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I was reading an article about how the Orion capsule just did the first of two burns that it will use to transfer out of its lunar orbit and back to Earth.

I understand the phenomenon of a gravity slingshot but, even so, I have to wonder why Orion isn't just using a single "direct" burn to break lunar orbit.

Is (was) its altitude so low that the amount of delta-V required to first reach escape velocity before transferring larger than the amount of delta-V required by lowering the altitude of its periapsis and then also doing a second burn at the periapsis?

Or is there another consideration at work that made the two-burn method more attractive than a single burn?

Orion flight plan

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  • $\begingroup$ It looks strange in this simplified drawing. But have a look at the actual orbit in this animation: en.wikipedia.org/wiki/Artemis_1#/media/… The two swing-by maneuvers add/remove about 1.6 km/s $\endgroup$
    – asdfex
    Dec 3, 2022 at 19:10
  • $\begingroup$ Isn't this just going into a lower orbit to take advantage of the Oberth effect? That's what it looks like from the diagram in the link, and it's not obvious to me that the animation shows something different, although I'm not sure. $\endgroup$
    – N. Virgo
    Dec 4, 2022 at 3:36
  • $\begingroup$ @n my understanding (admittedly only gained from playing Kerbal space program) is that what you're describing works for any orbiting craft? ie: The Oberth effect could work for a single burn in the same way as a dual burn. The burn at the periapsis would just be at a higher altitude and without a first burn. My understanding may be completely wrong, though. $\endgroup$
    – Rykara
    Dec 4, 2022 at 3:50
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    $\begingroup$ The core of the Oberth effect is that you get more orbital energy for the delta-V you expend when the spacecraft is moving faster. And in this particular case, the way to get that speed for the least delta-v, is to do burn 1 to drop your periapsis from the high retrograde lunar parking orbit to as near to the lunar surface as you can afford, and do the departure burn at periapsis. to get the orbital energy that gives you the desired lunar departure velocity to hit Earth. $\endgroup$
    – notovny
    Dec 4, 2022 at 4:42
  • $\begingroup$ @notovny's comment is what I meant. It works in KSP too, so you can give it a try: start in a high orbit and compare the delta-V cost of (i) doing the escape burn directly from the high orbit, vs. (ii) first lowering your periapsis as much as possible and then doing the escape burn at periapsis. You'll find that (ii) is often cheaper! $\endgroup$
    – N. Virgo
    Dec 4, 2022 at 7:40

2 Answers 2

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The drawing in this "flight plan" indeed looks like it would be trivial to get into a direct Earth return trajectory without doing two burns and a low fly-by at the Moon.

The actual trajectory can be seen much more clearly in this animation by Phoenix7777 on Wikimedia:

Artemis 1 Trajectory

The first departure burn happened late on December 1st, roughly at the point when Orion's trajectory crosses the Moons orbit inward. This is just a course correction to lower the periapsis during the Moon encounter a few days later from several 10,000 km to a few dozen kilometers. The effect of this burn can be seen comparing to another animation showing another mission profile having Orion stay close to the Moon for a full month: There is no close pass-by, but the orbit continues at a substantial distance to the Moon.

The second burn happens right during the closest encounter with the Moon and brings the orbital speed relative to Earth down. The departure swing-by brings the capsule from about 1.1 km/s orbital velocity down to almost 0 - the return to Earth then is basically a free fall from a height of 380 Mm.

This blog by ESA has a nice list of all the maneuvers during the whole mission. The two departure burns add up to a total of 430 m/s while more than the same amount is gained due to the very low fly-by of the Moon. Most of this gain can be attributed to the Oberth effect.

This is an advantage of not being in a low lunar orbit, but in a distant one and "just" doing a fly-by: The Apollo missions had to provide about 1 km/s of $\Delta v$ by themselves, because they needed to break free from their orbit.

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    $\begingroup$ So, they're literally dropping Orion from the sky like Newton's apple? That is so cool. $\endgroup$ Dec 3, 2022 at 21:21
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    $\begingroup$ @JörgWMittag They are in an orbit around Earth, only weakly coupled to the Moon. The easiest return path is a very elliptical orbit with a major axis close to the orbital radius of the Moon. This has an orbital velocity of close to 0 at its apoapsis. $\endgroup$
    – asdfex
    Dec 4, 2022 at 9:59
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    $\begingroup$ It's a bit hard to see in this animation where the two burns happen that we are talking about. $\endgroup$
    – Nobody
    Dec 4, 2022 at 18:29
  • $\begingroup$ @Nobody Added in the paragraph just after the image. $\endgroup$
    – asdfex
    Dec 4, 2022 at 18:37
  • $\begingroup$ @JörgWMittag: And to think Apollo returned in only three days. $\endgroup$
    – Joshua
    Dec 5, 2022 at 2:46
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Answer: The 2 burn transfer uses less fuel than the one-burn direct transfer.

Orion was in a Distant Retrograde Orbit. “Distant” means beyond the Lagrange Points L1 and L2. “Retrograde” means orbiting in the opposite direction to the Moon. These are elegant orbits because they are stable. Stability is a precious quality in 3-body orbits.

This orbital distance places Orion at the outer limits of the Moon’s Gravitational Sphere of Influence. This means, from a patched-conic perspective, the Earth’s gravity can be ignored inside the orbital radius … so we can think in Keplerian 2-body terms. Once Orion pops out of this orbital radius, we can ignore the Lunar gravity and think in terms of an Orion-Earth 2-body problem.

enter image description here

A direct return would require a single burn which would put Orion on a (roughly) elliptical return orbit to Earth. This burn must boost Orion's orbit out of the Lunar Sphere of Influence. But it must also cancel Orion's Lunar orbital speed. Otherwise the burn would leave Orion in a high Earth orbit, following along behind the Moon. Lots of delta-v required!

enter image description here

To save fuel, it was instead decided to perform a retro burn into a Lunar orbit which would permit a Oberth Effect burn. The Oberth Effect allows very efficient use of fuel, even if it sometimes requires a “wasted burn” to send the craft in the “wrong” direction.

enter image description here

At the periapsis, the Oberth Effect burn accelerates Orion into a hyperbolic Lunar escape orbit.

enter image description here

Once Orion leaves the Lunar Sphere of Influence (at about the altitude of its previous Distant Retrograde Orbit) it “falls into” a highly eccentric transfer orbit which intersects with Earth’s atmosphere.

enter image description here

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  • $\begingroup$ That's what it's so hard for me to wrap my head around. Seems like, if Orion is only just inside the moon's SOI, it should take less energy to "nudge" it out then to lower the altitude of its periapsis to allow for the Oberth burn. Clearly that's just a flawed assumption on my part! $\endgroup$
    – Rykara
    Dec 4, 2022 at 6:02
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    $\begingroup$ @Rykara If Orion was just “nudged” out of the Moon’s SOI then it would be orbiting the Earth in a similar orbit to the Moon’s, and need a lot more delta V to break that orbit and return to Earth. $\endgroup$
    – Mike Scott
    Dec 4, 2022 at 8:18
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    $\begingroup$ @Rykara ... 2 things make this easier to intuit: 1) In orbital mechanics, it takes as much delta-v to go "downhill" as "uphill". 2) The Oberth Effect means the faster you go, the more efficient your rocket is at converting propellant into kinetic energy. $\endgroup$
    – Woody
    Dec 4, 2022 at 16:35
  • $\begingroup$ Looks "analogous" to a bi-elliptic transfer. Adding an extra burn in "the wrong direction" in order to take advantage of the Oberth effect. In this case the first burn is in high lunar orbit so the periapsis changing burn is relatively small and then the ejection burn takes advantage of the Oberth effect. $\endgroup$
    – lamont
    Dec 7, 2022 at 19:35
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    $\begingroup$ And @Rykara it is also true that those delta-v maps for interplanetary burns are highly non-linear. You wouldn't want to go to another planet by first boosting to a very high weakly bound orbit and then doing the interplanetary ejection burn. You want to dump all your propellant near the Earth. The dV required for the ejection burn itself will be higher in a higher orbit, plus it'll cost to get to that higher orbit. See the graph in: old.reddit.com/r/KerbalAcademy/comments/e5fazy/… for just the cost of the ejection burn. $\endgroup$
    – lamont
    Dec 7, 2022 at 19:43

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