Formula requests for interception by pirates and missiles

[cgodfrey7]

I have probably bitten off more than I can chew, but sometimes my mind works that way

I have a pirate ship in a system, waiting for a luxury liner to appear. The luxury liner will appear 192,000 km away from the destination world. (Thinking in 2-dimensions, assume the luxury liner is due South of the world.) Using the world as a reference point and thinking in 2-dimensions, the pirate ship is off to the left of the straight-line North (up the y-axis) approach of the luxury liner by an angle of 33 degrees, at a distance of 160,000 km from the world. The luxury liner has 1G acceleration, and the pirates have 3G acceleration. What angle will the pirate ship have to fly at, and for how long, before the pirate ship intersects the luxury liner? (If it helps, make assumptions such as instantaneous acceleration is possible and that the pirate won't have to slow down when the ships intersect, or state assumptions. If there is an advanced formula for figuring out how to match acceleration after turnover, wonderful!!!)

What acceleration do missiles travel at? If target range for missiles is 90,000 km, and sensor range is 45,000 km for the luxury liner, how much time will the crew have to react to the missiles, assuming a succesful sensor check?

 

[Shadowdancer]

The only question I can help you with is missles -- they travel at 6G.

 

[Orionruse]

If you want to know precise times for burns, you would have to know more data than the game rules allow (i.e. mass of both starships involved, impulse rates {impulse ratings and perpetual motion due to the planet's gravity well}, etc.) and use some differential calculus to determine the answer.

In short, even NASA has a team of engineers to determine these things for everything from the shuttle to all of our various space probes floating around the Sol System.

As far as the game is concerned, use some simple vector analysis to figure it out. I know you have given some distances to the planet, but how far from the planet do you want the pirates to raid the liner? Furthermore, do they want to destroy the ship for some reason, or raid it? At their instantaneous accelerations, the ships will intersect at a point roughly 96,000 km south of the planet.

Also, how fast is each vessel travelling? You can still have an acceleration of 3g travelling at 320,000 km/h-- far from relativistic speeds. Which brings up another question... are they travelling at relativistic speeds? If so, you have to consider time dilation, which also affects your equation.

Best just to use GM discretion and make an educated guess. My solution would go something like this...

Both ships are travelling towards the planet, at a velocity similar to the orbital velocity of Earth (roughly 25,000 kph) at their listed accelerations. They will intersect somewhere around half of the distance of the liner's initial approach (via the Pythagorean Theorem, the pirate ship is travelling along the triangle's hypotenuse). These things being considered, just the travel time would make the encounter take place in about one hour and fifteen minutes. There are several things to consider here, because with sensors, the liner would probably pick up the pirates about fifteen minutes out from the encounter. The pirates are in a bad position, because even if they use their own mass to mask the missiles they fire, it will still give the liner some time to send a mayday. Surely, a passenger liner will be going to a civilized system, where planetary patrols can go full thrusters to the encounter, and tie up the pirates.

We have'nt even begun to discuss the time for a boarding action.

In short, if the pirates are attempting a raid, they will likely have a very short career. They should try a sneakier approach-- like hiding near some space debris, or even faking a distress call. Even ocean liners are required to answer a distress call if they are the nearest vessel in the area.