How to change orbital plane

IDNeon

Member

I wanted to take this question a step further and I don't have the vocabulary to ask the questions well but I'll try:

For the given plane that you are on, there is an apogee and perigee and I will call their position on this orbital plane "progression". I think progression is defined 0deg - 360deg as your progress along your orbit?

For the other directions I'll give it the X,Y, Z coordinate definitions.

So if you imagine looking at the X,Y plane with Z going straight in front of you...

For the purposes of the questions, the initial orbital plane's Prograde and Retrograde are +/- Y-axis/Z-axis. Basically you're looking at the orbital plane such that it is the Y-Axis orbiting around the X-axis.

Hopefully now you can imagine a circle (the orbital plane) centered on Y, with yaw rotating around the Z axis, roll rotating around the Y axis, and pitch rotating around the X axis.

Conceptualizing the orbital plane in this way, how do I approximate what the changes will be to the plane's position over the orbited body....

X,Y,Z coord.
If 0,0,+Z = Perihelion and 0,0,-Z = Aphelion....

Then to change the orbital plane around the X, Y, Z axes is dependent upon a 90deg yaw burn but is [PROGRESS] dependent, correct?

That is to say I can ONLY turn around the:

Y-axis when at 0deg or 180deg [PROGRESS]. (At Perihelion or at Aphelion).
Z=axis when at 90deg or 270deg [PROGRESS].

NOTE 1) Now I don't know how progress between those periods of orbit affects the angle but I can tell that somehow it's going to be affected and there will never be a solution where Y-axis is modified at 90deg or Z-axis modified at 0deg.

Correct so far?

What I mean by NOTE 1) is I'm not sure if it is a sin or cos or tan but it's some thing like this:

As I progress from 270deg to 360deg (0deg), assuming a 90deg yaw, my orbital plane will change 100% around the Z axis. But then determined by sin/cos/tan, it will diminish to 50% at 315deg [PROGRESSION], and change on Y-axis will increase from 0% to 50%.

By 360deg (0deg) [PROGRESSION] the Z-axis change will diminish to 0% and the Y-axis change will now be 100%.

NOTE 2)

Because I believe NOTE 1) to be intuitively true, I come to my first question.

QUESTION 1) does changing the YAW angle, relative to your orbital plane at a given DEGREE of [PROGRESSION], determine how effectively you rotate on a given axis of the coordinate system as above defined?

Such that if I angle correctly, can I rotate my orbital plane along the Y-axis, regardless where I am in the [PROGRESSION] of the orbit?

My intuition says no, there is never a case where that is true without substantially altering other parameters of the orbit.

So:

QUESTION 2) is all orbital plane maneuvers [PROGRESS] dependent?

Lastly:

QUESTION 3) how does one change the X-axis.

As above defined, rolling the orbit along the X-axis intuitively requires a 90deg orientation to that plane. Just as the others YAW 90deg at some [PROGRESS]

Then does 90deg Pitches (toward center of orbit or away from center of orbit) rotate the position of 0deg and 180deg [PROGRESSION] relative to the orbited body acting as the fixed coordinate?

If this is true, what's the mechanics of that?

I have noticed prograde/retrograde burns ALSO rotate the orbital plane over the X-axis, but this is at the expense of increased/decreased altitude. And to keep the same altitude but roll the orbital plane around the X-axis doesn't make sense to me.

Because to subtract the same amount of ENERGY from the system....would reverse the rotation around the X-axis of the orbital plane as well.

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Thanks for reading this far, sorry that it is probably confusing, but writing these questions without drawings or good vocabulary in orbital mechanics is difficult. So I hope this isn't that confusing.

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N_Molson

Donator
Please read Orbiter.pdf, you have a lot of basic things about basics orbital mechanics explained with pictures, you have to read the doc.

IDNeon

Member
Please read Orbiter.pdf, you have a lot of basic things about basics orbital mechanics explained with pictures, you have to read the doc.
K, you're talking about section 17.4

IDNeon

Member
All of the following makes some sense EXCEPT that this only changes the plane around ONE defined axis. the Radius-vector axis.

What about the other Axis which is perpendicular to that AN/DN Axis?

I like the part where Tn = half the burn time before AN or DN, because this keeps the burn symmetrical across the AN/DN nodes.

But doesn't this just confirm all of my OP? Where instead of burning at Aphelion or Perihelion there's also a burn at 90deg and 270deg?

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IDNeon

Member
The more I stare at it the more sense it's starting to make.

But, ugh, I don't know how to ask the next question.

There's a configuration of planes where this maneuver cannot achieve coplanar orbits?

If the planes are perpendicular to each other then applying the thrust on the Nodes just causes your nodes to traverse the target's orbit.

It doesn't actually bring your planes together?

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Urwumpe

Not funny anymore
Donator
If the planes are perpendicular to each other then applying the thrust on the Nodes just causes your nodes to traverse the target's orbit.

Remember, that you are only changing two velocity vectors there. nothing more complex. If v is your orbit velocity, you essentially just want to get from (0, v) to (v, 0), by adding another vector. To calculate this vector just subtract the target velocity vector from your reference velocity vector: You need to add a velocity change of (v-0, 0-v) = (v, -v), which is of magnitude sqrt(2)*v and is pointing straight into the middle between the two orbit normals.

EDIT: Also you don't burn at a specific true anomaly of the orbit, but where your two orbit planes cross. In theory, you want to change only the direction of the velocity vector, not the radius vector. In reality of course, this won't work out. For achieving this goal in the result, you need to change radius and/or velocity magnitude during the burn.

It doesn't actually bring your planes together?

Yes, of course. Now remember, that your burn does never happen in one tiny point in space, but has a duration. For small changes of relative inclination, this approximation is fine. For larger maneuvers, your longer burn time will mean you are most of the time burning in the wrong direction that way.

In that case, you have two ways to fix this: Change the orbit in multiple smaller maneuvers. Or use a more advanced guidance for determining how to end your burn in the right velocity vector with minimal fuel consumption, while under the influence of gravity.

IDNeon

Member
Please read Orbiter.pdf, you have a lot of basic things about basics orbital mechanics explained with pictures, you have to read the doc.
Also, what is the Delta-V given for a specific Delta-i ??

Is it obviously proportional such as Tangent? (Opp / Adj)?

So for angle 45deg between two orbital planes TAN = 1...so does that mean my delta-V has to be 1x(my current velocity)?

And that current velocity is whenever I conduct the burn?

IDNeon

Member
Remember, that you are only changing two velocity vectors there. nothing more complex. If v is your orbit velocity, you essentially just want to get from (0, v) to (v, 0), by adding another vector. To calculate this vector just subtract the target velocity vector from your reference velocity vector: You need to add a velocity change of (v-0, 0-v) = (v, -v), which is of magnitude sqrt(2)*v and is pointing straight into the middle between the two orbit normals.

Yes, of course. Now remember, that your burn does never happen in one tiny point in space, but has a duration. For small changes of relative inclination, this approximation is fine. For larger maneuvers, your longer burn time will mean you are most of the time burning in the wrong direction that way.

In that case, you have two ways to fix this: Change the orbit in multiple smaller maneuvers. Or use a more advanced guidance for determining how to end your burn in the right velocity vector with minimal fuel consumption, while under the influence of gravity.
I'm going to have to sit on the math for a second....

But, regarding the small changes over sequences of orbits, that all made sense.

I'm stuck on the idea that two orbital planes perpendicular to each other can be brought together by thrusting as only shown in the diagram, where the axis of the Nodes are.

In fact I'm trying to abstract in my imagination how you can always burn at Aphelion if you're supposed to burn at AN or DN?

Or is the AN / DN not actually the location of the burn but meant to show direction of your burn, depending on if your Aphelion is on the AN or DN side of the Node?

IDNeon

Member
Also, since Aphelion is prefered, how do you move Aphelion and Perihelion along the path of your orbit? I've seen that "rotate" so to speak, but don't know what I've done to cause that to happen.

I expect this answer might be that "X-axis rotation" I defined, where a burn toward center of orbit or away from center of orbit will slide Aphelion/Perihelion along the orbital path.

Urwumpe

Not funny anymore
Donator
Or is the AN / DN not actually the location of the burn but meant to show direction of your burn, depending on if your Aphelion is on the AN or DN side of the Node?

Ascending node and descending node are the location, where your orbit crosses the plane of the target orbit. Ascending = You go from perigee to apogee. Descending: You go from apogee to perigee. There are always two opportunities, usually with different DV requirement - the further away from the gravity body, the less DV you need, since you are slower (and changing the direction of a smaller velocity takes of course less effort). Yes, having one node at apogee would be great, but isn't always an option.

The direction in the Orbiter tutorials, which is good enough for small changes of inclination is usually orbit normal or antinormal, which is always perpendicular to your current orbit. If you do the math, you might notice that this fails for bigger maneuvers. For doing a 180° change (+v to -v), you need to burn retrograde (-2v), not normal. For your 90° change, you need to point at a 45° angle to your orbit towards the target orbit. And you need a whole lot of fuel and time.

IDNeon

Member
Ascending node and descending node are the location, where your orbit crosses the plane of the target orbit. Ascending = You go from perigee to apogee. Descending: You go from apogee to perigee. There are always two opportunities, usually with different DV requirement - the further away from the gravity body, the less DV you need, since you are slower (and changing the direction of a smaller velocity takes of course less effort). Yes, having one node at apogee would be great, but isn't always an option.

The direction in the Orbiter tutorials, which is good enough for small changes of inclination is usually orbit normal or antinormal, which is always perpendicular to your current orbit. If you do the math, you might notice that this fails for bigger maneuvers. For doing a 180° change (+v to -v), you need to burn retrograde (-2v), not normal. For your 90° change, you need to point at a 45° angle to your orbit towards the target orbit. And you need a whole lot of fuel and time.
Thanks!

I mistook ascending/descending to be relational to the target orbital plane.

How do I find the Normal? I mean mathematically. I read it is the cross product, but I haven't had to "calculate" for it, so dunno....

Does Normal change for positions of Apogee and Perigee in two orbits that are otherwise the same?

Assume two circular orbits in the same plane with very slight variation such that one's apigee is above the planet's 180 longitude and the other's apigee is above the planet's 0 longitude.

Will these two orbiting bodies have different Normals?

Urwumpe

Not funny anymore
Donator
Thanks!

I mistook ascending/descending to be relational to the target orbital plane.

How do I find the Normal? I mean mathematically. I read it is the cross product, but I haven't had to "calculate" for it, so dunno....

In Orbiter, there is a navigation mode for both normals.

Will these two orbiting bodies have different Normals?

No. Actually not. What you changed there is the argument of periapsis. But the orbit are coplanar. Now you only need to change the argument of periapsis. You can do this again at one of the two occasions where your current orbit will cross the other orbit. Again, your burn will be in direction of the velocity change. In case of your 180° example, its simple: You only need to flip the sign of the vertical component of your velocity vector, by burning radial or antiradial. The higher the eccentricity of your orbits, the more DV you will need.

IDNeon

Member
Well I'm going to have to consume your lingo for a while to catch up. What you said seems precise but I'm not sure what direction radial and antiradial are.

Here's what I did today so far.

I set out to see what happens if I burned toward inside of my orbit. And it seemed to move the whole orbit along the Z axis. While also rotating it (as I understand it) along the x-axis as I thought it might.

Inside burn rotated it retrograde so that the apigee moved retrograde from where it was previously in my orbit.

I think what I did describes the operation you said needed to be performed.

As my apigee would turn to match the targets that is Coplanar.

So is burning toward center of my orbit (perpendicular toward the planet) antiradial?

jedidia

shoemaker without legs
For the given plane that you are on, there is an apogee and perigee and I will call their position on this orbital plane "progression". I think progression is defined 0deg - 360deg as your progress along your orbit?
If I understand you right, what you are referring to is what is commonly called the longitude of the ascending node.

I think the major part of your confisuion is that you try to understand planes as distinct meaningful orbital shapes, and are looking for a crossing from one to the other in an absolute frame.

The trouble is, an orbital plane in and of itself is, unlike things like semimajor axis, eccentricity aso, not meaningful in and of itself. It only has meaning in reference to another plane. You can use the equatorial or ecliptic plane as a common reference, that can make visualising things easier, and then think about transitioning from one plane to another relative to that reference plane.

The problem with that is that it breaks down as soon as all three planes do not have the same longitude of the ascending node. Because now the reference plane becomes irrelevant, and the only thing you are interested in is the effective angle between your plane and the target plane (relative inclination, which depends * a lot* on the longitude of the ascending node - so much so that two planes with the same equatorial inclination can have a relative inclination of 180 degrees to each other! ), and where the two planes intersect (ascending and descending nodes). These things only exist, and only have meaning, in the direct comparison of two planes.

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IDNeon

Member
In Orbiter, there is a navigation mode for both normals.

No. Actually not. What you changed there is the argument of periapsis. But the orbit are coplanar. Now you only need to change the argument of periapsis. You can do this again at one of the two occasions where your current orbit will cross the other orbit. Again, your burn will be in direction of the velocity change. In case of your 180° example, its simple: You only need to flip the sign of the vertical component of your velocity vector, by burning radial or antiradial. The higher the eccentricity of your orbits, the more DV

If I understand you right, what you are referring to is what is commonly called the longitude of the ascending node.

I think the major part of your confisuion is that you try to understand planes as distinct meaningful orbital shapes, and are looking for a crossing from one to the other in an absolute frame.

The trouble is, an orbital plane in and of itself is, unlike things like semimajor axis, eccentricity aso, not meaningful in and of itself. It only has meaning in reference to another plane. You can use the equatorial or ecliptic plane as a common reference, that can make visualising things easier, and then think about transitioning from one plane to another relative to that reference plane.

The problem with that is that it breaks down as soon as all three planes do not have the same longitude of the ascending node. Because now the reference plane becomes irrelevant, and the only thing you are interested in is the effective angle between your plane and the target plane (relative inclination, which depends * a lot* on the longitude of the ascending node - so much so that two planes with the same equatorial inclination can have a relative inclination of 180 degrees to each other! ), and where the two planes intersect (ascending and descending nodes). These things only exist, and only have meaning, in the direct comparison of two planes.
Thanks. Yes this is starting to stort out a lot for me especially in the vocabulary.

I found that an outward velocity from the perigree moved the perigree counter clockwise where I define clockwise as the Prograde.

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