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During a space cold war, a ship from the ideological enemy is not allowed remain in orbit while some of their investigators visit a crash site.

  • The reason why is narrative – to separate the characters from their support ship.
  • Their stay will be a few weeks, and the ship is independent (no fuel or supplies needed).
  • The technology level is space opera – other planets are days/weeks away, other star systems are more than a month away. FTL technology is never explained (take your pick).

Would the ship move to Lagrange 4 or 5 to "park" and wait?

Would one have an advantage over the other in terms of getting back to the planet? Would the ship actually need to move all the way to the Lagrange point, or could it just "park" anywhere outside the planet's hill sphere for the short time?

The goal is to create a delay in getting rescued.

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You could also go the opposite direction. The enemy ship refuses to move, citing a reason why they shouldn't let the good ship pass (spying/sabotage/weapons transport, take your pick). This creates a stand-off with parallels to the Cuban Missile Crisis, but as a background to the present race-against-time to save the crew of the crashed ship.

It also makes narrative sense, as cold wars tend to have large amounts of saber-rattling, with the occasional fate-of-the-world standoffs in between. This would achieve the delay you need, while potentially setting up other plot lines

Edit:
Depending how long the stand-off lasts(Cuban Missile Crisis lasted 13 days), the location of a crash site(planet, moon with atmosphere), and damage inflicted by the crash, a number of things can happen:

Scenario 1 (2-4 week standoff)
- The crashed ship could have lost comms, but retain life support and supplies, with lots of duct tape emergency repairs by surviving crew
- The enemy ship and the good ship saber-rattle, and fire warning shots as they get closer.
- They each call for resupply, and already have military ships backing them up because they would've been scrambling at the beginning of this standoff

Outcome 1: Close call, but ultimately ends well due to diplomacy

Scenario 2 (1-week standoff)
- Crashed ship suffers significant damage, and comms either crap out after the send a full status report and casualty list, or stay up to broadcast the struggle to their gov't/the greater space community. They could have someone important to the government whose dying to help force the call to run the blockade
- The enemy ship and the good ship stand off, the good guys getting ever closer to the red line drawn by the enemy ship.
- The cavalry arrives for both sides, and the good guys run through it to save the crew, and a small skirmish ensues

Outcome 2: Cold war briefly heats up, may start in earnest depending on the political climate and reaction of the community to the actions of each side

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If they have FTL that they can safely use within a solar system, they don't really need to worry about Lagrange points or really gravity at all. The force of gravity is just so much lower than the force their engines are capable of that it's negligible. It may actually be truly irrelevant if their FTL tech manipulates gravity.

If you have FTL engines capable of reaching other star systems in months, any trip within the solar system will only take minutes. Maybe seconds.

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    $\begingroup$ +1 I think you are probably right. If the engines are not stressed then it wouldn't matter. There is intended to be a technology gap between the societies, so that may be a simple way to show it. $\endgroup$ – wetcircuit Jun 23 '19 at 2:34
  • $\begingroup$ Given that FTL is entirely handwavium, the author is of course free to decide on where and when the drives can be used. Given that they haven't shared any details of their FTL drives, I don't think you can make this assumption. $\endgroup$ – Starfish Prime Jun 23 '19 at 7:34
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    $\begingroup$ @StarfishPrime I agree, but the rules need to be made clear to the reader, or the Lagrange Point DMZ will seem like a plot hole. $\endgroup$ – Ryan_L Jun 23 '19 at 15:24
  • $\begingroup$ If you have FTL, you also have unlimited time travel. physicsmatt.com/blog/2016/8/25/why-ftl-implies-time-travel This generally blows apart most stories unless the FTL is extremely cumbersome and expensive to use. $\endgroup$ – SRM Jun 28 '19 at 6:30
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Either or, but if I were parking the ship I'd go for "somewhere outside the hill sphere" to be technically "out of orbit" and very definitely not a Lagrange Point. My reason for the latter is simply that Lagrange Points tend to accumulate junk, see the Jovian Trojans and Greeks there's nothing like as much material in the Lagrange zones of a small Earth-like body but they do still have a higher density of debris than the rest of the orbital tract.

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