the really nerdy mathematically accurate solution, there's plenty of this stuff in space stackexchange).

• +1 for illustrations. I should see about generating animations of that sort of thing. Mar 22 at 19:54
• And whilst I think of it, note that your lowest-delta-V intercept ends up with the lowest relative velocities of the missile and the target. That's bad from the point of view of using kinetic energy to smash all the things, and bad from the point of view of letting them see the missile and counter it. The more delta-V the missile uses for its intercept, the higher the relative closing velocities, the less time the target has to react and the more destructive any shrapnel will be. Mar 22 at 19:58
• Yeah, it's all about the projectile budget - there's a balance between ΔV and payload (kinetic? explosive? shrapnel? graphite dust?) and avionics (comms, RCS for course-correction) and ECCM (stealth coating? radiators?). Since this is world-building stackexchange and there's so many unknowns, I cannot venture to say what's the best. Mar 22 at 20:24
• Look up STK: Systems Tool Kit... Mar 22 at 23:59

Missile combat in space is way too complicated to answer this easily.

If you're looking for super-crunchy orbital combat mechanics in your writing, then this:

I would assume the missiles can't just accelerate faster directly forwards, given that they would gain delta V and rising up in orbit?(from basic physics, I don't know anything about orbital mechanics).

Is something you need to rectify.

Delta-V (dV) is basically a measure of how 'far' you can go in space. It is not gained by acceleration, in fact it's consumed by it. If I change my velocity by 500m/sec, I have to consume 500m/sec of dV to do so. This is determined by the mass, fuel supply, and ISP of the propulsion system.

For self-propelled weapons it is THE single most important statistic in space, possibly second only to sensor signature.

The moment the enemy sees the missile coming, they're going to start burning their engines to alter their trajectory. It doesn't even matter how they do so, unless the missile is undetectable until extremely close, because at orbital distances, all they need to do for the missile to miss is to not be where the missile is currently going to hit them.

The missile, in turn, will then have to make it's own adjustment burn to bring its course back to an intercept.

So now it's a game of "who's got more dV on board." If the target is able to force the missile to adjust course too many times, then it can run the missile dry of fuel and escape. (P.S. this is how you defend against air-to-air missiles as well, you change direction a lot, and drag the missile down to lower altitude, thicker air where it has to burn up its energy turning under high-drag until it lacks the energy to reach you anymore.)

Therefore the strategy behind employment of missile weapons is ULTRA dependent upon the relative dV of the missile, launch vehicle, and target. (The launch vehicle can maneuver before launching the missile in order to obtain a 'firing solution'. While the missile is in the launcher, it gets all of those velocity changes 'for free' - it doesn't expend its own fuel supply to do so.)

The only other factor that can help, and the only way launching from the other side of a planet makes sense, is if the missile itself is small enough, and has a long, silent cruise phase, so that you can launch it - and the enemy is either unaware of the missile's launch OR at the least has no idea where the missile is after it's been launched - and so now they have to try to dodge it without knowledge of it's current energy state.

That puts the whole thing into mind-chess territory, rather than physics.

For more information about how this looks, I strongly suggest watching Scott Manley's series of videos about Children of a Death Earth. That game is ULTRA crunchy, and Scott Manley does a good job of making orbital mechanics accessible.

Q: "how would the missiles burn their motors or engines to hit the other spaceship in as short of a time as possible?"

Ok, so your missiles have propulsion. For below idea you'll need some, but no excessive amount. It uses the planet's gravity as an extra accelerator.

## Slingshot above the upper atmosphere

Its fastest trajectory depends where your ships are. You'll have to calculate the trajectory anyway.

Use gravity as booster

Be careful, the orbit part near the planet should be above the upper atmosphere, else, your missile looses speed rapidly, by friction.

Approach a target on the right, with a low power (ion motor?) missile looks something like this:

Guided missiles

For a high speed guided missile, it is convenient to aim in a straight line to a point you want to reach, corrected for the gravitational field. Then you enter low orbit around the planet.. and when the target is in sight, the missile will focus on the target, switch on the engine and proceed in a straight line, like

.. the trajectory depends how your two ships are precisely aligned.

The missile has to rendezvous with the enemy ship, exactly the same way that vessels travel from Earth to the ISS. The only difference is that instead of docking to the enemy ship, the missile will rather have to impact at high velocity.

If the ships are in basically the same orbit, and you don't want to wait a few millennia for an opportunity of impact, then the missile has to change its orbit so that it has a different orbital period from the target, while still intersecting the target's orbit. If both ships are in very low orbit, then the missile necessarily has to speed up so that its new orbit is larger. Otherwise the ship can try a smaller orbit, which gives more opportunities for a "rendezvous" quicker.

At closest approach, which might take a few hours, the missile will very probably pass by the target a few kilometers away from it. So there are two things it can do: either it corrects its path prior to closest approach to guarantee a hit at many kilometers per second, but giving the enemy ship a lot of room to counter-maneuver... Or close to closest approach, the missile burns to match speed with the target. This means that for a few seconds, the relative speed between both will be close to zero while they are a few hundreds of meters away. At that moment, the missile burns like hell towards the target for a more guaranteed hit at a few kilometers per second.

Notice that you might just want to explode near the target rather than hitting it. This makes it easier to achieve a kill. Either way you have spoiled a lot of orbits for a lot of people for millions of years.

Shortcut.

Your missile will chase the other ship and catch up to it by traversing a smaller circle and skipping back up off the atmosphere.

http://ffden-2.phys.uaf.edu/212_spring2007.web.dir/Todd_Fortun/Incoming.htm

By adding its own velocity to that of the ship that launched it, the missile can fly lower than the parent ship: the lower the orbit the faster one must go to keep falling and keep missing the earth. It will catch its target ship both by going faster as well as taking a shorter route, like the inside track in a circular race track.

The missile then skips back up off the atmosphere to hit the target ship from below. I envision more like skipping a stone than the above more radical direction change. Hopefully the part of the above diagram where pieces fall off does not apply.

• To get to a lower orbit, it has to slow down. It will then be going faster once it gets to the lower orbit. Also, this isn't really going to work for ships on opposite sides of a planet. Yes, the lower orbit does mean a shorter orbital period, but only by minutes. It would take hours for the missile to catch up to the other ship. Mar 22 at 16:42
• You are right @RobWatts . It would take a long time to catch up but it would not need to burn the whole time. The atmospheric bounce would also work firing the rocket backwards but it would need a serious motor to get up to speed from starting at a good clip in the opposite direction. Mostly I wanted the bounce because I thought a bank shot was cool for a rocket and no-one else posted that yet. Mar 22 at 20:42

# Orbits are ellipses

You can get to the other side of the planet by traveling in any direction along the plane of your travel vector. So, just shoot backwards.

Note: Backwards does NOT mean shooting out the back of the ship, it means reversing the orbit. The pointy end of the weapon doesn’t go frontwards but don’t worry, use a computer. Well, actually, your in space. So pointy ends have no point. It can be shaped like a moose and work the same if you can make a moose shaped missile tube.

• Wouldn't the Missile fall out of the sky though, given that it was now below the orbital velocity(by quite a bit)? Mar 21 at 23:54
• I assume it has propulsion so it can accelerate into the new reversed orbit. It will obviously also need to give itself lift (pointy end goes up) during the correction. OP didn’t say this was a ballistic projectile, they actually said “torpedo,” which is propelled. But, a projectile could still do this with an enormous blast. Mar 21 at 23:57
• I see. So basically, the torpedo will need to have a thrust to weight ratio of greater than one, or be long with lots of height to spare, or else it will fall too low and burn up? Mar 22 at 0:00
• @itisyeetimetoday Well there are infinite scenarios depending on what your weapon can handle. If burning up is a problem then you have to stay at least above the atmosphere. But the lower you go, the faster you can go (and faster you get there). With the right timing, you goose it even more and climb out of your low orbit to hit bad guy. This is a high fuel cost option, if you have it. Also, torpedoes are “thrown” at some initial speed, so it all adds up. But the fastest way way is backwards, no matter how you slice it. Mar 22 at 0:12
• That is not how orbital mechanics works. Mar 22 at 0:16