# How does a satellite's mass affect its fuel consumption to maintain orbit?

Given two otherwise identical satellites in identical orbits, the more massive one's orbit decays more slowly from atmospheric drag: $$F=ma$$, same $$F$$ (drag), bigger $$m$$, so smaller $$a$$ (decay). So its orbit needs less boosting, so it needs less fuel.

But the more massive one needs more force to boost orbit, again because $$F=ma$$. So it needs more fuel.

Does one effect dominate the other?
Or do the $$m$$'s cancel out?
Over the long term, to maintain orbit, does the more massive satellite burn fuel faster, or slower?

Clarification: "otherwise identical" means same engines (same thrust and fuel consumption) and same frontal area. It means Identical twins except for mass of payload (which might mean more fuel, but that can't affect fuel consumption except maybe as the fuel depletes, the heavier twin becomes more like the lighter twin).
What may vary is when and how long the boost burns are, because the optimal behavior for each twin might differ.

Because fuel mass is likely a significant fraction of total mass, the Tsiolkovsky rocket equation may apply here. But I'm not sure how wet mass and dry mass fit in.

• Two otherwise identical satellites means identical thrust and fuel consumption of the engines? If this is true we need less frequent but longer boosting burns. If the engine's efficiency is constant for shorter and longer burns, fuel consumption would be the same. But if efficiency is smaller for the engine start and stop phases, fuel consumption will be smaller for the heavier satellite.
– Uwe
Commented Dec 19, 2023 at 17:25
• @Uwe yes. phil1008's answer notes this, and others have touched on it. I'll edit to clarify. (I can't imagine start/stop being more efficient!) Commented Dec 19, 2023 at 22:21
• drag isn't the only reason that satellites need to do station keeping. There's gravitational anomalies, solar pressure and magnetic forces as well. You've specified LEO, so drag will dominate, but I think you'll want to use the engines to account for second order effects from gravitational anomalies. You probably also want to look into the Tsiolkovsky rocket equation, if the mass of the fuel is a non-negligible fraction of the amount of the satellite (it usually is).
– craq
Commented Dec 20, 2023 at 4:25

If you re-boost them both at the same time interval, then the lighter satellite's orbit will decay more between re-boosts, it will experience more drag because it falls deeper into the atmosphere, and it will require more fuel to maintain its orbit.

But if you always re-boost them when their orbit decays to a specified minimum altitude, then I think they should be equivalent. However, the lighter satellite might still need more fuel because more frequent re-boosts may incur more engine startup and shutdown losses.

• Start/stop losses are almost certain, so either scenario means the lighter one must burn fuel faster. And by handwaving the mean value theorem, ditto for any other boosting protocol. So, the heavier (the more fuel onboard) the better, at least up to the launch vehicle's limits. Commented Dec 22, 2023 at 21:57

If you apply conservation of energy, fuel consumption should be the same since energy loss to air drag is identical.

• What about Oberth-effect-like voodoo? The heavier one has fewer but longer burns? Or is that lost in the noise? Commented Dec 18, 2023 at 21:27
• @CamilleGoudeseune ... depends on what you mean by "otherwise identical". Does the massive one have identical engines, or identical acceleration? Identical fuel load? Commented Dec 18, 2023 at 23:39
• @CamilleGoudeseune ... Oberth effect depends on velocity. Both satellites would be going the same velocity at the same altitude. Not knowing how to work out exact consumption, I'd guess Voodoo effects cancel out. Definitely not an SE quality answer ! Commented Dec 18, 2023 at 23:45
• Identical engines. I'd imagined identical except for heavier (denser) payload, but some of that payload might as well be fuel load. Which suggests the different question of how much fuel vs payload to carry. Commented Dec 19, 2023 at 2:20
• Oberth voodoo: the heavier one's rarer burns might be timed more precisely to exploit that? Or the lighter one's shorter burns are closer to the max-V Oberth ideal? I can convince myself either way. Commented Dec 19, 2023 at 2:23

The energy loss due to atmospheric drag is proportional to the frontal area of the satellite. If the 'otherwide identical' clause means they have the same frontal area, then they will lose energy at the same rate, and require the same amount of boosting (using otherwise identical engines and burn regimes).