Problem Flight plan to L4 and L5

[Mister Mxyzptlk]

How would flight plans to LaGrange 4 and 5 work? Since we have a couple addons that are hypothetical space colonies placed at L4 and or L5, how would we get there? I have been dinking around with Orbiter regarding this hypothetical scenario and it seems that you have to go around the Sun one way or another to get there, or some kind of retrograde orbit that posits an extreme amount of deltaV on both ends of the flight plan. Any tricks to get there from here in a reasonable way?

 

[Linguofreak]

How would flight plans to LaGrange 4 and 5 work? Since we have a couple addons that are hypothetical space colonies placed at L4 and or L5, how would we get there? I have been dinking around with Orbiter regarding this hypothetical scenario and it seems that you have to go around the Sun one way or another to get there, or some kind of retrograde orbit that posits an extreme amount of deltaV on both ends of the flight plan. Any tricks to get there from here in a reasonable way?

Well, part of it depends on *which* L4 and L5 you're talking about. Mostly when you hear about colonies there, you're talking about the Earth-Moon Langrange points rather than the Sun-Earth points, and the Earth-Moon points are about as easy to reach as the moon. (They would be the same, except for the fact that the Oberth effect from the moons gravity makes it slightly easier to get there).

 

[C3PO]

The best trick is to put a target ship there, and use it as a..... well.... target.

 

[n72.75]

This is what you're looking for:http://www.orbithangar.com/search_quick.php?text=lighthouse&submit.x=15&submit.y=9

 

[Mister Mxyzptlk]

I guess nobody is really reading my post carefully. I asked "How to do it" not "I need an addon to show me where it is at". Also the L4 and L5 I am talking about are the Earth/Sun points, specifically the points +60 deg. and -60 deg. from earth in Earth's orbit.

 

[Animal]

It's a timely question. STEREO just arrived at opposite sides of the Sun but did L5 flybys on the way. Also both satellites were launched on a single Delta II, I assume one rocket to both points is a cool enough trick?

Basically the two craft are launched on lunar swingbys. The first escapes and is ejected ahead of Earth into solar orbit. The second arrives at the moon later and enters a lunar orbit with a period of six weeks. The second lunar swingby then ejects it into a solar orbit behind Earth. Presto! You're on your way for minimal delta-v.

http://stereo.gsfc.nasa.gov/orbit.shtml

 

[Linguofreak]

I guess nobody is really reading my post carefully. I asked "How to do it" not "I need an addon to show me where it is at". Also the L4 and L5 I am talking about are the Earth/Sun points, specifically the points +60 deg. and -60 deg. from earth in Earth's orbit.

I did read your post, and noted that you were talking about the Earth Sun points. It's just that you mentioned colonies at the L4 and L5 points, and the only colonies I've ever heard of at Lagrange points, as well as the only Lagrange colony addon I can find searching Orbithangar, are *not* at the Earth/Sun points. You can go to the Earth/Sun points, but unless you edit the scenario you're flying to them in to have a colony there, all you'll find is empty space.

Anyways, as far as getting to the solar points, it's pretty much as you've said, you either go around the sun or make extremely high-energy burns. That's pretty much the way orbital mechanics works: If you want to get someplace for much less delta V than the orbital velocity of the objects involved, you're going to be taking an amount of time on the order of the period of the orbits involved, and if you want to get someplace in much less time than the period of the orbits involved, you have to expend delta-V on the order of the orbital velocities involved. It just so happens that Earth takes a year to orbit the Sun and has an orbital velocity of 30 km/s. You might be able to find a middle ground by adding a sunward (to reach the leading Lagrange point) or anti-sunward (to reach the trailing lagrange point) component to your burn, but depending on what you consider "reasonable" delta-V and time budgets, there's no guarantee that you'll consider any result "reasonable". If you don't consider anything result you can get reasonable, then you've figured out why we haven't really done much in space beyond Earth Orbit.

 

[Mister Mxyzptlk]

Kudos, Animal! I will read the article at the link you provided, and attempt to duplicate the flight plan if I can, and if not I will humbly entreat O-Sensei Flytandem to educate me (I had no idea there was a Stereo mission).

Bravo, Linguofreak! It is as I surmised. I just wanted to tap the more astute minds of this forum to see if I overlooked something. It seems a bit ironic that it is easier and quicker to go to Mars than it is to a point in our own orbit +/- 60 degrees from earth.

 

[flytandem]

Thanks. Made for a fun morning flight. Started by placing a DG about 60 degrees ahead of the sun using scenario editor. Getting its orbit to match Earth was easy but I had to guess at it being 60 degrees ahead. Maybe someone can suggest a way to be precise for 60 degrees. Anyway, TransX made for an easy eject similar to going to Venus but less energetic. From the burn to reach the moon's orbital height it is only about 200 m/s more deltav. The ship arrived at the target DG one solar orbit later and Earth had gone 5/6th's of an orbit. (about 10 months)

By coincidence I nearly hit the moon on the way out from Earth. I started with a date of current time. The moon is a new moon (evening crescent) and probably a couple or 3 days into its new cycle. So as I headed away from Earth it placed me missing the moon by about 4 lunar diameters. It didn't mess up the trajectory too much though. The burn to match the target speed was about 1800 m/s and was on Dec 12th this year.

Orbiter is so much fun I'm amazed it's legal.

 

[Mister Mxyzptlk]

[ame="http://www.orbithangar.com/searchid.php?ID=4582"]http://www.orbithangar.com/searchid.php?ID=4582[/ame]
Flytandem, if I did this right, this is the link to the LaGrange MFD that places the focused object (I think) at whatever Lagrange point you specify in the MFD menu.

Could you (if you have time) elaborate on your flight plan?

 

[dgatsoulis]

Thanks. Made for a fun morning flight. Started by placing a DG about 60 degrees ahead of the sun using scenario editor. Getting its orbit to match Earth was easy but I had to guess at it being 60 degrees ahead. Maybe someone can suggest a way to be precise for 60 degrees.

Hope this pic helps.:

After you match your ship's orbital parameters (relative to the Sun), with the ones of the Earth, it's the MnL (Mean Longitude at epoch), that changes how many degrees ("ahead" or "before"), your ship will be placed.

Orbiter is so much fun I'm amazed it's legal.

 

[Mister Mxyzptlk]

Flytandem, you don't have to elaborate on your flight plan. I did it. I realized it after I did it it is really transx 101, not really complicated at all.

 

[flytandem]

Thanks DGatsoulis. Had no idea what those numbers at the bottom were.

 

[wingnut]

To EML-4 with IMFD course offset

I'm trying to plan a trajectory to the Earth-Moon-Lagrange 4 with the IMFD course offset and I am having trouble figuring out what to enter into the MFD to actually get there.

My scenario setting is:
Delta-Glider in low Earth orbit with less than 0.1 degrees relative inclination to Moon’s orbit.

I have started IMFD’s Target Intercept program with Moon as the target and enabled the Target Offset.

If I understood the Course Offset program correctly, I would need to leave the values for Lat and Long at 0 because my target is to be 60 degrees ahead of the Moon in its orbit to be in the vicinity of L4.

To help me visualize and calculate this I made this drawing which assumes a circular orbit of the Moon:

When I enter the values
SMa = 384,399 km
a = 60 degrees
This results in 402,541 km + 10,921 km Moon’s circumference = 413,462 km as the Rad value in the offset program which appears not to be enough in IMFDs map view.

Could anyone enlighten me with the correct procedure and calculation to reach L4 with IMFDs offset program please since I seemed to not have fully understood how the offset is supposed to be used and my calculation likely is not correct as well?

 

[meson800]

Using the offset mode in IMFD would be more difficult than using a surrogate ship. Target offset calculates a point, at the intercept date, that is the user-entered radius ahead of the Lat/Long specified.

To use it, you would have to determine what lat/long determines the vector towards L4.
The coordinate (0,0) on the moon refers to the point on the Moon that directly faces the Earth. Using it in offset means that you are aiming at a point directly between the Earth and the Moon.
Info on Lunar coordinates: https://en.wikipedia.org/wiki/Selenographic_coordinates

Some quick math reveals that the L4 will be located above the Lunar coordinate (59.85 West, 0 North)

Use that for the Lat/Long value in IMFD

 

[wingnut]

Thanks Meson for your input. Unfortunately I fail to understand how you calculated the Lat/Long pointing to the L4.

Could you elaborate on that please?

Using the offset mode in IMFD would be pretty difficult

I read about a couple of people claiming to reach L4 points fairly easily with the IMFD offset, that is why I wanted to give it a try in the first place.

 

[dgatsoulis]

I am not on an Orbiter computer to check this right now, but try this:

Once you are in a LEO coplanar to the Moon

-Course→ Target Intercept
-Target Moon
-Change "Offset Disabled" to Vel.frame
-Rad = (Sma from OrbitMFD)
-Long = -30.00° **-see note

This should get you to an offset chord equal to the Sma with a direction -30° to the tangent of the moon's position in its orbit.

Thus, when you reach apoapsis, your ship the Earth and the Moon, will form an equilateral triangle with sides = Sma (and angles 60°).

Keep in mind that the Moon's orbit is not circular, so this will not get you exactly at L4, but you should be pretty close.

For better (and easier) results use a surrogate ship for a target.

**note: I don't recall if this has to be -30 or 30. First enter the Rad variable and then start changing the longitude until the chord touches the Moon's orbit.

 

[meson800]

Because the triangle is equilateral, it is also equiangular. Therefore the angle between the vector pointing towards the Earth (coordinates = 0,0) and the vector to L4 is 60 degrees. Because of the coordinate system, the target coordinates are (60 degrees West, 0 degrees north)

The 59.85 came from me just using a computer estimation, it should actually be 60.


As to my quote, that's why I edited it to this.

Using the offset mode in IMFD would be more difficult than using a surrogate ship.

---------- Post added at 09:20 PM ---------- Previous post was at 05:26 PM ----------

Dgatsoulis, why do you use a longitude of -30 degrees? Isn't the offset done from the center of the target?

Nevermind, you explain that it is -30 degrees from the tangent line of the Moon, not from the Moon's center

 

[wingnut]

Nevermind, you explain that it is -30 degrees from the tangent line of the Moon, not from the Moon's center

I don't understand what exactly is meant with that and how it results in the offset of -30 degrees to be entered into the MFD.

Which of the green, yellow or black lines in the following image would be the tangent line of the Moon you referred to (if any)?

-Course→ Target Intercept
-Target Moon
-Change "Offset Disabled" to Vel.frame
-Rad = (Sma from OrbitMFD)
-Long = -30.00° **-see note

This worked well:

Coasting to EML4:

In the vicinity of EML4:

After matching orbital velocity with the Moon:

 

[dgatsoulis]

I don't understand what exactly is meant with that and how it results in the offset of -30 degrees to be entered into the MFD.

Which of the green, yellow or black lines in the following image would be the tangent line of the Moon you referred to (if any)?

I haven't used the offset option that much, but as far as I understand it it's the black line. Keep in mind that the orbit is not circular and the difference of the green and yellow lines to the black line is only a Moon radius (~0.45% of the SMa).

The tangent of the moon is at 90° angle to the SMa line. -30° gets you at a 60° angle.

After matching orbital velocity with the Moon:

Still ~23 thousand km away from the L4. Not bad but not that good either.
Try another run like this:
Wait until the Moon is 45° away from apoapsis and this time use the Rad from Orbit MFD (instead of the SMa) as the value for the Rad in IMFD's offset.
It should get you closer.