Use gravity to achieve inclined orbits

[TranceaddicT]

There it is Title = Question.

So, I received a contract to "Position satellite in a tundra orbit" around Kerbol. Here's my question for the thought-monkeys out there, HOW do you determine an injection trajectory that will result in an orbit somewhat near the specified operational parameters?

Here are the contract Orbit Specifics:

Apoapsis: 2,999,575,139m

Periapsis: 16,513,514m

Inclination: 63.4 degrees

LAN: 61.4 degrees

APe: 270 degrees

I consistently use a slight relative inclination (+/- .5 - 2 degrees, depending on what I want to achieve) when launching to Mun to achieve inclined orbits. But, this is a wholly (holy? holey?) different beast ... or is it just an instance were size makes a difference?

Edited September 12, 2014 by TranceaddicT
Answered.

[Taki117]

What I would do (Assuming you are launching from the equator) is to launch into the inclination that your satellite needs to be on. Plane changes are best when done when your rocket is moving slowest, i.e at launch, or with an Ap near the SOI change. Also, if I'm not mistaken, you need to be within 5-7% of your target orbit so just get close, it doesn't have to be exact. Using the Mun for the plane change is inexact at best.

[einsteiner]

I received a contract to "Position satellite in a tundra orbit" around Kerbol.

Not Kerbin, right? 3 million km is inside Moho's orbit, you're going to have to use so much delta-V just to get down there, I wouldn't worry about trying to get out of doing the plane change. You can probably play some games with Eve intercepts to lose energy and increase your inclination, then Moho intercepts if you can time it right to lower it some more, but you'll need a lot of fuel no matter what you do, methinks.

[Kasuha]

I have no idea why is this called "tundra" orbit of it is necessarily around Sun (Kerbin's SOI can't hold such apoapsis).

Best way is probably to launch to Jool and use its gravity slingshot to reach desired inclination and periapsis. You will still need to come with extra energy or make the slingshot powered to achieve that. Then lower the apoapsis from periapsis.

As for answer how to determine that: I just launch at the body I want to slingshot off, then I manipulate the trajectory within the SOI from far away to achieve the desired ejection direction. If you do it from sufficient distance, these maneuvers cost single units of dv. Acquire an intercept, place a maneuver about halfway through the transfer, pull handles (or use mouse wheel over maneuver icons) and watch what your exit trajectory does.

Edited September 11, 2014 by Kasuha

[tomf]

I have the same mission and I am just waiting for the right launch window. My plan is leave Kerbin for a solar orbit with AP at ~6x10¹⁰m ~1800m/s. There I will do a burn to bring down my PE and increase the inclination until it is touching the desired orbit ~2270m/s. Finaly at the PE another burn to bring down the AP ~3500m/s.

The further out that you make the intermediate AP the more deltav you save on the inclination change, but the returns diminish while the time taken increases rapidly.

The correct time to launch is when Kerbin is lines up with the PE of teh desired orbit, as you are going to make two full half orbits to get there.

You could probably do better with some gravity assists but last time I tried for a polar Kerbol orbit by slingshoting around jool it a: took forever b: had limited affect c: cost more in adjustments to make the encounters than it saved.

[tomf]

It is called a tundra orbit after real orbits used on earth where the satellite appears to spend almost all of its time over a point in the tundra latitudes.

I did look at some alternatives such as inclining the escape orbit from Kerbin but the gain in DV required to change inclination was more than compensated for by the extra DV required to leave Kerbin.

[ratchet freak]

to get the slingshot you will need to burn normal/anti-normal during the mid transfer correction burn to go below/over the object you are slingshotting around

[Kasuha]

a: took forever

Yes, that's the problem with Jool assists.

b: had limited affect

That depends on how you enter Jool's SOI. If you're coming on optimal trajectory (Hohmann transfer), you can't lower your periapsis any further. So you need to use suboptimal transfer with way higher apoapsis, that will give you the impulse needed to be able to reach high inclinations or low periapsis. Or you can fix that by powered slingshot, i.e. burning at periapsis of the slingshot. Uses less dv but it is way trickier to set up.

c: cost more in adjustments to make the encounters than it saved.

Then you made your adjustments too late or at wrong places. Correctly made adjustments (if you already have an intercept) don't need more than single units of m/s dv.

Edited September 11, 2014 by Kasuha

[Rune]

Definitely Jool gravity assist is the way to go. Going into the settings.cfg file on KSP and setting the conic draw mode like this:

CONIC_PATCH_DRAW_MODE = 0
CONIC_PATCH_LIMIT = 5

...would help. That means conics are drawn inside each SOI with respect to the gravity well, so you can judge ejection angles and swingby trajectories more accurately, and makes it draw up to 5 consecutive orbits, while the default is set to three. As an example of what you can get with a Joolian gravity assist, I went into polar escape orbit once after a weird bug put me somewhere close to a Jool encounter upon exiting Kerbin's SOI. That's a 90º turn with a 1,000km periapsis, so I'm sure 60º is doable:

Rune. Hope that helps!

[Taki117]

This seems like a stupid question, but are you by any chance using RSS?

[Geschosskopf]

LAN: 61.4 degrees

APe: 270 degrees

I'm no genius at orbital mechanics but these 2 parameters seem greatly to complicate the problem. You can't just go for the desired inclination straight from launch or off a slingshot because then your LAN and APe will be luck of the draw. Then you could well end up spending about as much dV to drag the LAN and Pe into the correct positions as if you'd done the inclination change with a plane-change burn.

EDIT: 2000 posts. I talk too much.

[TranceaddicT]

Not Kerbin, right?

Well, the actual contract says "around the Sun"; I'm just trying to maintain a bit of immersion.

I have no idea why is this called "tundra" orbit of it is necessarily around Sun (Kerbin's SOI can't hold such apoapsis).

Best way is probably to launch to Jool and use its gravity slingshot to reach desired inclination and periapsis.

I don't get the necessity of a tundra (âуýôрð) orbit (essentially a double-period Molniya; I imagine so named for it's use by the Soviet space program to maintain aspect over country's tundra.) around Kerbol either, but that's just what the contract calls for.

I would think a Jool assist would work (much less give it consideration) as it's orbit is in the opposite direction. Why go out; just to come back in?

I have the same mission and I am just waiting for the right launch window. ... The correct time to launch is when Kerbin is lines up with the PE of teh desired orbit, as you are going to make two full half orbits to get there.

Nice to know someone else has it. I'll investigate the Pe window.

Definitely Jool gravity assist is the way to go. Going into the settings.cfg file on KSP and setting the conic draw mode like this:

<snip>

...would help. That means conics are drawn inside each SOI with respect to the gravity well, so you can judge ejection angles and swingby trajectories more accurately, and makes it draw up to 5 consecutive orbits, while the default is set to three. As an example of what you can get with a Joolian gravity assist, I went into polar escape orbit once after a weird bug put me somewhere close to a Jool encounter upon exiting Kerbin's SOI. That's a 90º turn with a 1,000km periapsis, so I'm sure 60º is doable:

<snip>

Rune. Hope that helps!

Seriously? Again, and I am faaaar from an expert, how does a relative outward trajectory benefit dV for an inward final orbit? I am truly perplexed by this.

And thanks for the config modification; good to know. Time to tweak KSP some more.

This seems like a stupid question, but are you by any chance using RSS?

Nope, it's in the contract system.

I'm no genius at orbital mechanics but these 2 parameters seem greatly to complicate the problem. You can't just go for the desired inclination straight from launch or off a slingshot because then your LAN and APe will be luck of the draw. Then you could well end up spending about as much dV to drag the LAN and Pe into the correct positions as if you'd done the inclination change with a plane-change burn.

EDIT: 2000 posts. I talk too much.

Yes, a random tundra/Molniya orbit is doable. But, those are the two that will be the most likely to kill any chance at success. Unfortunately, we don't have anything to plan orbits (that I know of) outside KSP nodes. Do we?

Edited September 11, 2014 by TranceaddicT

[Kasuha]

I would think a Jool assist would work (much less give it consideration) as it's orbit is in the opposite direction. Why go out; just to come back in?

Because orbital mechanics? Bi-elliptic transfer costs less dv than Hohmann transfer in this case, the inclination change is huge and by slingshot you save a lot.

I made a simulation; 6000 m/s dv just to lower your periapsis, another 2700 m/s to lower the apoapsis. That's already almost 9000 m/s dv and I'm not counting inclination change.

Gravity slingshot off Eve won't help you as much as Jool - you'll spend a lot of momentum on inclination change which costs a lot of dv at that place.

Using Jool, you'll get the inclination change and the periapsis together for about 2500 m/s. And lowering the apoapsis will come about 800 m/s more than from Kerbin leve, i.e. some 6000 m/s total. You'll be saving at least 3000 m/s dv on it.

Edited September 11, 2014 by Kasuha

[lincourtl]

I love the Fine Print mod, but some of those contracts should pay out 1000 times more than they do considering how much work they are.

Kashua's right that a bielliptic transfer will save you buckets of delta-v, at the expense of a whole lot of time. This video is a really good introduction on using gravity assists. The effects can be nonintuitive.

If you're lucky enough to make your Jool transit at the right time, and really really patient fiddling with the maneuver nodes, or we had better tools in-game, you could nail both the kerbolar APe and LAN from all the way out in the Joolian system, then just bring your apoapsis down. Otherwise, you'll need most of that delta-v you saved just fiddling around getting the osculating elements right.

[Geschosskopf]

Using Jool, you'll get the inclination change and the periapsis together for about 2500 m/s. And lowering the apoapsis will come about 800 m/s more than from Kerbin leve, i.e. some 6000 m/s total. You'll be saving at least 3000 m/s dv on it.

But how do you do this so that you get the required LAN and APe upon arrival in solar orbit? If those aren't correct when you get there, then you have a potentially large burn to drag your AN around the sun's equator to the correct longitude, which is itself a type of plane change, just not the type we usually do.

In fact, how is LAN for Kerbol even defined in KSP? Here, the sun's longitude is defined counterclockwise from the "First Point of Aries" but that's not in the KSP sky. Is there any external reference point you can use at all to determine this or can you only find out once you're in Kerbol orbit and then use MJ or whatever to show all the orbital elements that KSP doesn't show you by default?

[Kasuha]

But how do you do this so that you get the required LAN and APe upon arrival in solar orbit? If those aren't correct when you get there, then you have a potentially large burn to drag your AN around the sun's equator to the correct longitude, which is itself a type of plane change, just not the type we usually do.

In fact, how is LAN for Kerbol even defined in KSP? Here, the sun's longitude is defined counterclockwise from the "First Point of Aries" but that's not in the KSP sky. Is there any external reference point you can use at all to determine this or can you only find out once you're in Kerbol orbit and then use MJ or whatever to show all the orbital elements that KSP doesn't show you by default?

You're right, I forgot about these numbers. I guess the mod relies on the player using a tool calculating it the same way as the mod does, perhaps MechJeb or KER.

I guess in such case the best approach is probably about this: Slingshot off Jool to the correct inclination and slightly elliptic orbit. That unfortunately requires rather strong impulse or (preferably) powered slingshot low above Jool's atmosphere (strongest Oberth effect). Then brake at high apoapsis (about 2500 m/s) and then brake again at periapsis (about 3500 m/s). I did not simulate how much would the slingshot cost but I guess it will also be quite high number, that target orbit is kind of insane.

In images below I took it backwards - set up a ship in target orbit using Hyperedit, then drew maneuvers as if I wanted to return back (to Jool):

[TranceaddicT]

I love the Fine Print mod, but some of those contracts should pay out 1000 times more than they do considering how much work they are.

Kashua's right that a bielliptic transfer will save you buckets of delta-v, at the expense of a whole lot of time. This video is a really good introduction on using gravity assists. The effects can be nonintuitive.

If you're lucky enough to make your Jool transit at the right time, and really really patient fiddling with the maneuver nodes, or we had better tools in-game, you could nail both the kerbolar APe and LAN from all the way out in the Joolian system, then just bring your apoapsis down. Otherwise, you'll need most of that delta-v you saved just fiddling around getting the osculating elements right.

<snip>

lincourtl,

Thank you for that reference. I understood the general concept behind a gravity assist. I even diddled with it and use it to achieve a terminal orbit around a target body, but there was much more I was missing.

But how do you do this so that you get the required LAN and APe upon arrival in solar orbit? If those aren't correct when you get there, then you have a potentially large burn to drag your AN around the sun's equator to the correct longitude, which is itself a type of plane change, just not the type we usually do.

In fact, how is LAN for Kerbol even defined in KSP? Here, the sun's longitude is defined counterclockwise from the "First Point of Aries" but that's not in the KSP sky. Is there any external reference point you can use at all to determine this or can you only find out once you're in Kerbol orbit and then use MJ or whatever to show all the orbital elements that KSP doesn't show you by default?

Now, assuming I have a better understanding of GA, I would imagine that the LAN issue is a matter of:

1. timing the Kerbol approach trajectory such that it crosses at LAN

(this will mostly be determined at the time you make the burn for Jool)

AND

2. lining up the Jool assist so the Kerbol approach trajectory is approximates designated pro/retrograde orbit

(basically, the Jool approach should be above/below/aside opposite the final assist escape trajectory which subsequently will define the general direction of the target orbit)

After that, it's just a matter of tuning the orbit for the specified parameters. Yesh?

So the next question is when to burn for Jool?

[lincourtl]

In fact, how is LAN for Kerbol even defined in KSP? Here, the sun's longitude is defined counterclockwise from the "First Point of Aries" but that's not in the KSP sky. Is there any external reference point you can use at all to determine this or can you only find out once you're in Kerbol orbit and then use MJ or whatever to show all the orbital elements that KSP doesn't show you by default?

Don't ask me why it wouldn't be exactly 0 at UT=0, but...

In Kerbal Space Program, the Reference Direction for Celestial Longitude is not marked by any significant object, last I checked. In the universe of KSP, a ray drawn from Kerbin to the Sun at the epoch UT = 0.0 points about 0.09° east of the Reference Direction.

An Orbit whose Longitude of the Ascending Node is 180.0°, and whose Argument of Periapsis is 0.0° (abbreviated as LPE in KSP) will have an apoapsis that points in the Reference Direction. Through save file editing, you could add an object with a highly-eccentric elliptical orbit and a 90-degree orbital inclination around the sun to use its orbit as a pointer toward the Reference direction.

Edit:

In the above image, screenshotted a few minutes after UT=0.0, the apoapsis of the Reference Director spacecraft points in the Reference Direction for KSP Celestial Longitude.

[Geschosskopf]

Quoted out of order for clarity of discussion

(RE: Knowing when/where Kerbol's prime meridian is) Don't ask me why it wouldn't be exactly 0 at UT=0, but...

In the real world, the right ascension aka celestial longitude coordinate system of a planet/sun/whatever isn't time-dependent. It's based on a fixed point in the sky against the (not really) immobile starry field. So in our solar system, if you draw a line from the First Point of Aries (whatever the Hell that is) to the center of Sol, that line is always on the Sun's prime meridian, regardless of the Sun's rotation.

The KSP celestial longitude system is also fixed because LAN values in KSP actually have meaning (they wouldn't if it wasn't). The problem is, absolutely nothing in the stock game and damn little in a modded game gives you a clue in wich direction lies the celestial prime meridian of any body in space. To what point against the background of "fixed" stars do you draw the line?

AFAIK, the only way to get any sense at all of Kerbol's (or any other body's) celestial coordinate axes is to get into a very slightly inclined orbit around it and open up the appropriate info box from MJ, KER, or whatever, and see what your LAN is. And the real annoyance here is that because you have to be in Kerbol orbit for these mods to show your current LAN, you can't set Kerbol as your target, which is the only way the game will draw your ascending and descending nodes in the map view. Thus, even though you now know your current LAN, you have to guestimate where your AN is by rotating the map so Kerbin's orbit is a horizontal line and eyeballing where that line crosses your orbit on your way up. Then once you know more or less where your LAN is now, you'll have to guesstimate from there where the contract LAN is, and figure out how to do the "plane spinning" (as opposed to the usual "plane tilting") to drag your LAN around from where it is now to where it needs to be.

Now, assuming I have a better understanding of GA, I would imagine that the LAN issue is a matter of:

1. timing the Kerbol approach trajectory such that it crosses at LAN

(this will mostly be determined at the time you make the burn for Jool)

AND

2. lining up the Jool assist so the Kerbol approach trajectory is approximates designated pro/retrograde orbit

(basically, the Jool approach should be above/below/aside opposite the final assist escape trajectory which subsequently will define the general direction of the target orbit)

After that, it's just a matter of tuning the orbit for the specified parameters. Yesh?

So the next question is when to burn for Jool?

I was only married to an orbital mechanics guru, I was never one myself, and even that was over 20 years ago, so listen to Kasuha instead of me unless Kasuha deigns not to reply. But the problem I have with your methodology here is that you have no idea where Kerbol's celestial prime meridian is in relation to the skybox background so you have nothing upon which to base your 1st step.

It seems to me that the best way to change your LAN is by burning prograde or retrograde (EDIT: or radial in or out) as required when you're still more or less but not quite coplane with your target's orbit. Because this changes the eccentricity of your orbit, it changes where your orbit's plane crosses your target's orbit's plane, as you can see when trying to rendezvous with something you're not quite co-plane with. The basic problem of the game interface remains, however. Because mods only give you a LAN value when you're orbiting the central body, and when you're orbiting the central body the game won't draw your ascending and descending nodes, you still have to eyeball where they are. But at least that should tell you whether a prograde or a retrograde (EDIT or in or out) burn will move your LAN in the desired direction.

Because of all this, I'm thinking your only real option is to burn for Kerbin escape not quite in Kerbin's plane, so the mod you're using will give you a Kerbol LAN value. Then you burn prograde or retrograde (EDIT or in or out) as required to get your LAN set. This might require you to scrap that launch and start over with a retrograde instead of a prograde escape. Who knows? But once you've got the LAN down, then you do the plane change to the inclination required, then burn your Kerbol Ap and Pe to where they need to be. This all sounds hugely expensive in dV, probably to the point where the contract is nonremunerative. So TBH, I'd just default on this contract .

Edited September 12, 2014 by Geschosskopf

[TranceaddicT]

Geschosskopf,

I agree on all counts. Fortunately, when you accept the contract I provides you with the terminal orbit displayed about the parent body. That is the only reason that the need for knowing Kerbol's prime is moot.

I also too a page from Kasuha and Hyperedited the orbit in a default save. WOW!! That periapsis, I think, would be considered well within what should be Kerbol's corona. I had to zoom out for fear of burning Kerbol's center mass onto my screen.

[Geschosskopf]

I agree on all counts. Fortunately, when you accept the contract I provides you with the terminal orbit displayed about the parent body. That is the only reason that the need for knowing Kerbol's prime is moot.

Ah, well, in that case, can you target that desired orbit and get the game to draw your ascending and descending nodes to it? If not you still have to eyeball things but the LAN problem is reduced to doing a normal + or - burn where you current orbit looks like it crosses the plane of the desired orbit. So figure out from the displayed target orbit and its required APe whether you need to go over Jool's north pole or under its south pole when you get there to end up going the right way around Kerbol, and shoot yourself into something approximating the desired inclination. Then do a plane change where your orbit crosses the target orbit to set your LAN. The magnitude of this burn, and probably whether you slingshot up or down, will depend on where Jool is in relation to the desired LAN when you get there. It seems like a Jool slingshot can help you with inclination and Ap but you'll still have to do some major burns for the LAN and Pe.

Again, I wonder if the game is worth the candle. Does the contract slso specify the design of the satellite you need to put there? If you've got a free hand there, an ion drive on a tiny probe might be the only economical solution, at the expense of immense burn times. But money is not the only concern. At your point in the game now, does the contract provide a meaningful Science! reward? I mean, you're going to be doing this with a probe so won't get much if any rep regardless of what the contract says. And even if the reward is attractive, do you have the time before the deadline? It's going to take a year +/- just to get to Jool, then you're looking at least at several more years to finalize tweaking your orbit.

[tomf]

I wouldn't bother slingshotting of Jool, getting there when it is corectly alligned will be a pain, and doingh the inclination change and lowering PE without it is *only* 2330 so that is the maximum you can save Getting to jool on the non-hohman transfer you are going to need in order to get anything out of the sliggshot is going to eat up most of that. Getting the 3500 you will need to bring down your AP is much more of an issue.

[Kasuha]

doingh the inclination change and lowering PE without it is *only* 2330

You need to get into highly inclined transfer orbit from Jool or you'll be spending a lot of dv forming your final orbit into correct LAN and APe. Doing the change in Jool orbital altitude without Jool is going to cost at least 4000 m/s (with 2000 m/s burn from Kerbin). Still better than trying to reach that transfer orbit directly from Kerbin (>10,000 m/s) but you still lose over 3 km/s compared to using the slingshot.

But yes, it is matter of taste. Building stronger rocket might be simpler than getting the timing right.

Edited September 12, 2014 by Kasuha