I'd do the math on how much thrust you'd get out of sticking one portal at the bottom of the Mariana Trench and the other in a ship, but I think it'd maybe be slightly tricky because you've got yourself an inertialess thruster right there, which is slightly illegal according to physics.
The Einstein cops are gonna show up and impound your spaceship
BTW, as a variant on the kzinti lesson, the portals are extremely dangerous as a weapon, because of how good they are as a weapon.
Ignoring the obvious ways to fight with them like opening a portal on the enemy's hull, shoving out a nuke and then closing the portal...
You could also just have a rock that you're letting accelerate to arbitrary speeds in a vacuum. That's free unbounded kinetic energy, the only limitation being the "charge" time.
Like, the worked example from Atomic Rockets has 7 kilograms of cat litter moving at 90% of lightspeed hitting a stationary target with 195 megatons of kinetic energy.
https://www.projectrho.com/public_html/rocket/spacegunexotic.php
But yeah this is the ultimate doomsday weapon. You can accelerate indefinitely for free, you just have to wait.
(and if you can put your portals in orbit of a more massive object, you get faster acceleration than 1g)
So you don't need more than a portal gun, a tungsten rod, and some time to blow the atmosphere off a planet.
There's also the gravity interaction: an infinitely falling object that never reaches the bigger body is also accelerating the bigger body.
Your forever falling object is shoving the earth upward, very slowly. That could matter in the long enough term... But it seems kinda meaningless compared to the other ways you could use a portal.
Still, might be handy if you need to adjust the orbit of a planet and are willing to wait.
@Amikke @foone This makes me wonder how gravity interacts with portals in the first place. If you put one on the ceiling on Earth and the other on a piece of material floating in space, would an apple floating just in front of the space portal fall into it? My experience with the games suggests not, but why? The obvious answer is "portals transport matter but not forces," but then what force holds matter together as it passes between them?
@foone this brings up another interesting issue, if you placed the portals in places with enough gravitational difference, the gravity pulling on whatever you stick through the portal will rip it off as soon as it can overcome tension keeping both sides of the body together. It may even turn it into dust, since the tension will pull more of the object through the portal, which will be ripped off, but not before exerting enough force to pull more…