OVERVIEW: Highly inclined low Earth orbits can be changed into Geosynchronous orbits in a variety of ways. Some are very fuel costly and others use far less fuel. The least fuel use is actually to sling retrograde around the moon and use the moon to change the plane to equatorial and also the Pe of the return to Earth made very close to the 42.16M meters radius of geosynchronous.|
This tutorial is intended for use with this scenario called Challenge.scn. Extract the file into your Orbiter folder and run it in window mode.
A playback of the flight with some comments added is also available here. (Extract into your Orbiter folder and it will create a playback scenario called Challenge_2006.) I think it takes about 8 or 9 minutes to watch. Have the "Play at recording speed" option checked.
Starting your own flight:
One should first understand the concept that the moon's orbit is inclined about 28.5 degrees relative to the equator at the date of this scenario. If we want to sling around the moon and return in plane with the Earth's equator we should sling the moon when the moon is passing though it's node, ie; the moon is above the Earth's equator. With the provided scenario power up an MFD and bring up Map. Then target "moon". Notice the orbit of the Deltaglider has it's node very close to the node of the moon, meaning both the moon and the ship cross the equator at the same points. This was provided intentionally to allow the best chance of returning to Earth as close as possible to equatorial alignment. But passing it at the node is not enough on its own. We must also sling around the moon at the right inclination. (that will come later)
The first trick is to know WHEN to do the trans lunar injection so that arrival at the moon is at the moon's equatorial node. Bring up Orbit MFD and make the frame equatorial, target moon, projection target as in the next image.
Notice the yellow radius line pointing about the 1 o'clock position. It is going counterclockwise and the dashed yellow line is the nodal axis. We want to do the trans lunar injection when the yellow line is about 45 or 50 degrees before getting to the node. This is based on it taking about 3.5 days and 3.5 days is about 1/8th of the moon's 28 day period. The moon goes around the Earth about 1 and 1/13th times in 28.25 days. (387 degrees in 28.25 days) So 1/8th of 387 degrees is 48 degrees.
There will be an opportunity of several orbits lasting more than half an Earth day when we could shoot for the moon from our polar orbit of this scenario. By estimating the date then trial of a few TLI attempts to fine evaluate the options, I found that TLI at about 7AM June 1st is a good opportunity. So we sit in our starting orbit and go round and round for several days. (sorry about that but the early scenario start date was done to hide the obvious use of the moon)
Let's warp ahead. (warp 1000 will probably work). Watch the date. Slow down in the early morning hours of June 1st and come to real time at about 6:45 AM. Note that when I flew the scenario for the recorded playback flight I used warp 1000 and made sure the orbit didn't change during the warp period. But to save the viewer waiting 6 minutes, I edited the warp speed for a short time to 10,000 reduce the wait to a bit over 30 seconds. This did not change anything but the wait since no engine burns were done and it does not affect the recorded position and attitude of the craft.
The TLI Burn
Bring up TransX
click "++" for moon,
click "VW" for "View: Manoevre"
click"++" to turn manoevre mode "On"
click "Var" and "Adj" and "++" as learned in earlier tutorials to set the following...
Prograde = 3.147k
Date = 53887.2944
Try to get the encounter view (stage 2) to be something like the following...
Notice the inclination is between 140 and 180, the closer to 180 the better but anything above 140 is good enough. And also it has the encounter Pe under the moon's surface. TransX doesn't model accurately the Earth moon system and experience shows that the encounter Pe grows during the flight so set the initial Pe to about 1.2 to 1.4 M. (the image has this at 1.253M)
It's hard to get the inclination right... the date adjustment is extremely sensitive even on "ultra". Go back and forth with date and very light clicks to happen (by a bit of luck) upon a nice retrograde encounter. It's a bit like throwing darts to get within 2" of a bullseye (the way I play anyway). My personal wish list has the adjustment increment smaller for "ultra" in TransX.
Burn the manoevre as usual using the target and green x. If you start the burn (full throttle of mains) at between 47 and 48 seconds prior to the center of the burn ("T to Mnvre") it should be fairly well centered. Use a bit of LIN after the mains are shut off if needed to get make a clean and precise burn.
ON THE WAY TO MCC
Warp ahead to between midnight and 5 AM on June 4th.
This correction will be the most important part of the trip.
It was with some trial and error that I found that using between -10.5 and -11.0 degrees as a sling inclination in TransX will result in a fairly equatorially inclined return to Earth. (My personal good luck inclination is -10.6) It didn't actually take very long for the tests of the inclination angles. I simply did a non recorded flight up to the beginning of the MCC and saved the scenario for testing. Then I kept trying the sling using different inclination angles to see what happens. Each test might take 4 to 6 minutes of time to set up the manoevre and warp past the moon to see the resulting inclination back at Earth. After a half dozen or more tests in about an hour it was easy to zero in on a good sling angle. So using my test results do your MCC as follows...
click "FWD" for Stage 2
click "VW" for "Setup",
click "++" for "Escape"
click "FWD" for Stage 3
click "VW" for "Sling Direct"
using "Var" and "++" "--" adjust as follows...
The outward angle is an eyeball guess that is done looking at the given "Focus PeD" and then adjusting the dashed yellow ellipse to be a bit greater or lesser than the green ellipse at the Pe visually as needed. TransX does not allow the hypothetical sling adjustment result Pe back at Earth to be shown as a number. It instead the number shown is the actual result based on your current path. If it's low (like 38.35 in the next image) then swing the dashed ellipse wider at the Pe for example. In the image below the outward angle chosen was -117.9001. Even though the dashed ellipse is closer to earth at the Ap, the Pe is a bit wider if you look closely.
Then set up a manoevre and burn the radius line into place making "R.Inc:" close to zero and "Pe Ratio:" close to 1. If you have no idea how to do this, it's best to complete the tutorial "Voyager Flight" first. (sorry about that). Once it's burnt into place it could look something like the following.
Do a second correction burn if needed to get the Pe distance closer if you like. But personally I think that anything between 39M and 43M is probably adequate at this stage. If you do more than 50 m/s in corrections here you might not finish the trip so waste not want not. The playback file has a single 15 m/s midcourse burn at this stage of the flight.
Now bring up Orbit MFD and reference moon.
Warp slowing ahead watching the gravity factor at the bottom of Orbit...
and when it reaches 50 slow to real time and turn "Prograde".
Turn on TransX again.
click "BCK" as needed to be in stage 1.
click "VW" to "View: Slingshot"
Look at your Inclination angle (this image shows it as .2162)
Killrot, then use LIN RCS up and down (2 or 8) as needed to burn the inclination angle to as close to zero as possible as shown in the following image.
Then bring up Orbit again and warp slowly ahead to approach the moon Pe. As you get closer within 200 seconds, turn prograde.
The Pe position of the lunar sling is a great opportunity to adjust the Pe of the return to Earth. (Just Killrot once in the prograde attitude and use a few bursts of LIN) In general if you speed up at this point you will reduce the Earth Pe. If you slow down you will increase the Pe. Just 5 m/s could change the Pe by a couple Mm. I've found it reads a bit lower than what you are actually going to get so the following image shows what it looks like to change the prograde speed to get the Pe to a bit above 39M. Yes 39 is my good luck number at this point. In the playback I used about 4 m/s increase speed as I recall. It dropped the Pe from about 42 to 39. In addition I turned off the sling direct setup information since all I care about now is the return Pe. I did this by making stage 1 target= none and clicking forward, then making stage 1 target escape and clicking forward again. The following image shows the data after the lunar Pe LIN adjustment.
And an outside camera view showing the DG and an earthrise after its sling around the moon.
All that's left now is to see how you did. Warp carefully back to Earth. Bring up Map reference Earth. When close enough your orbit will appear and hopefully it is fairly close to the equator. Orbit MFD will show your arrival at Pe for the burn to drop the Ap to 42.16. And I found getting the alignment to read zero is easily done by using Surface MFD to watch your latitude position to know when to turn DN (or AN) and to do the light burn to bring the inclination as shown in Orbit down to 0.00.