Polar Orbits

[kerbalfreak]

There is something that is very confusing to me. The two orbits below are perfect circular, with the same height and at 90º. What is the paramenter that makes them different? Orbits at 0º are always on the same plane.



How can I choose this using Mechjeb? Is possible to align polar orbits on a moon with polar orbits at a planet? Like this:



Thanks!!

[DrLicor]

Hey, it's because the planet you're launching from, also has it rotation period. Inclination means the angle of the orbital plane of the object, reffering to the plane of a planet. The thing that causes your situation, is the difference in 'longitude of the ascending node'. 

More info kan be found here:

https://en.m.wikipedia.org/wiki/Orbital_inclination

If you want to launch a craft in the same orbital plane as the past, pick a menu in mechjeb or KER, that visualizes the 'relative inclination', when this number is zero, it means you launch in the same longitude of the ascending node.

Hope this helped you out a bit.

Edited December 28, 2017 by DrLicor

[GoSlash27]

The parameter that makes these two orbits different is the argument of right ascension, aka the longitude of ascending node.

HTHs,
-Slashy

Edited December 28, 2017 by GoSlash27

[Starman4308]

To elaborate a bit, there are five orbital elements to specify the shape and size of an orbit, with two more to specify where you are in that orbit, for a total of seven orbital elements. For something to be coplanar, you not only have to match inclination, but also LAN (Longitude of the Ascending Node).

This is, by the way, very much related to specifying x,y,z coordinates, velocities in x,y,z, and a time of observation.

 

For an elliptical (non-escape) orbit:

First, one defines a plane of reference (usually the equator), and a direction of reference (in the real world, usually the First Point of Aries, in KSP, a random point in the skybox).

 

Semi-major axis defines the size of your orbit.

Eccentricity defines how oval vs. circular the orbit is; for elliptical orbits, the range is 0 <= e < 1. If e=0, it is perfectly circular, with higher values indicating a greater difference between apoapsis and periapsis.

Inclination is how tilted your orbit is with respect to the equator, with values from 0 to 180 degrees.

Longitude of the ascending node (LAN), AKA the argument of right ascension, is the eastwards angle from the reference direction to the ascending node. This is the primary difference between your two orbits, and represents where the tilt (inclination) is, on the equatorial plane, with respect to the reference direction.

Argument of periapsis (AOP) is the angle (along the orbit) from the ascending node to periapsis. This represents the relative positioning of the semi-major axis (eccentricity) with respect to the equator.

 

As promised, these five elements represent the shape, size, and orientation of an orbit. If SMAs are equal, they are isoperiodic (same orbital period). If inclination and LAN are equal, they are coplanar. If all five of the above are equal, they follow the same orbital track... but might be at different points on that track.

 

Mean anomaly at epoch (MAE) defines how far along the orbital track the object was at an arbitrary point in time called "epoch". In KSP, this ranges from 0 to 2*pi. Divide your orbital period by 2*pi, multiply it by MAE, and you get the number of seconds it would take to travel from periapsis to the vessel's position at that arbitrary epoch. Effectively, it's an offset from periapsis at an arbitrary time.

Epoch is that arbitrary point in time; in the real world, there are some common epochs such as J2000.

Edited December 28, 2017 by Starman4308

[Geschosskopf]

4 hours ago, kerbalfreak said:

What is the paramenter that makes them different? Orbits at 0º are always on the same plane.

The parameter is Longitude of Ascending Node (LAN).  Just as in the real world, in KSP there's a "celestial prime meridian" that is defined as a specific direction outwards from the solar system out to the background stars.  This direction is LAN = 0 and "celestial longitude" is measured around the circle from this direction.  So, an inclined orbit crosses the celestial equator in 2 places, its ascending (AN) and descending (DN) nodes.  The place where the AN is in relation to the "celestial prime meridian" is the LAN for that orbit.  Thus, as in your picture above, the 2 orbits have the same parameters for everything EXCEPT LAN, because their ANs are in different directions from the "celestial prime meridian".

NOTE:  The exact direction of the "celestial prime meridian" is totally arbitrary and there's no visual reference to it on the skybox texture.  So don't lose any sleep over trying to figure out where it is.  It doesn't matter.  If you're tring to match a contract orbit with a specified LAN, or otherwise get orbits lined up, then just worry about the numbers shown for LAN.  Or, even easier, just make sure your ship's AN is in the same place on the map as the target's AN.

 

4 hours ago, kerbalfreak said:

How can I choose this using Mechjeb? Is possible to align polar orbits on a moon with polar orbits at a planet? Like this:

Yes, this is possible.  Both probes would need to have the same LAN (LAN being based on the "celestial prime meridian", it's independent of the body you're orbiting).  I can't remember if MJ has a "change LAN" function but it's not hard to do manually.

• Select the ship orbiting Kerbin, open MJ's Orbit Info, and write down the LAN.
• Fly the other ship to Mun, entering a fairly inclined, very wide orbit (wide to save fuel during several orbital tweaks).  It helps to time your trip so that you arrive at Mun as close to the desired LAN as possible, which you'll have to eyeball.
• Fix the Mun ship's LAN first because doing this will change the other parameters, but changing the others later won't change the LAN.  To change your LAN, burn normal or anti-normal when at your most "polar"places in your orbit (highest or lowest above/below the equator).
• Once the LAN is set, adjust inclination to 90-ish and then put your Ap and Pe where you want them.

[kerbalfreak]

Many thanks!! I have read that was longitude, but that didn't made any sense, because the longitude changes. I didn't know that was a fixed celestial longitude. I still don't fully understand the concept of ascending and descending nodes when you don't have a target, but everything is much clear now.

I just want orbits to be aligned and looking good, nothing really important. I will just set 00º00'00" with Mechjeb, and then 90º. My constellations around Kerbin, Mun and Minmus are not aligned, but they are relatively easy to be redone.

Starting right in Duna and Ike 

Edited December 28, 2017 by kerbalfreak

[Geschosskopf]

9 minutes ago, kerbalfreak said:

I still don't fully understand the concept of ascending and descending nodes when you don't have a target, but everything is much clear now.

OK, just as there's a celestial prime meridian, there's also the celestial equator (which corresponds to Kerbin's equator).  Any inclined orbit thus crosses this celestial equator in 2 places, the AN and DN.  This always happens whether or not you have a target.  Every inclined orbit always has an AN and a DN (and the AN always has a LAN).  KSP just doesn't draw them on the map unless you've got a target, which is one of the many ways in which KSP's ridiculous lack of stock in-game instrumentation perpetually irks me.

[Mr. Peabody]

Getting a polar orbit isn't hard and you certainly shouldn't need mechjeb to do it. Just gravity turn in the correct direction and then adjust your inclination using a maneuver node once orbital.

[Starman4308]

15 minutes ago, The Dunatian said:

Getting a polar orbit isn't hard and you certainly shouldn't need mechjeb to do it. Just gravity turn in the correct direction and then adjust your inclination using a maneuver node once orbital.

He wasn't asking for how to achieve a polar orbit. As point of fact, the stock game doesn't even give the orbital parameter of interest, longitude of the ascending node.

[Zhetaan]

2 hours ago, Starman4308 said:

To elaborate a bit, there are five orbital elements [... snip]

@kerbalfreak:

To elaborate a bit more, some of these elements have different names, as @GoSlash27 indicated when naming the parameter you were seeking as both argument of right ascension and as longitude of ascending node.  It's also the case that there are other elements that either derive from the seven given or can be derived from them, which is important because KSP doesn't always give the more common elements.

For example, the semi-major axis and eccentricity can both give or be derived from the apoapsis and periapsis (plus the planetary diameter, because KSP reports apsides as altitudes from the surface, not distance from gravitational centre), and the apsides are what you see on the screen.  Interestingly, the internal computation is based on semi-major axis and eccentricity--when it shows you apsides, it's calculating them from SMA and ECC.

KSP stores inclination but reports it with the ascending node--and of course the descending node, which may also be used to calculate inclination--and does not report ascending node except as relative to a target, so finding the inclination with respect to the equator is only possible if your target is also at the equator.

KSP knows longitude of ascending node (LAN) but doesn't report it numerically.  It does report LAN visually in map mode by showing you where the ascending node is on the orbit, which makes things especially fun when you have an orbit contract that requires a specific LAN and all you can do is eyeball it.  The same is true of argument of periapsis (which can also be calculated from longitude of periapsis), but KSP at least reports periapsis without needing to pick a target.

Mean anomaly at epoch can also be considered in terms of time of periapsis passage--or actually, time of passage for any defined point on the orbit.  Orbital period about a given gravitational point is dependent on semi-major axis and no other thing--not even eccentricity.  A circular orbit and an eccentric orbit with the same SMA will always have the same period--but keep in mind that the eccentric orbit will both have an extremely low periapsis and a corresponding high apoapsis, and the orbital speed will be similarly very fast at close approach and extremely slow when far away.

KSP doesn't appear to use a common epoch for all vessels (that would be the obviously simple choice of 00:00:00:00:00.000, the start time of the game); if I were forced to guess, I would say that the epoch value it stores is the time of launch.  That makes sense; using any particular reference time is the same as using any other so long as the relationship between references is known (and the relationship is known because all reference times are in terms of seconds since game start), but that choice of time allows KSP to calculate both the mean anomaly at epoch and the mission elapsed time from one stored value.

I will additionally clarify that the direction of reference in KSP is not so much a random point on the skybox as it is a specific point that cannot be found via what we would call normal astrogation.  Calling it random suggests that it changes, which is of course self-defeating for a reference line.  In real life, the First Point of Aries is something that can be located because of its relationship to the surrounding stars (and from first principles, Earth's axial tilt, which would be a problem in KSP).  In KSP, the sky is 'painted on' to an otherwise completely featureless box (hence, skybox) and the stars that you see in it are mere decoration.  You can't point to them in the sense of having them as valid targets because they have no definition as celestial structures--this is one of the many necessary simplifications needed for KSP to work as a simulation in the Unity environment.  There's no need to process other stars, and the Unity system gives a zero-angle direction anyway, so why not use that without care for where it points, so long as it always points the same way?

[ElWanderer]

1 hour ago, Zhetaan said:

KSP doesn't appear to use a common epoch for all vessels (that would be the obviously simple choice of 00:00:00:00:00.000, the start time of the game); if I were forced to guess, I would say that the epoch value it stores is the time of launch

I believe the epoch time is reset at regular intervals for the active vessel. I have been told it was deliberately done this way as part of the effort to avoid the Kraken (i.e. keeping the current vessel at the centre of the game universe to avoid floating point errors building up too high).

This is second-hand knowledge, I've not checked it myself, but it's what I was told when I asked if the epoch was the beginning of the game (i.e. time 0).

[Zhetaan]

5 hours ago, ElWanderer said:

I believe the epoch time is reset at regular intervals for the active vessel. I have been told it was deliberately done this way as part of the effort to avoid the Kraken [snip]

That makes sense.  I know that Krakensbane works by defining the active vessel as the centre of the coordinate system, so it is plausible that it would need (or could use) something similar for the temporal coordinate, too.  Of course, barring one of the staff confirming this, we'll just have to rely on ever-wilder speculation and be happy with that.

[Geschosskopf]

18 minutes ago, Zhetaan said:

Of course, barring one of the staff confirming this, we'll just have to rely on ever-wilder speculation and be happy with that.

The weird intricacies of the KSP coordinate systems is discussed in the docs for the kOS "DIY autopilot" mod.  Here:  http://ksp-kos.github.io/KOS_DOC/math/ref_frame.html?highlight=coordinate system  It's actually weirder than you'd expect.