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Inspired by this question: How Earth can defend herself in a future war with Mars?

Suppose there are two planets within one star system. One of them is bigger. The both are self-sufficient. They have similar population density (the bigger has greater population accordingly) and similarly related industrial capacity.

The smaller planet can launch lots of barrels with pollutants and/or nukes to the bigger one because of smaller gravity well.

Is the smaller gravity well crucial for winning? Is there a strategy for the bigger planet that can make it win?

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  • $\begingroup$ This is a good place to start: rocketpunk-manifesto.com/2009/06/… $\endgroup$ – Thucydides Jan 2 '16 at 5:04
  • $\begingroup$ What year / timeframe / technology level are we looking at? Are both at "today's" timeframe? $\endgroup$ – Mikey Jan 2 '16 at 23:17
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I'd go ahead and propose that no, it does not matter.

Technology and environment.

Mickey in a comment and M-i-ech also indicated: it really depends on the technological level.

But generally, we will have to accept that the technology of space travel has develop well enough to have actual ground to start a way. So sending space shuttles to the other planet would not be too difficult for either.

From that we could suppose that they have some space stations orbiting their own planets, or based on natural satellites, or even relatively closed planets. So we don't talk about two planets at war, but two planetary systems.

Distance and orbits.

The two planets orbit the same star. This is a problem for your military tacticians. You need to spend quite sometime calculating precisely the trajectory for your ballistic missile to reach a valid target on the other planet. And that is including your respective revolutions.

If the planets are too far from each other, that's going to be a real pain. And sending your ICBM from another place might be more useful.

If, on the other hand, they are too closed, they will end up orbiting one another.

You should also note that the further you are, the more the other guys can anticipate your missile re-calculate the trajectory and possible aims.

Costs analysis

So both use the same resources to build the missiles ($M$), but the LimaPorters, the inhabitants of the Large Planet have to place more fuel or slightly smaller missiles. Note that the escape velocity is $v\propto\sqrt{m_p}$. To simplify, we will write the total cost for the missile as

$$C=M+L\sqrt{m_P}$$

Your theory was then to say that it's easier for the smaller planet to send those missiles and thus they'd gain an advantage. However, all else being equal, they also dispose of less resources. We have $M\propto R^3$, the radius of the planet. So the cost, in proportion to the natural resources (modelled by the surface) becomes

$$\frac{C}{S} = \frac{M+L\sqrt{m_p}}{S}\propto\frac{M+L\sqrt{m_P}}{R^2}\propto\frac{M+L(m_p^{1/2})}{m_p^{2/3}}$$

which strongly reduces the advantage of the smaller planet. Furthermore, with the same charge, the same precision, they'll hit the same number of people. Which, due to the same density, will be much more damaging for the smaller planet.

Thus, while the absolute cost is much higher for a much larger planet, and the absolute effect is the same, the relative cost is actually smaller and the relative effect is much stronger.

Likely warfare

With the given technology and environment, it is very likely that they'd launch their missiles from a moving base (spaceships) as they would provide a more flexible and tactical advantage, comparing to launching from your ground.

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    $\begingroup$ Or in other words, surface gravity increases slower than surface for small rocky worlds capable of holding an atmosphere, where surface equals GDP. Why is M a function of R^3 not R^2 tho? Are we talking surface or volume? $\endgroup$ – Serban Tanasa May 19 '16 at 22:34
  • $\begingroup$ @SerbanTanasa $m_P$ is related to the volume, with the same density for both planets. However, the only resources available are on the surface. Arguably for some distance, but that does not change the logic. $\endgroup$ – clem steredenn May 20 '16 at 4:40
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Depends on tech level. All in all I'm convinced that if gravitational well matters then there's no point in war, when war starts to make economical/political/other sense it's because gravitation stopped to be important.

Present day/near future

If your only option for war is launching ICBMs IPBMs at each other, war doesn't really make much sense. There's no trade or physical contact worth mentioning, so war is just some version of MAD. Best you can acquire in war are enemy technologies, nothing else. You can't take goods, occupy land, and without shared market you can't even extort money. You can only extort knowledge, assuming that you even know they know something you don't. With only radio contact, you most likely only know what they told you - you can't send spies, and you can only try to bribe locals to spy for you, but again, you can only bribe with knowledge. Your best bet at espionage it to let your scientists talk to the other planet, while maintaining VERY close eye on them, fully anticipating other planet to do the same.

Casual interplanetary flight with planet-bound industry

Whatever machines of war you build, you need to launch them, but at this point, costs or difficulties of launching ships are relatively small. At this point you should have thousands of cargo and passenger ships crossing the void hauling goods, resources and people back and forth. You can have combat ships carrying missiles, gunships carrying railgun mass drivers, dropships carrying special forces to carry out planetary operations, etc. One planet is going to be taxed more on launching their ships, thus being forced into defensive role, but at this point difference is not going to be big.

Casual interplanetary flight with off-world industry

Advantage in this phase depends on location of star and asteroid belts. Planet closer to star will have clear advantage in power generation supplying their orbital shipyards with energy, planet closer (closer, as in lower difference of gravitational potential) to asteroid belts will have advantage in raw materials supplying their shipyards with elements. Planet having both will have huge industrial advantage.

Transition between near future and casual flight

Here the dependence on grav well is the biggest. You should have physical contact between planets, maybe a dozen ships carrying scientists, explorers, diplomats or extremely valuable cargo. There's still no shared market and no capacity to take stuff or occupy area, but at this point, war isn't supposed to be MAD. Here, planet with lower gravity can launch more IPBMs and more interceptor vehicles which gives them a good chance of exterminating population of other planet while surviving retaliatory strikes. I can't really see a reason to do that, though. Sure you may be able to glass or genocide them, but you literally gain nothing out of it and you are very likely to take multiple hits yourself. Moreover, after you develop casual spaceflight, planet will likely be too messed up to colonise and surviving planetary installations too dilapidated (through war and lack of maintenance) to be of any use, that's assuming that other planet even is in your biochemistry's goldilocks zone.

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A simple answer to your question is kind of. Crucial? No. Does it have any effect? Yes. When firing projectiles at an enemy world, the higher the planet's gravity, the less energy those projectiles need to get to your target. This means faster projectiles and longer weapons ranges. Getting the crucial positions at the top of the gravity well will give you these advantages, but it won't gauruntee your victory. You can't calculate the outcome of a war, and there is no formula for achieving victory.

The other thing to consider is the fact that the bigger planet has more resources and a larger workforce. Although, as LukeN said, the smaller gravity planet has cheaper projectiles, the bigger planet has more money to buy projectiles with. I say, that this cancels out the gravity advantage. Of course, I'm assuming that each planet is as well managed and as prosperous as the other, but the big planet may have a communist government, and thus have a poor economy to support its military. Or, the small planet might be inhabited by a peaceful race, who don't allocate as many resources as they could to their military.

LukeN also mentioned information as an important factor. That's true, assuming you don't want to just throw a dinosaur killer at the enemy planet, then you don't need to know where on the planet their facilities are, because you just take out the whole thing. But, if you don't choose to do that, then you'd have to worry about the fog of war. Often, your military information will be incomplete, or flat out wrong. Deception can also have an impact.

But, the real gravity advantage won't come from the planet's gravity, but from which planet is closer to the sun. The sun's gravity will affect every object in the system, and the projectiles will have an easier time hitting the world closer to the sun. The various gravity fields that will be in the path of the projectile, as well as the orbits of the objects of the system will have great influence over how you fire your weapons.

The planetary gravity wells will only have an impact on the tactical level, not the strategic level. The war will come down to strategy, material assets and their utilization, and morale, like in any war that a human would normally be familiar with. Whichever sides' morale breaks first will ultimately fall. Victory is mainly psychological and complete destruction of the enemy is a costly solution at best.

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  • $\begingroup$ When something hits you on the head, it doesn't really matter all that much if it does so moving at 6000 m/s or 12000 m/s or 30000 m/s; while the specific kinetic energy will obviously be larger in the latter case, even a pebble hitting you at 6 km/s would hurt pretty well. We have sent a spacecraft past Pluto just recently; range by itself isn't a problem. Calculating an appropriate transfer orbit, taking other celestial bodies into account, is something we know well how to do; we did that in the 1970s with the Voyagers, and to a lesser extent with many other solar system probes. $\endgroup$ – a CVn Jan 10 '16 at 19:06
  • $\begingroup$ I didn't say that it would be hard to figure out how to hit the other planet, I just said that you needed to take those things into account. I also didn't say that the planet closer to the sun couldn't strike the enemy effectively, I just said that their shots would have less momentum. The projectiles of the people from the outer planet would hit their targets sooner, because of having much more speed due to gravity. $\endgroup$ – Lololololol Jan 10 '16 at 19:11
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Based on very quick googling and wild guesses, it seems it could cost about \$500 million to send a big rocket to Mars and \$200 million for the (IPBM) missile itself. If one planet had half the gravity well, maybe it could save ~30% of the cost, so you would expect they'd be able to launch more of the projectiles.

But I suspect that you can't just win by having 30% more projectiles. More important is: information. Where will the high value targets be (requires a lot of prediction since it takes so long to travel between Mars and Earth)? and where will your enemy's projectiles be? All things begin equal, information-gathering satellites are probably the most important tool of warfare, and the smaller planet will have a cheaper cost to get more satellites into space.

That said, I think that a small difference in technology -- for instance a cryptography break-through, a prediction algorithm, etc. -- would probably be most important. So to answer your question: While it may be helpful, I wouldn't think gravity is the most crucial element of interplanetary warfare.

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