From my understanding of orbital dynamics, this will only be useful to spacecraft already in a precisely matched orbit. So it's not useful to think of this as an orbital gas station that spacecraft can just pull up to in order to refuel.
This depot is in a sun-synchronous orbit. There are a ton of long-term, extremely expensive, Earth-observing satellites between 600 and 800 km with inclinations of 98 degrees in this area. Yes, it's a large volume of space, and yes, it's not like you can just point yourself at another satellite, fire a thruster, and coast over to it, but if you could extend the lifetime of your billion-dollar meteorological satellite for a few million you might want to have this thing fly over to refuel you.
I doubt that they'll be moving massive satellites with huge telescopes, radars, communication dishes, and solar arrays to the tanker, rather, they'll fly the tanker to the satellites.
Edit: correcting a typo
The pitch for in-orbit refuelling is clear. Less clear is the advantage of a tank in (a close, but wrong) orbit over one on the ground with a launch booked.
Rockets become more efficient as they get larger, you get lower structure to payload weight ratios and you suffer fewer losses to drag in the atmosphere. The same scaling goes for your fuel tanks. You want to get the biggest fuel tank you can in orbit and then use efficient ion engines to move for whatever delta-V corrections you need.
Doing some back of the envelope calculations, a single 20,000 kg depot could provide fuel at approximately 10% of the cost of individual launches even with an extraordinarily inefficient 300 m/s of delta-V change for every refueling. Realistically you could probably get under 1% with efficient planning.
Kind of like remaking the old hub and spoke model, with Starship being the bulk 747, similar to the era when air travel was prohibitively expensive and demand was still too low to support direct point to point everywhere.
First, you can have several tankers in orbit which would allow for an "any day of the week / time of day" launch schedule from Earth for a payload satellite, that then rendezvoused with the tanker in the orbit it found itself in, fueled up, and then did a transition burn to the orbital plane it wanted to be in.
That "wins" because the satellite can go up with empty tanks for its orbital maneuvering thrusters, (so more mass can be allocated to the satellite), and the insertion 'tug' can ride along like an unfueled third stage. That eliminates things like "instantaneous launch windows" which keep satellites grounded if everything doesn't come together at exactly the right time.
Second, station keeping lifetime can be extended (most common value) and that means you can amortize the satellite's costs over a longer lifetime. Many geosynchronous satellites are "retired" not because they don't work, but because they are about to run out of fuel for keeping their place. If you can refuel a $5M satellite and get another 10 years of life out of it, that is a pretty big deal.
And third is the ability to gain fuel post launch as part of a retro-propulsive return profile. The heat shielding of all spacecraft is there because they use "friction" return profiles where they use the atmosphere to slow them down. That is fine but limits the amount of mass you can return because the more mass you displace, the more heat you generate in the return.
If you could fill up on fuel on orbit and use that to cancel your orbital velocity, you could do a return to earth that would stay within the heat limits of ordinary steel which would be safer and easier on the spacecraft.
ULA was circulating design ideas for a cryogenic fuel depot on orbit that were pretty neat.
These are but a few of the limitations that are imposed by having to carry all of the fuel you will ever need on every flight. On orbit refueling would make it much easier to work in space.
The flip side of amortizing the cost of the satellite over a longer mission is being able to cut your losses a bit in the event that the duration turns out to be 0.
The amount of fuel required to align spacecraft in similar orbits is miniscule compared to the cost of getting fuel into orbit to begin with. You're talking 10s of m/s of delta-V.
Source: 1000+ hours in KSP :P
The delta-V for such an orbit change is exceedingly small compared to the cost of a launch.
Also, for future reference, please consider this site's guideline "Please respond to the strongest plausible interpretation of what someone says, not a weaker one that's easier to criticize. Assume good faith."
I wasn't assuming bad faith on your part; I merely believed that your response could be confusing. You might consider that guideline as well.
"The delta-V for such an orbit change is exceedingly small compared to the cost of a launch."
In that context, I think it seems appropriate to point out that it's not true as a categorical statement.
Delta-V to launch to orbit is measured in km/s. If you are in a servicing orbit for a given orbit - how do you spend km/s repositioning (!)?
8% doesn’t sound like a lot, until you start doing the math on how much that is compared to orbital velocity. The Space Shuttle’s Orbital Maneuvering System was good for 300 m/s of delta v, which is only 3.8% of the minimum speed to keep orbit. If the shuttle was flying faster, those numbers start to fall.
I think at best the shuttle could probably afford to change its orbital plane by maybe 2 degrees.
Anyways, it'll be interesting to see where this all develops. Starship is clearly going to do in orbit refueling for their moon and other missions so there are clear situations where the delta-v for in orbit isn't too bad - match the plane on launch etc.
Let's remember that a 5 degree change in plane shifts the satellite over 590 km. If we pretend for a moment that satellites in LEO were evenly distributed, that 5 degree slice would contain the orbits of 53 of them. In reality, satellites tend to be placed in similar orbits.
Also your equation is for circular orbit inclination change at constant altitude, in practice you can do much more efficient plane change maneuvers by going into a higher and more elliptical orbit, changing inclination, and then returning to your original altitude and eccentricity.
I'd have to do the math, but I'd be curious about the confluence of launch market dynamics that would make pre-launched depots which need to change orbital planes cheaper than depots launched on demand into the right orbit from the start.
Of course, that’s gambling on those hundred customers to exist, on refueling to be reliable, etc.