TransX EEJ flight plan around 2020

wingnut

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I'm trying to create an Earth-Earth-Jupiter flight plan around the year 2020 with TransX. The Trajectory Browser as well as the [ame="http://www.orbithangar.com/searchid.php?ID=5418"]trajectory optimization tool[/ame] suggest that this is possible.

In TransX however, I cannot get the closest approach to Jupiter actually close enough for an actual encounter. At the end of the post is one of my attempts and the report of the trajectory optimization tool.

I think the Earth flyby date in the TransX plan is close enough to the traj. opt. tools report but when I tweak the encounter MJD in TransX to be close to the date in the report with just the outward angle, Jupiter is way off. Changing the inclination in that stage quickly results in an even worse closest approach.

Has someone done a similar flight plan and might have some tips for me?

Code:
BEGIN_DESC
Contains the latest simulation state.
END_DESC

BEGIN_ENVIRONMENT
  System Sol
  Date MJD 58954.0058771777
END_ENVIRONMENT

BEGIN_FOCUS
  Ship GL-01
END_FOCUS

BEGIN_CAMERA
  TARGET GL-01
  MODE Cockpit
  FOV 50.00
END_CAMERA

BEGIN_HUD
  TYPE Surface
END_HUD

BEGIN_MFD Left
  TYPE User
  MODE TransX
  Ship  GL-01
  FNumber 5
  Int 1
  Orbit True
  Vector  -3154733.83829 967691.937969 5449864.94235
  Vector  -336.547907833 92.2880495285 -211.202568637
  Double  3.98600439969e+014
  Double  58954.0058769
  Handle Earth
  Handle NULL
  Handle NULL
Select Target
 0 Escape
Autoplan
0 0
Plan type
0 0
Plan
0 1
Plan
0 0
Plan
0 0
Select Minor
 0 None
Manoeuvre mode
0 0
Auto-Centerٍ
0 0
Base Orbit
0 0
Prograde vel.
 1  0
Man. date
 1  58954.0053384
Outward vel.
 1  0
Ch. plane vel.
 1  0
Intercept with
0 0
Orbits to Icept
0 0
Graph projection
0 0
Scale to view
0 0
Advanced
0 0
Pe Distance
 1  7645212
Ej Orientation
 1  0
Equatorial view
0 0
Finvars
  Finish BaseFunction
  Int 2
  Orbit False
  Handle Sun
  Handle Earth
  Handle Earth
Select Target
 0 Earth
Autoplan
0 0
Plan type
0 2
Plan
0 0
Plan
0 0
Plan
0 1
Select Minor
 0 None
Manoeuvre mode
0 0
Auto-Centerٍ
0 0
Base Orbit
0 1
Prograde vel.
 1  0
Man. date
 1  58954.0058765
Outward vel.
 1  0
Ch. plane vel.
 1  0
Intercept with
0 0
Orbits to Icept
0 2
Graph projection
0 0
Scale to view
0 0
Advanced
0 0
Prograde vel.
 3  5099.70972896
Eject date
 1  58954.0004909
Outward vel.
 1  0
Ch. plane vel.
 3  0.9
Finvars
  Finish BaseFunction
  Int 4
  Orbit True
  Vector  -3230602597.41 2391586.87093 8700969905.86
  Vector  1645.53585251 -1.68070115895 -4896.98023055
  Double  3.98600439969e+014
  Double  59670.6411156
  Handle Earth
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  Handle NULL
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Autoplan
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Plan
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Plan
0 1
Plan
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  Int 3
  Orbit True
  Vector  -128540279493 1869741.48294 -79868493914.7
  Vector  17392.1280201 0.592738394835 -30096.2253314
  Double  1.32712838556e+020
  Double  59691.3523283
  Handle Sun
  Handle Earth
  Handle Jupiter
Select Target
 0 Jupiter
Autoplan
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Plan
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Plan
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Advanced
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 1  0
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 5  0.213251658392
Inc. angle
 1  0
Inherit Vel.
0 0
Eject date
 1  59691.3523283
Finvars
  Finish BaseFunction
  Int 5
  Orbit False
  Handle Jupiter
  Handle NULL
  Handle NULL
Select Target
 0 None
Autoplan
0 0
Plan type
0 1
Plan
0 0
Plan
0 2
Plan
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Select Minor
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0 0
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Prograde vel.
 1  0
Man. date
 1  58954.0005475
Outward vel.
 1  0
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 1  0
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Orbits to Icept
0 0
Graph projection
0 0
Scale to view
0 0
Advanced
0 0
Draw Base
0 0
Finvars
  Finish BaseFunction
END_MFD

BEGIN_MFD Right
  TYPE User
  MODE TransX
END_MFD

BEGIN_SHIPS
GL-01:DeltaGlider
  STATUS Landed Earth
  POS -80.6824940 28.5967940
  HEADING 330.01
  RCSMODE 0
  AFCMODE 7
  PRPLEVEL 0:0.995000 1:1.000000
  NAVFREQ 94 524 84 114
  XPDR 0
  GEAR 1 1.0000
  PSNGR 2 3 4
  AAP 0:0 0:0 0:0
END
END_SHIPS

BEGIN_ExtMFD
END

Code:
TRAJECTORY OPTIMIZATION TOOL v2
Optimization Report - 14-Jan-2015 19:38:20
Flight Plan: EEJ 2020
----------------------------------------------------------------


RESULTS
--------------------------------
OPTIMUM EARTH DEPARTURE DATE: 9/8/2020 14:37:59 - C3: 90.1377 km²/sec²
OPTIMUM EARTH SWINGBY DATE: 5/28/2022 23:52:9 - Powered Delta-V Required: 3.3249e-006 km/sec
OPTIMUM JUPITER BARYCENTER ARRIVAL DATE: 12/19/2024 13:14:26 - Body-centric Arrival Velocity: 5.8187 km/sec

TOTAL COST: 197.7315505


ORBITAL ELEMENTS - J2000 Ecliptic Reference Frame
--------------------------------
LEG 1 (Number of Full Revolutions: 0)
-Semi-major Axis: 232078105.9956491 km
-Eccentricity: 0.4154591
-Inclination: 0.0029463 deg
-Long. of Ascending Node: 177.0795112 deg
-Argument of Periapse: 120.3432078 deg
-True Anomaly (start): 48.6939094 deg
-True Anomaly (end): 309.9015247 deg

LEG 2 (Number of Full Revolutions: 0)
-Semi-major Axis: 455597028.6213902 km
-Eccentricity: 0.6700455
-Inclination: 3.1096967 deg
-Long. of Ascending Node: 247.2732039 deg
-Argument of Periapse: 11.8618472 deg
-True Anomaly (start): 348.1892673 deg
-True Anomaly (end): 177.8032643 deg



GENETIC ALGORITHM INFORMATION
--------------------------------
Termination Reason: Maximum number of iterations exceeded.  Consider increasing maximum number of iterations in the optimization options. 
Number of Generations Computed: 250.0 
Number of Fitness Function Evaluations: 63147.0 
Random Number Generator Type: mt19937ar
 

boogabooga

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Earth-Earth encounters are tricky.

Your TOT results looks like a "bad" solution. C3 = 90.1377 km²/sec² is too high. You would be better of going to Jupiter on a direct Hohman transfer.

Look at solutions on Trajectory Browser. Notice that all practical EEJ solutions have major deep space maneuvers at apogee before the Earth flyby. That is the way to get a non-resonant encounter efficiently. However, TransX does not take into account the deep space maneuver on its own. (Neither does TOT). So you end up with weird/wrong results.

Look for dgatsoulis' Rosetta tutorial for info on how to edit Sol.cfg to add in the DSM locations.

Edit
Here is a TransX solution that is close to your TOT solution and requires no deep space maneuver, non-optimal as it may be:

Code:
BEGIN_DESC
Contains the latest simulation state.
END_DESC

BEGIN_ENVIRONMENT
  System Sol
  Date MJD 58954.0514942551
END_ENVIRONMENT

BEGIN_FOCUS
  Ship GL-01
END_FOCUS

BEGIN_CAMERA
  TARGET GL-01
  MODE Cockpit
  FOV 50.00
END_CAMERA

BEGIN_HUD
  TYPE Surface
END_HUD

BEGIN_MFD Left
  TYPE User
  MODE TransX
  Ship  GL-01
  FNumber 5
  Int 1
  Orbit True
  Vector  -4333326.48579 1401498.90365 4455096.35786
  Vector  -257.411084705 126.331603333 -290.117153666
  Double  3.98600439969e+014
  Double  58954.0514931
  Handle Earth
  Handle NULL
  Handle NULL
Select Target
 0 Escape
Autoplan
0 0
Plan type
0 0
Plan
0 1
Plan
0 0
Plan
0 0
Select Minor
 0 None
Manoeuvre mode
0 0
Auto-Center™
0 0
Base Orbit
0 0
Prograde vel.
 1  0
Man. date
 1  58954.0511813
Outward vel.
 1  0
Ch. plane vel.
 1  0
Intercept with
0 0
Orbits to Icept
0 0
Graph projection
0 0
Scale to view
0 0
Advanced
0 0
Pe Distance
 1  6571000
Ej Orientation
 1  0
Equatorial view
0 0
Finvars
  Finish BaseFunction
  Int 2
  Orbit False
  Handle Sun
  Handle Earth
  Handle Earth
Select Target
 0 Earth
Autoplan
0 0
Plan type
0 2
Plan
0 0
Plan
0 0
Plan
0 1
Select Minor
 0 None
Manoeuvre mode
0 0
Auto-Center™
0 0
Base Orbit
0 1
Prograde vel.
 1  0
Man. date
 1  58954.051262
Outward vel.
 1  0
Ch. plane vel.
 1  0
Intercept with
0 0
Orbits to Icept
0 1
Graph projection
0 0
Scale to view
0 0
Advanced
0 0
Prograde vel.
 1  3819.25555804
Eject date
 1  59100
Outward vel.
 1  8660.66109183
Ch. plane vel.
 1  -0.6177
Finvars
  Finish BaseFunction
  Int 4
  Orbit True
  Vector  -6823399017.03 -1721659.3135 -6285116251.93
  Vector  6967.46841342 -1.2499343637 6432.1957059
  Double  3.98600439969e+014
  Double  59716.5796122
  Handle Earth
  Handle NULL
  Handle NULL
Select Target
 0 Escape
Autoplan
0 0
Plan type
0 1
Plan
0 0
Plan
0 1
Plan
0 0
Select Minor
 0 None
Manoeuvre mode
0 0
Auto-Center™
0 0
Base Orbit
0 0
Prograde vel.
 1  0
Man. date
 1  58954.0514921
Outward vel.
 1  0
Ch. plane vel.
 1  0
Intercept with
0 0
Orbits to Icept
0 0
Graph projection
0 0
Scale to view
0 0
Advanced
0 0
View Orbit
0 0
Finvars
  Finish BaseFunction
  Int 3
  Orbit True
  Vector  -58703409169.2 5035174.03862 -139742427945
  Vector  36275.6350699 1828.61825827 -11812.3654661
  Double  1.32712838556e+020
  Double  59727.8735813
  Handle Sun
  Handle Earth
  Handle Jupiter
Select Target
 0 Jupiter
Autoplan
0 0
Plan type
0 2
Plan
0 0
Plan
0 0
Plan
0 2
Select Minor
 0 None
Manoeuvre mode
0 0
Auto-Center™
0 0
Base Orbit
0 0
Prograde vel.
 1  0
Man. date
 1  58954.0514712
Outward vel.
 1  0
Ch. plane vel.
 1  0
Intercept with
0 0
Orbits to Icept
0 0
Graph projection
0 0
Scale to view
0 0
Advanced
0 0
Velocity.
 1  0
Outward angle
 1  -0.38529888567
Inc. angle
 1  -0.194988184033
Inherit Vel.
0 0
Eject date
 1  59727.8735813
Finvars
  Finish BaseFunction
  Int 5
  Orbit True
  Vector  -466228934976 54119719049.8 104152562818
  Vector  5634.92264982 -639.615392353 -1262.93027259
  Double  1.26686534397e+017
  Double  59699.4536561
  Handle Jupiter
  Handle NULL
  Handle NULL
Select Target
 0 None
Autoplan
0 0
Plan type
0 1
Plan
0 0
Plan
0 2
Plan
0 0
Select Minor
 0 None
Manoeuvre mode
0 0
Auto-Center™
0 0
Base Orbit
0 0
Prograde vel.
 1  0
Man. date
 1  58954.0514921
Outward vel.
 1  0
Ch. plane vel.
 1  0
Intercept with
0 0
Orbits to Icept
0 0
Graph projection
0 0
Scale to view
0 0
Advanced
0 0
Draw Base
0 0
Finvars
  Finish BaseFunction
END_MFD

BEGIN_MFD Right
  TYPE User
  MODE TransX
END_MFD

BEGIN_SHIPS
GL-01:DeltaGlider
  STATUS Landed Earth
  POS -80.6824940 28.5967940
  HEADING 330.01
  AFCMODE 7
  PRPLEVEL 0:0.995000 1:0.999797
  NAVFREQ 94 524 84 114
  XPDR 0
  GEAR 1 1.0000
  PSNGR 2 3 4
  AAP 0:0 0:0 0:0
END
END_SHIPS

BEGIN_SpaceNetwork
END

BEGIN_ExtMFD
END
 
Last edited:

dgatsoulis

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Ripley; said:
Just wait for dgatsoulis to crunch the numbers...
:) That's some number-crunching indeed.

@wingnut
Earth-Earth slingshots are a good demonstration of the fact that there is no such thing as a free lunch.

Notice that in both your scenario and in the one posted by boogabooga, you end up back to Earth with almost exactly the same velocity you left it. (V.enc is almost exactly the same as Total DV).
So an Earth to Earth slingshot is pretty much useless, unless you combine it with some kind of DSM. (as boogabooga already noted in his post).

By escaping Earth and performing a perihelion lowering maneuver at the time you reach aphelion, you change the position that you'll be crossing Earth's orbit and more importantly the angle of interception. If you select your aphelion carefully, you can perform a relatively small maneuver there (<1000 m/s), and significantly change your Encounter velocity with Earth, thus giving you the ability to sling to Jupiter.
What you need to aim for is an encounter back to Earth with a relative velocity almost identical to the Total DV from the direct plan , as close to the injection date of the direct plan as possible.

Neither TransX nor IMFD can help plan this from the ground, so you'll need to set up a spreadsheet.

First find a direct E-J plan with the arrival on the date you want it. This will give a dV base to compare against. With the departure in 2022 (adding a couple of years, to allow time for the Earth-Earth portion of the journey) , TransX and IMFD give a Total DV of ~9.11 km/s for a departure on 59742 and and arrival at 60551.
First, calculate the TJI ΔV, in order to have something to compare against. You'll need the velocity of the parking orbit at an altitude of let's say 200 km.
[math]V_{orb} = \sqrt{\frac{\mu_{earth}}{R+alt}} = 7788.48 \ m/s [/math]and the injection ΔV for the TJI burn is
[math]\Delta V = \sqrt{2V_{orb}^2+V_{\infty}^2}-V_{orb} = 6.505 \ m/s [/math]
So you have a base of ~6.5 km/s to compare against. To make the effort worth your while, try to save at least 1000 m/s.

Now setup a spreadsheet. You can get fairly accurate results if you approximate Earth's motion around the Sun as a circular one, with a radius of 148.9 million km (period 365.25 days), giving a constant velocity of 29785 m/s.

On the first 2 cells, write the date of departure (59742) and the DV (9110 m/s). DV is important, because you need to setup an encounter back to
Earth with almost the same relative velocity, if you want to make it to Jupiter.

Step1
set up the first 7 cells in such a way, that you can get the Earth Injection dV, for the first (Earth-Earth) leg of the flight. We want to see the dV
required for a given Aphelion distance and also the time to reach Aphelion and the Aphelion velocity.

The first cell is the Aphelion in meters (user input).
The other cells are from these equations:
SemiMajor Axis [math] a = \frac{PeD+ApD}{2} [/math]T to Aphelion [math]T_1=\frac{\pi \sqrt{\frac{a^3}{\mu_{sun}}}}{86400}[/math] (days)
Perihelion Velocity [math]V_p=\sqrt {\frac{2 \mu_{sun}R_a}{R_a2a}}[/math]Aphelion Velocity [math]V_a=\sqrt {\frac{2 \mu_{sun}R_p}{R_p2a}}[/math]Hyperbolic excess velocity [math]V_{\infty} = V_p - 29785[/math]Injection ΔV [math]\Delta V_{inj} = \sqrt{2V_{orb}^{2}+V_{infty}^2}-V_{orb}[/math]
Step2
you need to setup another column, that calculates the resulting trajectory for a given retrograde burn at aphelion. We will need the following cells:
DSM ΔV (user input)
Resulting Aphelion Velocity [math] V_{a2} = V_a - \Delta V_{DSM}[/math]
Resulting Perihelion [math]R_{p2}=\frac{R_a}{\left(\frac{2\mu_{sun}}{R_aV_{a2}^2}-1\right)}[/math]Resulting SMa [math]a_2=\frac{R_a+R_{p2}}{2}[/math]Velocity @ Earth's orbit [math]V_{@earth}=\sqrt{\mu_{sun}\left(\frac{2}{R_{earth}}-\frac{1}{a_2}\right)}[/math]eccentricity [math] e = 1-\frac{R_a}{a_2}[/math]T to perihelion [math]T_2=\frac{\pi \sqrt{\frac{a_2^3}{\mu_{sun}}}}{86400}[/math] (days)
True anomaly @ Earth distance [math]\nu = 2\pi- acos\left[\frac{\left(\frac{a_2(1-e^2)}{R_{earth}}-1\right)}{e}\right][/math]flight path angle @ Earth's distance [math] \phi = atan \left(\frac{esin\nu}{1+ecos\nu}\right)[/math]Velocity relative to Earth [math] V_{rel} = \sqrt{V_{earth}^2+V_{@earth}^2-2V_{earth}V_{@earth}cos\phi}[/math]
Finally in the third (and trickiest) step you need to find out whether Earth will be there, when the spacecraft arrives at the Earth's distance from the
Sun. You have two points of intersection with Earth's orbit (one on the way "in" and one on the way "out"), so you need to calculate if Earth will be
there for both of them.

Set up a 3rd column with these cells:
First you need the eccentric anomaly when the spacecraft arrives at Earth's distance from the Sun.
[math] E = acos \left(\frac{e+cos\nu}{1+ecos\nu}\right)[/math]The ToF from Aphelion to Earth's distance from the Sun.
[math] ToF_1 = T_2-(E-sinE)2T_2[/math] (days - inbound intersection)
The ToF from Perihelion to Earth's distance from the Sun
[math] ToF_2 = (E-sinE)2T_2[/math](days - outbound intesection)
The total time to the first encounter:
[math]T_{enc1} = T_1+Tof_1[/math]The total time to the second encounter
[math]T_{enc1} = T_1+T_2+Tof_2[/math]Earth's position at the first encounter:
[math]\nu_{earth} = mod(\frac{T_{enc1}}{365.25}360°,360)[/math]Earth's position at the second encounter:
[math]\nu_2{earth} = mod(\frac{T_{enc2}}{365.25}360°,360)[/math]Ship's true anomaly at second encounter
[math]\nu_2 = 2\pi-\nu[/math]Using the absolute difference of Earth's position and ship's true anomaly at either of the encounters, you can estimate whether Earth will be there or not, when you arrive. You need to aim for a difference of less than 1°.

Finally, you can use the time to the Earth encounter, to determine when you need to launch.

Remember that the spreadsheet is just an approximation to help you with the planning, because Earth's orbit isn't exactly circular.

Here is a link to the spreadsheet all set up.
Earth-Earth Slingshot calculator.
Remember to create your own copy, otherwise you'll not be able to edit/use it.

First you need to enter the Departure MJD and Total DV of a direct Earth-Jupiter plan, and then, by changing the parameters in two cells (Aphelion distance and DSM DV) the spreadsheet will tell you everything else you need.

I'll be posting an example on how to use it later today.

---------- Post added at 18:48 ---------- Previous post was at 09:03 ----------

Here is an example flight.

Step 1

Run Orbiter and select an Earth→Jupiter trajectory with the arrival whenever you want. Make a note of the departure date and the Total DV on their respective cells on the spreadsheet.

Untitled1_zpsof4ac4gu.jpg


By entering and adjusting the values in the cells for aphelion distance and DSM DV, try to get an encounter with Earth, with the relative velocity as close to the Total DV of the direct plan as possible. Make sure that you get the encounter on the 2nd Intersection.

Untitled2_zpshi6xubgf.jpg


As you can see in the pic above you get all the info you need.

In Orbiter, set the date to ~0.5 days before the launch date, and the following TransX plan:
Stage1: MAJ Earth, Target: Escape (FW)
Stage2: MAJ Sun, Target: Earth (FW)
Stage3: MAJ Earth, Target: Escape (FW)
Stage4: MAJ Sun, Target: Jupiter

On Stage2, set the Prograde to the Earth V∞ cell, the Pl.Change to 0.01 (to get the line of nodes to stop jumping around) and the Eject Date to the Launch MJD from the spreadsheet. Launch into the parking orbit when you get a heading close to 90°.

Untitled3_zpsdboktebp.jpg


Once in the parking orbit, advance the time 'til you are ~10 mins away from the "Begin Burn" value in TransX stage1. Now open IMFD on the other side and select the Course→Delta Velocity program. Match IMFD's "TEj" and "dvf" values to TransX's "Begin Burn" and "Delta V" respectively.

Untitled4_zpsojwnwmpz.jpg


On the side you hade TransX, open IMFD and link it to the first IMFD. Open the Map program, set the reference to the Sun, and press Dsp, PG, Plan and MOD. Adjust the TEj and dvf values, until you get a minimum EqI on the Map program and the MJD of the Apoapsis to match the "Aphelion MJD" from the spreadsheet.

Untitled5_zps333wvvqs.jpg


All set. Autoburn the plan on the right MFD . Once the AB is finished, you may have to add in (or subtract) a little bit of linear RCS to match the aphelion MJD exactly. Remember to press the "Plan" button on the Map program, in order to remove the plan after the burn is finished.

Untitled6_zpsubw7t41x.jpg


Done. Now time-warp all the way to Aphelion and go back to x1 time-accel, when you are ~1000 secs from it. (Check with OrbitMFD, REF: Sun, ApT value). Setup a maneuver in TransX in order to get an encounter with Earth close to the date the spreadsheet says (within a couple of weeks), and more importantly close to the Encounter Velocity the spreadsheet says, In a perfect world, you'd only need a negative prograde DV same as the DSM value, but because Earth's orbit isn't exactly circular, you'll also need some outward velocity.

Untitled7_zpsv0z0bvjb.jpg


Once you have a good Cl.App value (< 10M), go to Stage3 and adjust the Slingshot variables to get an encounter with Jupiter. If your Earth encounter velocity was close enough to the calculated value, it should be pretty easy to do.
If your Pe/Pl ratio is slightly lower than where you'd want it (minimum 1.02), or if the trajectory to Jupiter can't get a very close approach, try re-adjusting the maneuver variables, so that you get an encounter with Earth with a slightly higher relative velocity. See an example below:

Here is the encounter after first maneuver setup. The Pe/Pl ratio is slightly lower than the Earth's surface and the Jupiter encounter is too far away.

Untitled8_zpsk8qpqc3f.jpg


After adjusting the maneuver variables, we get a slightly faster encounter with Earth, and the slingshot works itself out just fine.

Untitled9_zpsbxcygobi.jpg


From here on you continue as any other single slingshot plan.
When it comes to Earth encounters, it is better to use TransX's Cl.Approach value instead of IMFD's Map program, up to the point where you get close to Earth. (OrbitMFD, REF Earth, G = 0.01). From there on, use IMFD's map program, since it should give you a more stable Pe altitude prediction. YMMV.

Hope this helps
:cheers:
 

boogabooga

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There are a few places in the spreadsheet (J6, J9) where Earth's period is 360.25, instead of 365.25.

Other than that, the technique seems to work well. I converted the spreadsheet to .xlsx format. I set the Excel solver up to solve the problem so I don't have to do trial and error myself. I can share if there is interest.

One thing I do differently is to launch using IMFD's "Higher Orbit" programs instead of TransX. This lets you specify the oV, which is known from the spreadsheet for orbit eject. (It is the first time I have ever had a use for "higher orbit".)

Is this the trajectory type that JUNO used?
 
Last edited:

dgatsoulis

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Sparta
There are a few places in the spreadsheet (J6, J9) where Earth's period is 360.25, instead of 365.25.

Thanks for checking. I've corrected the cells on the spreadsheet. I'd been consistently getting a difference of ~10-14 days for the arrival back to Earth, but I thought it was due to Earth's non-circular orbit. :facepalm: Should have seen that the error was too big.

Other than that, the technique seems to work well. I converted the spreadsheet to .xlsx format. I set the Excel solver up to solve the problem so I don't have to do trial and error myself. I can share if there is interest.
Please do, it would save some time finding the correct combination of Aphelion distance and DSM DV.

One thing I do differently is to launch using IMFD's "Higher Orbit" programs instead of TransX. This lets you specify the oV, which is known from the spreadsheet for orbit eject. (It is the first time I have ever had a use for "higher orbit".)

Same here. Tried it just yesterday and it was first time I had to use it too. :)

Is this the trajectory type that JUNO used?
I've not read the paper, but from the animation below, it looks like it.
[ame="http://www.youtube.com/watch?v=mdGMXKzu7K0#t=69"]Juno Mission Design (Trajectory Overview) - YouTube[/ame]
 

wingnut

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Oh wow, that's a detailed answer. I need some time during the weekend to read it carefully as it is a busy time to do that right now.
 

boogabooga

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I'm attaching a modified version of dgatsoulis' spreadsheet.

First, I've made some ergonomic changes. I've moved the aphelion distance input cell to beneath the DSM delta-V input cell so that all input cells will be together in a block of four. I've also changed the units of the aphelion distance input cell from meters to millions of kilometers, as I found that entering nine zeros was a bit of a pain.

I've also set up the Excel Solver to solve the problem. Solver is an Excel feature that may require special set-up but IIRC it does come with Microsoft Office (At least it did with the 2007 version). Basically, Solver is like goal-seek or what-if analysis on steroids. It is a proper optimization module that allows multiple cells to be changed to maximize or minimize the value in a cell subject to multiple constraints. I DO NOT KNOW if it works with Open/Libre Office, Google Docs Spreadsheet, or anything else. I only use actual Excel.

You will need to manually set up the input cells with "reasonable" guesses for the solver to work properly. Also, I've noticed that there are multiple solutions to the problem. So, the initial guess will decide which solution the solver converges on. You can play around with your initial guesses and try to find the different solutions and select the one that you like. I've include some example solutions. It seems that a higher aphelion distance allows less delta-V on the DSM, but less overall savings. (But the high aphelion might be the best one if you can get the extra delta-V from the launch vehicle.)

To exclude "junk" solutions, I've constrained the DSM to less than 1000 m/s, you can change this in the solver set-up, if you wish.
 

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