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Is there any current launch system that could get a 75,000 kg object to geostationary orbit? If not, am I correct in assuming the Saturn V could have gotten such an object there?

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Is there any current launch system that could get a 75,000 kg object to geostationary orbit?

No. (Starship/Super Heavy can, of course, do anything, but it's not a current launch system.)

If not, am I correct in assuming the Saturn V could have gotten such an object there?

No.

According to the Silverbird calculator, a Saturn V could get about 60 metric tons to a geostationary transfer orbit of 185 km x 35786 km and 28.5º inclination, that is, an orbit with apogee at geostationary altitude but with a very low perigee.

That 60-ton payload could circularize and plane-change into equatorial GSO, requiring about 1811 m/s of ∆v. If this is done with hypergolic propellants at ~300 s specific impulse, the rocket equation tells me it would require about 28 tons of propellant, so something like 30 tons of useful payload could have been put into GSO by a Saturn V.

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  • $\begingroup$ GTO -> GSO can be done wihout hypergolic propellants. The Centaur can coast long enough. Source: en.wikipedia.org/wiki/Atlas_V $\endgroup$ – Joshua Jan 1 at 23:04
  • $\begingroup$ What about two Saturn V, one used as a tanker? $\endgroup$ – ikrase Jan 2 at 5:29
  • $\begingroup$ @RussellBorogove. What if the Saturn V was launched from a site on the equator? $\endgroup$ – Bob516 Jan 2 at 11:46
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    $\begingroup$ @Bob516 That gets you another ton into the transfer orbit, and also significantly reduces the cost to inject into the final orbit (assuming you want equatorial geostationary in both cases, not just geosynchronous), so you're up to about 43 tons of useful payload. Of course, that now means you have to build a VAB, MCC, and launch pad at the equator; it might be easier to just build a bigger booster. $\endgroup$ – Russell Borogove Jan 2 at 18:38
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No, but nuclear pulse propulsion could do far more than that.

Back in the 1960s, some rocket scientists working for the US government experimented with theoretical designs for rockets propelled by small nuclear explosives, going so far as to test small-scale models that used conventional chemical explosives, before the program was cancelled due to the Nuclear Test Ban Treaty banning the civilian use of nuclear explosives.

If such a rocket were to be built, they would, IIRC, be capable of carrying 6,000 tons to the Moon and back on one tank of fuel, an amount of cargo far exceeding the 75,000 kg you have specified in your question.

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    $\begingroup$ current means exsisting now,so could be built does not count as an answer. $\endgroup$ – trond hansen Jan 2 at 13:02
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    $\begingroup$ @trondhansen Hence why my answer starts with “no”. $\endgroup$ – nick012000 Jan 2 at 21:52

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