May 23 2015

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An Examination of Delta-v in Cis-Lunar space

SpaceWikia defines Cis-Lunar space thusly:

(ed: er…I thought you just said no news sights?
I’m making an exception for research or looking up things — it would be difficult to blog effectively without references.
ed: sigh…whatever)

Cislunar space (alternatively, cis-lunar space) is the volume within the Moon’s orbit, or a sphere formed by rotating that orbit. Volumes within that such as low earth orbit (LEO) are distinguished by other names. Practically, cislunar space is a useful label for “the volume between geostationary orbit and the moon’s orbit”. Beyond cislunar space lies translunar space.

Cis-lunar is Latin for “on this side of the moon” but also “not beyond the moon”. Therefore, one might regard the Lagrange points L4 and L5, the stable regions of the Moon’s Trojan points, as cislunar, but in practice they are so interesting as to be likely to be talked about in their own right.

For our purposes here, we’ll go with the Cis-Lunar terminology, and I’ll go ahead and include L4 and L5 — they are caused by the Moon’s orbit, after all. The graphic above is about the best map I’ve seen of Cis-Lunar space. As with anything space-related, depicting an accurate scale either reduces the Earth and Moon to atomic sizes, or makes the map so large (like room or hall-way sized) to be unusable. I therefore made the below Cis-Lunar map with three different distance scales to give us an idea of the miles (tens of thousands of miles) between Cis-Lunar points of interest:

Thus, there are the following points of interest in Cis-Lunar space:

  • Low Earth Orbit
  • Mid Earth Orbit
  • Geosynchronous Earth Orbit
  • Earth-Moon Lagrange points L1, L2, L3, L4, and L5
  • Low Lunar Orbit
  • The Moon

Physical distances between points don’t really begin to tell the story for these points of interest, though. Much more interesting is Delta-V (a measure of the amount of propellant required to to move from one place to another) and the time required to move from one location to another. Time is money and propellant is money.

The below graphic shows both. The top number for each vector is Delta-V in km/s (rounded to the nearest 10th), and the bottom number is the calculated number of days it would take to get from one point of interest to another. Note, for example that LEO, MEO, and GEO all take one day, but more than 10 km/s in Delta-V. L3, L4, and L5 are all similar in Delta-V and time (though in reality L3 takes a bit less than L4 and L5 — maybe I’ll update the graphic), so they’re boxed together.

Looking at the above, there are a couple of things to note:

  • Transit among the Earth locations (Earth, LEO, MEO, GEO) all take a day (or less), though the Delta-v required to change from one to the other are some of the highest observed in Cis-lunar space.
  • Of the Lagrange points, L1 is optimal both in time required and from a Delta-v perspective.
  • As HHeinlein said, one you get to LEO, you’re half way to anywhere. Escaping Earth’s gravity well takes literally tons of Delta-v, but once there, propellant requirements reduce radically.

Permanent link to this article: http://www.newspaceraces.com/2015/05/23/an-examination-of-delta-v-in-cis-lunar-space/

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