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There are 2 orbits:

  1. Circular orbit with 200km altitude
  2. Circular orbit with 800km altitude

The space tug is already on the first orbit. Its dry mass is 960kg, the total mass of fuel is 5250 kg. It supplies a satellite from the first orbit to the second.

Using the Hohmann transfer, I got the first impulse ≈ 168 m/s, the second ≈ 164 m/s. Using the Tsiolkovsky equation (assuming Isp=331s) I calculated, that the maximum mass of payload may be ≈ 47 tons!

Is this theoretically correct? Is this practically feasible?

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  • $\begingroup$ Going from 200 km altitude to 800 is a breeze. The key challenge is going from 0 km altitude and not orbiting to 200 km and orbiting. $\endgroup$ – David Hammen Nov 18 '18 at 13:58
  • $\begingroup$ @DavidHammen This problem assumes the usage of a tug, placed on 200x200 orbit. The question is, what maximum mass may be supplied to the 200x200 orbit from the Earth (because from 200 to 800 it may supply 47 tons, which is not a realistic scenario in practice). $\endgroup$ – Leeloo Nov 18 '18 at 14:08
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    $\begingroup$ Instead of looking at the vehicle going from 200 km to 800 km above the Earth's surface, look at it as the vehicle going from 6578 km to 7178 km from the Earth's center of mass. The first point of view makes this appear to be a large change in orbit. The latter point of view shows that this is not the case. $\endgroup$ – David Hammen Nov 18 '18 at 15:54
  • $\begingroup$ @DavidHammen As I said, the problem assumes that the tug is already on the 200x200 and I shouldn't change this $\endgroup$ – Leeloo Nov 18 '18 at 15:58
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Is this theoretically correct? Is this practically feasible?

I get the same result using the rocket equation, yes.

The tug described can move a 47 ton payload through that Hohmann transfer; it will then be completely out of fuel and unable to maneuver anywhere else.

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  • $\begingroup$ So, one can laucnh 47 tons of payload to 800x800km orbit just with 5 tons of fuel? And there are no restriction for that? $\endgroup$ – Leeloo Nov 18 '18 at 13:29
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    $\begingroup$ I wouldn't say "launch" as that implies starting from Earth's surface. But you can transfer 47 tons of payload from a 200x200km orbit to an 800x800km orbit with 5 tons of fuel, yes. We both just did the math to show that, right? $\endgroup$ – Russell Borogove Nov 18 '18 at 13:32
  • $\begingroup$ Right, but I'm worried about its practical feasibility. Do we know the maximum mass may be supplied by Soyuz to the 200x200 orbit from Earth? $\endgroup$ – Leeloo Nov 18 '18 at 13:37
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    $\begingroup$ Wikipedia says 6.9 tons to LEO on a Soyuz FG; I don't know if that's a 200km orbit or something else. $\endgroup$ – Russell Borogove Nov 18 '18 at 13:40
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    $\begingroup$ The usual caveats apply -- if the burn isn't instantaneous, it's less efficient; the engine might underperform its rated specific impulse; you want to provide a safety margin, and so forth. Try running the math again for 350 m/s ∆v and 320 seconds specific impulse, to get a feel for how that changes the payload. $\endgroup$ – Russell Borogove Nov 18 '18 at 13:42

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