Update on DSLWP-B eclipse manoeuvre

A few days ago I discussed the manoeuvre performed by DSLWP-B in preparation for the lunar eclipse. The manoueuvre raised the periapsis of DSLWP-B by around 385km. Wei Mingchuan BG2BHC has now informed me that the manoeuvre was performed on 20 Jul 2018 10:47:09.657. There were two motivations for this manoeuvre: first, to avoid eclipse, as I showed in the previous post; second, as Wei tells me, to prevent DSLWP-B from crashing into the Moon in a few months (more on this in a future post).

Wei doesn’t know the delta-v used for the manoeuvre, but estimating it is an easy exercise using GMAT, which is what I will do in this short post. In this simulation I am taking the orbital state for DSLWP-B from the first line of the 20180714 tracking file published in dslwp_dev. I will assume that the manoeuvre was a prograde burn performed at apoapsis that raised the periapsis by 385km. The GMAT script I have used is lunar_eclipse_manoeuvre.script.

First I propagte the orbit to the date mentioned by Wei. I note that the spacecraft is a little short of apoapsis, so I propagate to apoapsis, which happens at 20 Jul 2018 10:49:33.178 UTC. Then I propagate to periapsis and take note of the periapsis radius, which is 3030.91km. Finally, I use GMAT to estimate a burn that will achieve a periapsis radius of 3415.91km using a differential corrector.

The differential corrector finds a delta-v of 17.2m/s. The iterations of the differential corrector can be seen in the figure and text below. A more difficult exercise is to find a burn that stitches together the orbits described by the 20180714 and 20180727a tracking files. I will leave this as an exercise for the reader. Something very similar was done in DSLWP-B’s journey to the Moon: part II.

Differential corrector solving for the periapsis raise burn

*** Performing Differential Correction (using "DC1")
*** 1 variables; 1 goals
   Variables:  ImpulsiveBurn1.Element1
   Goals:  DSLWP_B.Luna.RMAG
   SolverMode:  Solve
DC1 Iteration 1; Nominal Pass
   Variables:  ImpulsiveBurn1.Element1 = 0
   Goals and achieved values:
      DSLWP_B.Luna.RMAG  Desired: 3415.91  Achieved: 3030.9126862  Variance: 384.997313797

   Completed iteration 1, pert 1 (ImpulsiveBurn1.Element1 = 0.0001)

DC1 Iteration 2; Nominal Pass
   Variables:  ImpulsiveBurn1.Element1 = 0.01
   Goals and achieved values:
      DSLWP_B.Luna.RMAG  Desired: 3415.91  Achieved: 3250.438899  Variance: 165.471101004

   Completed iteration 2, pert 1 (ImpulsiveBurn1.Element1 = 0.0101)

DC1 Iteration 3; Nominal Pass
   Variables:  ImpulsiveBurn1.Element1 = 0.0173366659916
   Goals and achieved values:
      DSLWP_B.Luna.RMAG  Desired: 3415.91  Achieved: 3419.17974811  Variance: -3.26974810893

   Completed iteration 3, pert 1 (ImpulsiveBurn1.Element1 = 0.0174366659916)

DC1 Iteration 4; Nominal Pass
   Variables:  ImpulsiveBurn1.Element1 = 0.0171973163032
   Goals and achieved values:
      DSLWP_B.Luna.RMAG  Desired: 3415.91  Achieved: 3415.91211393  Variance: -0.00211393450536

*** Targeting Completed in 4 iterations.
*** The Targeter converged!
Final Variable values:
   ImpulsiveBurn1.Element1 = 0.0171973163032

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