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Jump astrogation question

Because once the pirates shoot out the M-drive, the planet's gravity will not pull the incoming target vessel moving toward it ever inwards to eventually crash on the surface?

Why are pirates shooting at ships they can't recover in the first place? If they're going to shoot at anybody, you'd think they shoot at ships trying to LEAVE the system, so when they shot out their drives, the ships would simply coast in to deep space, where perhaps the pirates can actually take the time to hunt them down and recover them, rather than thrust headlong in to the teeth of the planetary defenses, or watch their plunder burn up in the atmosphere and/or lawn dart into deep ocean or some remote steppe.

How much Free Trader will survive uncontrolled re-entry anyway?

(What I am saying is all planetary approaches need to be indirect and orbital -- rather than surface -- approaches for safety; in case of drive failure, the need to escape pursuers [sandcasting in particular requires not decelerating when being pursued], or whatever. Otherwise a ship on a direct-to-surface course that does not decelerate enough for some reason will crater itself unwelcomely for all concerned.)

Most approaches are de facto tangential to the body, simply because they want to orbit the planet. You don't orbit the planet by flying headlong toward the center of the planet, perpendicular to the surface, then making a sudden "hard right" when you each orbital altitude. It's implicitly an oblique approach designed to enter your assigned altitude as you decelerate in to orbital speed. If your drive fails, then you skip off never to be seen again.

Since the ship can have any of several approaches when leaving jump, based on when they left jump in comparison to destination position, there's going to have to be some routine course correction. But drive failure can happen at any time, even with "bad vectors", even without piracy. And if a ship is on an unavoidable collision course with the planet, perhaps there's a mechanism to scuttle it and blow the thing up in to smithereenies after the crew escapes safely, so as to better ensure the ship burns up on entry. Seems like the polite thing to do.
 
Why are pirates shooting at ships they can't recover in the first place?

To board and loot and perhaps even take the entire ship aboard in a hanger or else in tow, I should think.

As discussed above, for general safety all planetary approaches will be parabolic or hyperbolic orbits initially with the intent to make them elliptical or circular if landing clearance is delayed (on-orbit customs inspection, for example).

If pirates (or blockaders or what have you) can disable an inbound ship -- preferably by shooting all the fuel off of it which minimizes the damage and maximizes the reduction in combat effectiveness -- and there is not enough time to dock with it and tow it away from the planetary defenses before getting too close to the mainworld, there should be an opportunity after the now-ballistic missed approach for them or their colleagues to intercept the stricken vessel as it coasts outbound after the missed planetary approach. Provided the planetary navy/guard does not fly out to meet them and/or rendezvous with the drifting vessel first.

If they're going to shoot at anybody, you'd think they shoot at ships trying to LEAVE the system, so when they shot out their drives, the ships would simply coast in to deep space, where perhaps the pirates can actually take the time to hunt them down and recover them, rather than thrust headlong in to the teeth of the planetary defenses, or watch their plunder burn up in the atmosphere and/or lawn dart into deep ocean or some remote steppe.

Indeed, and I think it makes more sense for corsairs to do it that way (racing away from planetary defenses rather than into the teeth of them), but as above outbound is not the OP scenario. (And it is not always an option for blockading forces, in the other type of scenario where is an inbound intercept -- partial or complete -- may be a tactic of necessity, based on whatever the inbound ship is carrying as payload and what preferred fate/use each side might intend for it.)

Extending the scenario opportunities in the present consideration, it could be contrived that one squadron attacks the target with the intent to chase it toward the mainworld and prevent it from decelerating into a parking orbit by forcing it to make a missed approach (whether or not it is still maneuver-capable), while another squadron moves into position on the "other" side of the planet (just outside the range of planetside defensive batteries) to finish the job and snatch the object of the exercise and head out to the 100D limit before planetary navy/guard craft can drive them off and/or take the target in tow themselves.

This type of double-teaming will work best with faster would-be targets (such as dedicated, high-G blockade runners), but it could still work with slower vessels if the pirates are strong enough to stand up to the mainworld's space-based defenses once those are scrambled.

But I otherwise agree; for something comparatively pokey such as a Free/Far/Fat Trader, reconnoitering it in port and quietly transmitting whatever intel that yields to colleagues waiting to pounce on it while it is heading back out to the 100D limit will work much better for basic pirating purposes.
 
If a jump can be plotted such that a ship arrives at an "ideal" arrival point to get to the target planet in the shortest time, could a jump arrival point be predicted given an estimate of when the target left the prior system? Astrogation in reverse as it were.

As I see it you could have more than one "ideal" arrival point in a target system, assuming that you start with minimal velocity. Note, your ship is still going to have the velocity of the stellar system that you are jumping from to compensate for in the arrival system. Arrival points as follows.

1. Arriving 100 diameters ahead of the target planet in its orbit.

2. Arriving 100 diameters from the North Pole of the planet.

3. Arriving 100 diameters from the South Pole of the planet.

4. Arriving 100 diameters farther from the target planet's star in line with the planet and star.

5. Depending on the relation of the departure system and target system, arriving 100 diameters closer to the target planet's star, on a line from the star to the planet.
 
As I see it you could have more than one "ideal" arrival point in a target system, assuming that you start with minimal velocity. Note, your ship is still going to have the velocity of the stellar system that you are jumping from to compensate for in the arrival system. Arrival points as follows.

1. Arriving 100 diameters ahead of the target planet in its orbit.

2. Arriving 100 diameters from the North Pole of the planet.

3. Arriving 100 diameters from the South Pole of the planet.

4. Arriving 100 diameters farther from the target planet's star in line with the planet and star.

5. Depending on the relation of the departure system and target system, arriving 100 diameters closer to the target planet's star, on a line from the star to the planet.

The target planet is well within the stellar jump shadow, I was thinking point of closest approach ahead of the planets orbit such that the planet would arrive in it's orbit about the time that the characters ship arrived on an intercept vector. If that made any sense. Kind of a moot point since I rolled 12 for initial range. If the pirates are at the jump shadow boarder they are sadly out of place, if they are between the characters and the planet they are well inside the jump shadow.
 
You left other possibilities out:

Jumping such that you arrive "behind" a world (or even star) such that it masks the arrival from "stuff" elsewhere in the system you don't want to know about your presence.

Since the various planets can be in very different positions in their orbits timing you arrival to one may make it hard for someone on another to move to your location or even jump there before you do whatever and get the .... out of Dodge.

These two scenarios would be useful for smugglers, spies, surveillance of the system, etc., assuming that the outer worlds or gas giants aren't occupied. Another reason why any advanced system might want to do such a thing.

As Spartan obliquely mentioned you could also jump to 100 diameters from a world ahead of it's arrival. If you look at some orbital velocities of planets you might find it quicker to do this and let the planet come to you than move to it.

With extended system generation, it is often the case that you have one or more gas giants with secondary "systems" of worlds that are like a mini-system or other planets that are significantly populated and productive. In such systems it may become useful to jump within the system as opposed to between systems. Anytime a conventional transit takes more than 7 days, plus a bit, jumping becomes a viable option.

Satellites of gas giants are another important option. If you have one that is far enough out from its parent planet and has suitable resources it can become a "gas station" for ships as an alternative to the starport. You can move to it, and it's far enough out from its parent that the gravity well is small making in and out transit times much lower.
 
The target planet is well within the stellar jump shadow, I was thinking point of closest approach ahead of the planets orbit such that the planet would arrive in it's orbit about the time that the characters ship arrived on an intercept vector. If that made any sense.

It pretty much does.

If we take the notion of "stationary" as applied to the relationship between a starship and whatever it is outside the 100D limit of, it would might more sense in this situation to calculate the Jump exit point as stationary with respect to the primary and not the mainworld.

So yeah, the arriving starship could simply start maneuvering with a vector more-or-less perpendicular to the mainworld's orbit, and only need to match the mainworld's orbital velocity and orbital position at some future time for orbital insertion around the mainworld and/or landing on it.

If the pirates are at the jump shadow boarder they are sadly out of place, if they are between the characters and the planet they are well inside the jump shadow.

They might still be able to make a play for the target while it is inbound, if they are fast enough and the Jump shadow is big enough; otherwise, as discussed above, ambushing the target while it is outbound to the next and ultimate destination star system could still be an option (and maybe a better one at the end of the day from the pirates' point of view), couldn't it?
 
With extended system generation, it is often the case that you have one or more gas giants with secondary "systems" of worlds that are like a mini-system or other planets that are significantly populated and productive. In such systems it may become useful to jump within the system as opposed to between systems. Anytime a conventional transit takes more than 7 days, plus a bit, jumping becomes a viable option.

Satellites of gas giants are another important option. If you have one that is far enough out from its parent planet and has suitable resources it can become a "gas station" for ships as an alternative to the starport. You can move to it, and it's far enough out from its parent that the gravity well is small making in and out transit times much lower.

Several issues here -
  • 7 days isn't the time benchmark. 8 days is - the high end of normal jumps. Why? Because if you can get there in 8 days or less, jump can't guarantee being there earlier (counting 100 diameter travel times as 2×0.15 days), as jump is 6.3 to 7.7 days.
  • The time benchmark is itself a false decision point for most things. See also the Concord vs the Boeing 747, Douglass DC-10, Airbuss A-300... It's cost-benefit. Is the time lost worth more than the increase in price?.
    For most durable dry goods (including many foodstuffs), price is the main benchmark.
  • The price benchmark is more like 10-15 days. J1 typically carries about 30% of hull in cargo, while 2G no jump drive is usually around 65%. And with about half the operational costs.
  • The 1G week is about 12.25 AU; 2 is 48.9 AU. Given that Traveller M-Drives canonically include deflector beams to prevent particle impacts (see Beltstrike)...
  • The 8 day marker is, at 1G: 15.9 AU. Most of the way to Uranus. Earth to Saturn year round is 8-10 AU.
  • The 9 day marker is at 20.2 AU... Earth-Uranus year round.
  • If most worlds senior corporate execs have a 1000:1 pay versus the average income (which generally also equals the GDP per Capita), and 10K:1 for base level labor (Current US figures are around that), then the opportunity cost for the extra travel time past 8 days are about...
    • Senior Major Corp Exec KCr71 per day
    • Senior Minor Corp Exec KCr7 per day
    • Professionals & Managerials: Cr710 per day
    • Senior blue-collar, most white collar: Cr 71 per day
    • Working Stiffs: Cr35 per day.
    • Base Labor: Cr7 per day.
  • Passage costs for STL 8 days vs 1J1
    • 1G, SO, MP: Cr4000 (roughly)
    • J1, SO, MP: Cr8000
    • 1G, Cargo Ton: Cr300 (roughly)
    • J1, Cargo ton: Cr1000
    So... STL is in fact cheaper to about 16 days less the opportunity costs... so assume 12 days is 4 days lost, added to MP costs of Cr6000... Senior execs jump. Manangement and professionals take the STL...
 
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