In Portal, using the portal gun to get to the moon is the obvious space travel usage, but I think people are overlooking how it'd let you trivially break the rocket equation.

Hell, you could build a >1g torchship using nothing but the ocean.

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

And that's just thinking about a static arrangement of portals. You could also use a dynamic arrangement where you use gravity to accelerate mass to arbitrarily high speeds and then fling it out the back

If you could make portals bigger you could also have a fun setup where you build your spaceship and then just let gravity accelerate it though a portal-loop.
You get going as fast as you want, then just swap the portals so you're now aimed at Mars.

Anyway the lazy, boring way to use a portal and pretend you aren't violating a bunch of physical laws is to just use it for fuel transport.
You have a bunch of fuel on the ground, a tiny tank on your rocket, and you keep topping off the rocket's tank by piping in the fuel.

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.

This isn't a ship-destroying weapon, this is a civilization-ender if not planet-killer.

You've got a projectile moving at a significant fraction of the speed of light. This is a relativistic weapon: it's going to hit harder than if it was a nuke.

You can also make it bigger by not using a roughly round rock and instead using a long rod of the densest material you can get your hand on.

But mass you pay for, speed you don't.

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.

Sir Isaac Newton may be the deadliest son of a bitch in space, but the deadliest son of a bitch in the Half Life universe is Cave Johnson.

The Nihilanth could teleport an entire army to earth, the combine can conquer a planet in hours, the g-man has control over time and space, but Cave Johnson's invention could put a hole in a planet

Alternate ending to Half Life Alyx where it turns out the scary thing the Combine has locked up in the vault is Chell.

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.

It would be a very Cave Johnson thing to try to fix global warming by pushing the earth away from the sun.

The only thing more Cave Johnson would be using relativistic weapons to blow up the sun

The lab boys tell me that if you dump enough iron into a star, it'll turn off. Well, we don't have that much iron on hand, but what if it's moving at 99% the speed of light?
They told me that wouldn't help, but I said pack your bags: We're doing it anyway

Portal 2 does establish that the portal-placing shot moves at the speed of light, but that just raises the question of how fast you move through the portals themselves.

It basically can't be slower than light, or you'd chop yourself in half if you moved halfway into one and then backed out.

So it has to be lightspeed: which means, if relativity is still correct, that it's also a time machine.