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Removing debris from LEO requires a significant delta-V which most schemes propose to accomplish via rocket propulsion.

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The ratio of launch fuel to payload mass is often given as 9:1 for LOE.

What is the equivalent fuel:debris mass ratio for de-orbiting?

The obvious answer is “it depends”. Orbital altitude (particularly periapsis altitude), ballistic coefficient and time to deorbit are all relevant.

For this question, consider a “typical” deorbiting task:

  1. circular orbit 700km altitude
  2. ballistic coefficient 50 kg/m2
  3. target time to deorbit 25 years

The fuel:debris mass ratio is important when comparing the cost of non-propulsive deorbiting schemes such as tethers, light sails and drag chutes.

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    $\begingroup$ based on the chart in your other question it looks like the fuel cost is zero, am I missing something? $\endgroup$
    – BrendanLuke15
    Oct 30, 2022 at 23:50
  • $\begingroup$ @BrendanLuke15 ... Yes, you are right. Everything de-orbits... eventually. But most of the junk above 700km will take more than 25 years to do so. And in that time, they may have collisions which fragment them into more pieces of junk. Current standards recommend all new satellites have a de-orbit plan for less than 25 years. Junk has no plan so it may need to be helped. Surgeons have a saying, "All bleeding stops.... eventually." But, like deorbiting, sooner is better. $\endgroup$
    – Woody
    Oct 31, 2022 at 2:40
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    $\begingroup$ 9:1 fraction - isn't payload fraction confused with propellant fraction here? Propellant, indeed, is about 90 % of rocket's mass. But rockets also have several stages, and stages get most of the rest mass. Payload to LEO is usually 3-4 % or less. $\endgroup$
    – Heopps
    Oct 31, 2022 at 12:09
  • $\begingroup$ @Heopps ... published figures are confusing to me because they often include the dry weight of the top stage, which makes it to orbit but isn't really "payload". The ratio I'm interested in for the context of this question is "what is the fuel cost to launch a kilo of fuel to LEO?". I want to compare this with the fuel cost to deorbit junk since the deorbit fuel needs to be launched to LEO. $\endgroup$
    – Woody
    Oct 31, 2022 at 15:45
  • $\begingroup$ @Woody I mean based on the chart a 50kg/m^2 object at 700 km has a deorbit time of ~25 years already $\endgroup$
    – BrendanLuke15
    Oct 31, 2022 at 23:41

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Deorbiting is not a particularly expensive task; the Shuttle orbiter only used 90-170m/s for the job. That’s a very, very, very small burn compared to the 9,400m/s needed to get to LEO. About one percent. Remember that three quarters of the shuttle fell off on the way up (ET and both SRBs) so the only fuel you have is the OMS and RCS you have left after your mission.

The problem is that the debris is in orbit, and your de-orbiter device isn’t… Or, if it is, it’s not in-phase with your de-orbiter, and worse, its inclination is wrong, too. You will have to spend propellant to catch it. Sometimes the ”cheapest” way to catch it is to send a brand-new rocket to orbit.

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  • $\begingroup$ Krail ... Some proposals suggest a device that is launched once, then deorbits many bits of junk. Once launch fuel is a "sunk asset", the marginal cost of an additional deorbit is rendezvous fuel plus deorbit fuel. The deorbit fuel: mass ratio is an important component of mission cost calculations because of the cost of launching fuel into orbit. The ratio is also important calculating the relative advantage (if any) of propulsionless orbital maneuvering and deorbiting $\endgroup$
    – Woody
    Oct 31, 2022 at 2:49
  • $\begingroup$ Krail... The orbiter weighs 54,000 lb. The rocket equation says the orbiter would have used 2.5% of the shuttle's weight in fuel to deorbit if SSME exhaust velocity=3560m/sec. $\endgroup$
    – Woody
    Oct 31, 2022 at 4:08
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    $\begingroup$ @Woody the SSMEs were useless after External Tank separation. Deorbiting was nominally done with the OMS engines. Isp = 316 sec. $\endgroup$
    – Organic Marble
    Nov 8, 2022 at 0:25

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