Starship can carry 1200t of propellant.
Starship has three Raptor 2 Vacuum engines, each with about 3.5km/s of delta-V
ISS has an orbital velocity of 7.66km/s , escape velocity is 11.2 km/s.
ISS weighs 400 tons.
There are unknowns, how much acceleration can the ISS support without falling apart. Since this is a two step process (change the orbital plane and change the orbital altitude) one will have to plan for avoiding other things in similar orbits. Finally, while I suspect a fully fueled Starship could do this with one tank, if you need to refuel between steps it would be more efficient to change the orbital plane, refuel and then change the orbit.
Putting it into an Earth/Sun concentric orbit might be easier.
[1]: Yes, its all wikipedia and such and no I haven't built a Kerbal model and run it, and yes it would be a "stunt" but penciling it out with some fellow space nerds the numbers aren't "ridiculous." But it absolutely does require the ability to fill up the tanks (maybe more than once) while on orbit.
ISP for an efficient rocket engine like raptor in vacuum is 360 s, you get a ratio of 9.7. If (Station +fuel mass)/(Station mass) = 9.7 so fuel required = 8.7x the station mass.
The space station is 420,000 kg, so we need 3,650,000 kg of fuel. Falcon 9 payload to LEO is 22,000 kg, so this is 167 Falcon 9 cargo launches.
Starships hypothetical cargo is 120,000kg to LEO, so 30 starship launches would be required just for fuel to move the space station.
Some starships would have to act as engines and fuel tanks for the space station, further increasing the mass and number of launches. Starship fuel capacity is 1,200,000 kg and the empty mass is 100,000kg, so you would need at least 3 starships as tanks, which adds another 300,000kg of mass to move.
Not to mention: even if it were possible to move the ISS to L4/5, and get it there in one piece... why? We don't have the infrastructure to keep the station supplied, and it's likely to overheat badly (since it's no longer in Earth's shadow half of the time). It's a lot of effort with no clear payoff.
Starship can carry 1200t of propellant. Starship has three Raptor 2 Vacuum engines, each with about 3.5km/s of delta-V ISS has an orbital velocity of 7.66km/s , escape velocity is 11.2 km/s. ISS weighs 400 tons.
There are unknowns, how much acceleration can the ISS support without falling apart. Since this is a two step process (change the orbital plane and change the orbital altitude) one will have to plan for avoiding other things in similar orbits. Finally, while I suspect a fully fueled Starship could do this with one tank, if you need to refuel between steps it would be more efficient to change the orbital plane, refuel and then change the orbit.
Putting it into an Earth/Sun concentric orbit might be easier.
[1]: Yes, its all wikipedia and such and no I haven't built a Kerbal model and run it, and yes it would be a "stunt" but penciling it out with some fellow space nerds the numbers aren't "ridiculous." But it absolutely does require the ability to fill up the tanks (maybe more than once) while on orbit.