When a planet is under seige, obviously its airports, missile silos, and launch sites are the first targets of bombardment, to prevent a counterattack. It thus seems that submarines, which can fire missiles and then submerge and swim away, and only have to resupply at a port every few years, are the logical choice for anti space defense. If the attacked spacecraft survived and quickly aimed its lasers and railguns at the submarine, how deep would a submarine, with modern military hull thickness, have to submerge to prevent destruction by the spacecraft's 100 gigawatt laser? Would double or single hulled submarines be more effective at stopping laser damage? How deep would a submarine have to be to survive the spacecraft's other weapon, a "rods from the gods" type attack with a 1 ton 10 meter long pointed titanium projectile railgunned at it at 5000 m/s?
Lets assume for this consideration that your spaceship can detect the exact location of the attacking submarine within a few seconds after the attack is launched.
Rod of the gods The spaceship will be in an orbit of at least a few hundred kilometers, if not much higher. So even with an instant counterattack the submarine gets more than a minute to dive and move. As titanium is roundabout 4.5times as dense as water your rod will loose its full impulse within 45 meters into water. I can't find exact speeds for diving down but there are proven stories about submarines diving up more than 300 meters within two minutes, so I think your submarine has more than enough time to dive deep enough and far enough for not beeing hit at all.
Laser As the speed of light is a little bit higher than 5000m/s it would be possible to hit the submarine, just looking for the speed. The problem here is the refraction of our atmosphere. Even with an absolutely clear sky much energy of the laser will be lost when reaching the surface for most of the possible wavelengths. Some clouds in the sky -> even for the few optimised wavelengths a high degree of laserlight is scattered away. If our submarine beginns to dive instantly after firing their own weapons the spaceship has no time to take a good position before firing back so there occurs another problem: the high reflection-factor of light transfering from air to water under less then 90°. As the sea-surface is in motion all the time a high level of light gets reflected by just centimeters of water. Furthermore the cooling-effects of water help the submarine to survive laser impact a few seconds more.
Thereby I conclude that your submarine could be save with just a few securitymeassures against laser (highly reflective hull, attacking from a sharp angle and such).
Edit: added some details for the laser-attack and corrected some writing mistakes.
I think the key obstacles are submarine detection from space and spaceship detection from underwater.
- Most submarine detection systems today are sound-based, and they rely on receivers in the water. Even aircraft (which are in the atmosphere) drop sonobuoys.
- There are some non-sound systems, like MAD, but they are short-ranged.
- Some things are possible from orbit, e.g. wake detection and thermal signatures.
Regarding the specific attacks, consider that nuclear depth charges were retired. Wikipedia says that homing torpedoes were better, I guess there was also a hesitation/revulsion to employ nuclear weapons in that role. (What good is an ASW weapon when you have to phone the White House for each shot?)
I expect that the efficiency considerations will apply to the KE and laser attacks as well.
Modern SSNs don't necessarily need to come to periscope depth to fire. It's possible to pop out encapsulated missiles that only launch AFTER the launching sub cleared datum. While currently they are only used for AGM's on SSKNs, there are no reasons why they couldn't also be applied to VLS tubes, or even apply them to ICBM tubes, albeit a new gen of missiles will probably need to be designed for ICBMs or VLS tubes. Basically, the capsule will "hang" just under the surface until it is time to launch, then it'll pop up, and launch, even hang vertically in the water.
God Rod Analysis
- Dropping anything from orbit produces 31mj/kg.
- A telephone pole sized mass of tungsten weighs slightly less than 13 metric tons.
- 31mj * 13000kg ~= 400GJ. That's around 100 tons of TNT (1/10th of one kiloton).
- It takes an object dropped from orbit around 15 minutes to reach the surface of Earth.
- 100 pounds of TNT has a kill radius of 3-4 meters, and a disable radius of 8-10 meters on a modern hull.
- To maintain the necessary energy density over a larger radius, the energy must increase by the cube of the radius. So while a tungsten light pole traveling at 10 times the speed of sound has 1000 times more energy than a depth charge, it won't have anything like 1000 times the blast radius. More like 5 times the disable radius.
- One can expect a sci fi sub to be significantly more durable than a modern one, further reducing the disable radius.
With a 15 minute lead time, a dropped God Rod is unlikely to land anywhere near its target. Even with the effective kill radius of 100 tons of TNT, it's extremely unlikely that a kinetic weapon will threaten a submarine. OTOH, a dropped rod might be relatively subtle until it really got moving. A fired rod might drastically reduce that time and increase the impact energy. If it comes out of a mass driver at relativistic speed, the warning time shrinks drastically while the impact energy skyrockets.
So dropping stuff on a sub isn't going to work. Shooting at it could be just fine.