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Based on the data about the Dragon 2 that I can find, here are the relevant specs, from Wikipedia on Dragon 2 and on Draco engines, and their FAA filing for its pad abort test (page 8):

  • Dry Mass: 6,400 kg
  • Propellant: 1521 kg
  • Payload: 3,310 kg to ISS (but, as a guesstimate, I lowered the payload to 3 tons)
  • Draco engine Isp : 300 s

I have no idea what the payload would mass for this mission. I decided to use 3,000 kg, and from that the capsule would be capable of a delta V of about 440 m/s. Maybe the payload to support 2 people for the duration of the mission would be less than 3 tons, if that makes sense then by all means estimate a lower payload.

It looks like when the Apollo missions did their TLI burn, they increased their speed by about 3.1 km/s.

After SpaceX's proposed 'tourist' mission to fly around the Moon did its burn for TLI, would the vessel be capable of aborting to return to Earth early (if there is a system failure a la Apollo 13)?

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    $\begingroup$ Yeah, once they're on the TLI trajectory I don't think they'll be able to significantly shorten it. (Apollo had an absolutely gigantic maneuvering capability in comparison to other manned craft.) $\endgroup$ – Russell Borogove Apr 23 '17 at 23:30
  • $\begingroup$ @Hohmannfan Do you think 400 m/s in the normal-nadir direction would get the craft back in the atmosphere after the completion of TLI burn? $\endgroup$ – Russell Borogove Apr 23 '17 at 23:33
  • $\begingroup$ @RussellBorogove Given the velocity at apogee is 190m/, 400m/s of delta-v means that the manoeuvre can be done much earlier than waiting for apogee, so I guess yes, but perhaps only after several hours. (after almost a revolution though, returning directly sounds impossible) $\endgroup$ – Hohmannfan Apr 23 '17 at 23:39
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    $\begingroup$ "...Columbia and Eagle slipped into the Moon’s sphere of influence. For the past three days, still under the tug of Earth’s gravity, their speed had rapidly decreased from 39,000 km/h immediately after TLI to just over 3,200 km/h; now, as the Moon’s gravitational pull became dominant, they began to ‘fall’ towards it, gradually speeding up to 9,000 km/h. " (americaspace.com/2012/07/15/… -- literally the first halfway credible source I found via Google) $\endgroup$ – Russell Borogove Apr 23 '17 at 23:55
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    $\begingroup$ Comments are not for extended discussion; this conversation has been moved to chat. $\endgroup$ – Hohmannfan Apr 24 '17 at 0:06
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Immediately after a TLI burn, the craft is not moving much radially; an ideal impulse would be tangential to the circular parking orbit. 400 m/sec in the opposite direction to the TLI burn would not return the craft fast, but it would surely cut the apogee of the orbit to a lower altitude than the nominal transfer orbit and return it to low Earth orbit altitudes sooner than that orbit would have.

There is a catch though. Apollo missions did not use Hohmann orbits, which have an apogee just tangential to Luna's orbit, for two reasons. They used more energetic orbits with apogees far beyond the Moon's orbit, partially because this would speed up the transfer to Lunar distance--the bigger orbit would have a much longer period than the Hohmann orbit would but the Apollo would travel only a fraction of the half-orbit before encountering the Moon. The other and even more important reason was to allow a "free return orbit," or after Apollo 12 anyway, one near one. For complicated reasons boiling down to the fact that the Moon's gravity, close up to it, changes the orbits, a Hohmann orbit is not free-return. The more energetic Apollo orbits were chosen because on an unpowered close encounter, the effect of the Moon would be to throw it back toward Earth on a similar energetic orbit to the one it approached on, coming back to the same perigee--or actually a bit lower, so it would reenter the atmosphere.

If SpaceX is not going to provide a souped-up super-Dragon with lots of extra propellant for heavy delta-V near the Moon on the nominal mission, but plans a simple flyby, they need to send the Dragon on an extra-energetic transfer orbit similar to those used by Apollo. Thus the TLI speed near Earth is slightly higher than for a Hohmann orbit. If they were planning to use a Hohmann orbit it must be that the Dragon does need have thousands of meters/sec delta V available. I conclude they are doing a free-return flyby.

In that case, the apogee of the planned transfer orbit is far beyond the Moon's orbit, and while any slowing of the speed immediately after TLI will lower that apogee, it has to be lowered a lot for the return to be sooner than the planned loop around the moon. Otherwise they fall between stools, missing the Moon because the timing is off, flying far out into translunar space--not as far as they would without the braking burn, but then they'd have encountered the Moon as planned. And since the Moon interrupts their outward orbit halfway and sends them back down going fast, they'd do better to just let it ride, unless they had so much delta-V they could lose a lot of speed and get to an orbit with apogee far closer to Earth than the Moon's orbit.

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    $\begingroup$ IIRC Apollo TLI placed the spacecraft on a circumlunar free-return trajectory, and a later mid-course correction required to reach the landing sites chosen for Apollo 13 and later missions meant that the trajectory was no longer free-return. Since the Apollo 13 accident occured after this MCC, they couldn't just wait it out but had to maneuver under power to get back onto a free-return trajectory; if my understanding is correct, had the explosion occured before the MCC, Apollo 13 would still have been on a free-return trajectory thus reducing everyone's headache somewhat. $\endgroup$ – a CVn Apr 25 '17 at 11:15
  • $\begingroup$ @aCVn The explosion probably changed the trajectory. I don't know if that change in trajectory would have been enough to push it out of the free-return trajectory. $\endgroup$ – kasperd Dec 21 '18 at 22:53
  • $\begingroup$ @kasperd Good point. It certainly would have needed consideration at the time. (Though to nitpick slightly, I do imagine that the ongoing O2 leak would have been a bigger headache than the explosion itself.) $\endgroup$ – a CVn Dec 22 '18 at 11:43

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