How do launch and stationkeeping fuel costs vary with altitude?

Question

I'm not a physicist or an engineer, so my apologies if I messed up any technical details. I've looked through the SE and found a few questions that touch on this issue (this one gets at the benefits of altitudes; this one at the fuel costs associated with launching from different altitudes; this one is again about the benefits of different altitudes; this one gets at stationkeeping fuel costs), but I haven't been able to put an answer together from them.

Consider a firm trying to launch a payload into orbit. The firm is trying to choose between two identically-shaped orbits at different altitudes, H and L (H>L). The orbits are not "too far" from each other, maybe H=L+150km. There are two fuel costs associated with H and L. One is the launch fuel cost, l(), where l(H) > l(L). The other is the stationkeeping fuel cost, where s(H) < s(L).

(My understanding is that the coverage area g() of orbit H will be greater than the coverage area of orbit L, i.e. g(H)>g(L), but I'm mainly interested in the fuel costs for now.)

My question: Is it possible to unambiguously rank the fuel costs associated with these orbits? That is, can I make a statement like, "l(H) + s(H) > l(L) + s(L)"? From what I've read, it seems like the fuel mass required for launch is orders of magnitude greater than the fuel mass required for stationkeeping, but I haven't been able to figure out the associated costs per unit of fuel.

I imagine this will depend on the altitudes H and L. I'm thinking about relatively low orbits, maybe L=700km. I've used the transfer orbit calculator here to get an idea of the magnitudes involved, but I'm not sure how to convert the delta-V difference (~40m/s for 700km to 850km) into $ cost, and I haven't been able to figure out the stationkeeping fuel requirement.

Any thoughts or suggestions would be much appreciated. Thank you!

Answer 1

Your question is hard to answer because it's the reverse of how things are normally done.

Typically satellite missions are driven first by the orbital and lifetime requirements, which determines the needed amount of stationkeeping fuel, which determines launch mass of the satellite, which constrains the selection of launcher and thus provider.

Selection of the launcher in conjunction with payload mass and destination orbit determines how much fuel will actually be loaded.

But what really sets the cost is negotiation between the satellite owner and the launch provider. The number of future launches the satellite owner can offer to the provider has a much larger impact on the launch cost than the altitude of the orbit.

That said, a 40 m/s difference in ∆v is about 0.4% of the total ∆v budget for orbital launch. ∆v changes aren't linear with fuel mass; at the margin the slope might be 3-5x linear, so you're looking at 1%-2% marginal increase in fuel load. That should let you make an estimate, but fuel costs are rarely given to more than 2 places of precision, and "around \$400,000" times 1.02 is still "around \$400,000".