Mike’s Tweets

SpaceFlight 101 Site covers LADEE Mission analysis and trajectory design

Patrick Blau’s (@Patrick_S101) excellent site “SpaceFlight 101” covers the LADEE mission design here:

LADEE Mission and Trajectory Design.

Here we’ve been worried for years about what things we can and cannot post due to our very special “ITAR” regulations, and Blau’s German web site does it all for us. He mostly gets it right (having to dig through GSFC and Ames postings freely available on the web).

  • Do you know how much LADEE saved in delta-V by using these repeated elliptical orbits over the usual trans-lunar injection delta-v?

    Bob Clark

  • LADEE didn’t save any TLI delta-v by using phasing loops. The total delta-v to go to the Moon is the same as if it had gone direct. However, delta-v is saved in the trajectory correction requirements imposed by the Launch vehicle. The Minotaur V, which is a stack of 5 solids, isn’t considered to be a particularly precise rocket. In other words, if we were to ask for a 6.3 day orbit, we might get a 5 day orbit, or we might get an 8 day orbit. In a direct injection trajectory (such as the 3-day missions used by Apollo), injection errors can only be corrected out after good amount of tracking can be done (~ 24 hrs normally) to determine the orbit (OD, or “Orbit Determination”). However, as the spacecraft gets further and further away from the Earth, the cost of correcting out launch errors gets larger as well. Often times, by the time enough tracking data can be gathered, the cost of correcting out any launch errors can be 5-10 times the actual size of the error. So a 5 m/sec error would take 25 m/sec to correct, etc.

    If, instead of using a direct approach, you use phasing loops (like LADEE) the cost is a lot closer to 1:1 (i.e. a 5 m/sec error in launch costs 5 m/sec to correct, or can even save you fuel).

    Assume that you’re going to launch to a 6.4 day orbit and that you’ll then transfer to an 7.6 day orbit, and then a 10 day orbit, and then spend 5 days getting to the Moon (total of 29 days). The cost of transferring to the 5-day lunar transfer from the 6.4 day starting orbit is always the same. Now say that your rocket doesn’t give you exactly what you want, and instead of a 6.4 day orbit, you are inserted into a 7 day orbit. Instead of doing a TCM to correct out that error, you simply replan your trajectory profile. You spend 7 days in the first orbit, but instead of transferring to a 7.6 day orbit, your first maneuver is zero, and you stay in the 7 day orbit for 2 days. So your first rev is 7 days, second rev is 7 days, and then you transfer to a 10 day orbit, and take 5 more to get to the Moon (still 29).

    Same thing if you are launched to a 5 day orbit. The second orbit can be 9 days, the third 10, and 5 days to the Moon (29 days total again).

    You get the picture.

    The total delta-v to get to the Moon doesn’t really change, but your orbit profile is flexible to large dispersions in your injection.

    Phasing loops have been used on many other missions (Clementine and WMAP are 2 good examples). I designed the phasing loops on LADEE to accommodate the Minotaur V dispersions. The LADEE spacecraft barely had enough fuel to do its science mission, and the choice of phasing loops allowed the mission to accommodate the Minotaur V dispersions, at the cost of some extra time in cislunar space. The operations costs are not free (of course), but if you can’t fit on the rocket, sometimes you don’t have a mission.

    [Funny thing is that although the Minotaur V is “supposed” to have large dispersions, the fact is that the launch last Friday (Sept 7, 2013) was just about perfect. We got almost precisely the nominal trajectory, in what probably is the most precise injection a Minotaur rocket has ever done. Had we known in advance that we could have gotten such an injection, we probably would have gone direct.]

  • Jonathan McDowell

    Nice explanation!