Planet of Slighty Lesser Death (Blaa Eohn YZ-G d10-0)

[LCU No Fool Like One]

The Canonn plugin alerted me to the fact that I was close to a GMP System called The Planet of Slightly Lesser Death

Like the infamous Monde de la Morte (Spoihaae XE-X D2-9), this system consists of a planet which orbits perpendicular to the core white dwarf's jet cones close enough to pass through them at either end. While not passing as near as the exclusion zone unlike its eponym, the cones themselves still create a severe hazard for landing which should not be attempted while the planet is inside the jets themselves.

Discovered during preparation week for the Distant Worlds 2 Expedition the system's general proximity to the bubble proved to be a decent journey and risk experimentation with spectacular views down the cone of a white dwarf for early explorers and veterans alike.

So I dragged myself over there and was a little underwhelmed to be honest. The cone does not seem to be very close to the orbiting planet. Looking at the orbits in the orrery it looks like the cone will only be pointing directly at the planet twice per year and due to the mild eccentricity (of the orbit not me) its probably only going to cook the planet once per year. Fortunately a year is only 2.5 days in these parts.

I didn't want to miss the opportunity to supercharge my fleet carrier so I was wondering how to calculate the time that it would next pass through the cones of death. If it was days I would move on. If just hours I would carry on my way.

According to the journal at 2022-04-07 14:36:24 the meanAnomaly of AB 1 was 335.894091 degrees which is essentially the number of degrees it has orbited since the last periapsis (closest approach). So this means that the next periapsis will be in 24.105909 degrees. But we could also express the progress around the orbit as time. The orbital period is 2.5 days (217290.538549 seconds actually) So all we need to do is convert degrees into seconds. 217290.538549 = 360 degrees so that means that 1 degree = 603.5848293027778 seconds.. so we can multiply that by the number of degrees until periapsis and we will have a time of 14,549.96096895329 seconds.

So that means I should expect to pass the cone of death 04 hours 02 minutes and 29 seconds after 2022-04-07 14:36:24 and thenceforth every 2.5 days

Me: looking underwhelmed.

So at the allotted time I returned to my ship and the cone was still some distance from the ship but clearly had approached much closer. So I waited and approximately an hour later the alarms on my ship started going crazy. But as I was still docked I was't taking any damage. The carrier was clearly shielding me somehow.

By 20:37 UTC the carrier was completely engulfed in the cone.

Me: looking overwhelmed.

Clearly I need get to grips with the orbital mechanics a bit better but i think this gives us a decent baseline for timing these events.

Perhaps you might want to have a go yourself Sunday, 10 April 2022, 07:51:30. I can't guarantee your carrier will be able to jump 1000 light years afterwards but I think you will have fun.

 

[Edelgard von Rhein]

It is not correct to convert degrees of orbit directly into the time of an orbital body to traverse a fraction of that orbit (unless a perfect circle) - remember Kepler's laws: it is equal areas in equal time.
That said, you got close enough that you got to experience something spectacular - a shame you can't boost the carrier range! (Of course, you need a fuel scoop to get the boost but FCs don't have them...).

 

[LCU No Fool Like One]

It is not correct to convert degrees of orbit directly into the time of an orbital body to traverse a fraction of that orbit (unless a perfect circle) - remember Kepler's laws: it is equal areas in equal time.
That said, you got close enough that you got to experience something spectacular - a shame you can't boost the carrier range! (Of course, you need a fuel scoop to get the boost but FCs don't have them...).

I understood from the passage below that you could do that if you were using the mean anomaly as opposed to the true anomaly but I'm not astronomer so happy to be corrected. I'm keen to get the maths right because I need to calculate future dates when these events occur so other people can enjoy them.

In celestial mechanics, the mean anomaly is the fraction of an elliptical orbit's period that has elapsed since the orbiting body passed periapsis, expressed as an angle which can be used in calculating the position of that body in the classical two-body problem. It is the angular distance from the pericenter which a fictitious body would have if it moved in a circular orbit, with constant speed, in the same orbital period as the actual body in its elliptical orbit

This is the prototype calendar https://canonn-science.github.io/canonn-calendar/ if you have any events that would be worth adding you can submit them here

Event Submission

Please use this form to suggest events to add the the Canonn Calendar. We are looking for things like planetary collisions and significant anniversaries and planetary alignments.

forms.gle

 

[Edelgard von Rhein]

I am getting old and my brain struggles with math so I'll try and keep this simple:
imagine a planet with an orbital period of 360 days and a perfectly circular orbit.
Now imagine that you encounter a comet with a period of 360 days and an eccentricity of 0.99.
1 day after the comet passes periastron it will have passed 1/360 of its orbital period
1 day for the planet with an orbital period of 360 days corresponds to 1 degree angle
However, the part I struggle with is that 1 degree for the comet does not correspond to 1 day at this point in the orbit - it will pass through many more degrees in this time at periastron and fewer at the most distant point in the orbit. It is equal areas in equal time, not equal angles. So I just don't get mean anomaly. Like I said, it could just be age and I don't get things anymore.

 

[Neilski]

I always wondered what "mean anomaly" meant but had somehow never looked into it, so I'm delighted to finally learn the answer today
@Edelgard von Rhein - if you check out https://en.wikipedia.org/wiki/Mean_anomaly (source of the text that @LCU No Fool Like One posted above) you should see that it's just a simplification of the real situation - you are thinking about the actual* angular position of the body rather than the fictitious circular-orbit-equivalent one.
(* the "true" anomaly in astrometrics speak, I also learned today)

And now, having made it clear that I'm clueless about this stuff, I will note that I don't see any obvious errors in the workings above. However, if the orbit is reasonably close to circular, one guess might be that the periapsis wasn't quite where you thought it was? Or maybe that's clear from one of the other bits of data about the body.
(I'll be really honest here and add that while I had noticed the orbital elements mentioned on the system info screen, I kinda always thought they were somewhat "made up" so it's a nice surprise to find that they are meaningful!)

 

[LCU No Fool Like One]

@Edelgard von Rhein you are actually right! But my calculation is also right.

This video helped me understand better,

Source: https://www.youtube.com/watch?v=cf9Jh44kL20


If I was trying to calculate the position at any point other than Periapsis or Apoapsis using my method then I would have got it wrong. However the True Anomaly, Eccentric Anomaly and Mean anomaly all co-oincide at Periapsis and Apoapsis. Given that the mean anomaly is a constant speed then I can convert degrees to seconds.

I think the reason why the timing was off is because I had assumed that the cone was pointed at the planet at Periapsis but I think I probably need to look at the inclination to make a more accurate calculation. However having it an hour off is probably a good thing as you probably wouldn't be able to get the carrier orbited in the cone.

A bigger problem I have right now is that I did calculations for Cyanean Rocks and Rhubarb and Custard collisions using 3306 dates and it turns out that the Pilots Federation didn't make 3308 a leap year so I'm a day out!

 

[HRDiagram]

(I'll be really honest here and add that while I had noticed the orbital elements mentioned on the system info screen, I kinda always thought they were somewhat "made up" so it's a nice surprise to find that they are meaningful!)

This is the reason why, to me and many others, the other space games are not really alternatives (or even space games, in some cases).
The Stellar Forge was the selling point for me.

 

[LCU No Fool Like One]

This is fun https://www.geogebra.org/m/GfKnqTwt

 

[Orvidius]

Yeah, this stuff gets confusing real quickly. I had to brush up on the math when I tried making an Orrery simulation based on the crowdsourced journal data. There are some mathematical tricks to convert between the different Anomalies, but not all of them are perfect clean equations. There's some iterative approximation involved. It's enough to make your head spin (in an elliptical orbit, no less).

 

[LCU No Fool Like One]

Yeah, this stuff gets confusing real quickly. I had to brush up on the math when I tried making an Orrery simulation based on the crowdsourced journal data. There are some mathematical tricks to convert between the different Anomalies, but not all of them are perfect clean equations. There's some iterative approximation involved. It's enough to make your head spin (in an elliptical orbit, no less).

I'm trying to get something working in python so I can get reference dates for planetary collisions so I can put once in a lifetime collisions in the diary. But I'm really struggling to get the True Anomaly calculated..

 

[Neilski]

I'm trying to get something working in python so I can get reference dates for planetary collisions so I can put once in a lifetime collisions in the diary. But I'm really struggling to get the True Anomaly calculated..

I'd put money on there being python libraries out there that will do most of this for you. I haven't actually looked though, cough.

 

[MattG]

I'm trying to get something working in python so I can get reference dates for planetary collisions so I can put once in a lifetime collisions in the diary. But I'm really struggling to get the True Anomaly calculated..

If you're interested, I have a pre-release ObsCore plugin to do exactly this, right here. It'll calculate to nearest minute where there is enough data available in Journals. It's eventual intention was to build a calendar of collision events - so it does transmit the Scan lines for the 2 bodies to me. It's quite frustrating EDSM doesn't record the necessary details to calculate these.

As it's pre-release, it doesn't send notifications nor have an option to disable data transmission.
Edit: it also only works on moons currently

 

[LCU No Fool Like One]

If you're interested, I have a pre-release ObsCore plugin to do exactly this, right here. It'll calculate to nearest minute where there is enough data available in Journals. It's eventual intention was to build a calendar of collision events - so it does transmit the Scan lines for the 2 bodies to me. It's quite frustrating EDSM doesn't record the necessary details to calculate these.

As it's pre-release, it doesn't send notifications nor have an option to disable data transmission.
Edit: it also only works on moons currently

Thank, I'll have a look at that. It might help me figure out where I am going wrong.

 

[Orvidius]

For my anomaly code, I used a combination of info from here: Introduction of the six basic parameters describing satellite orbits, and also did a view-source here (specifically this).

The code gets a bit messy. But since we get orbital period, current mean anomaly at the time of the scan, and a timestamp in the journal, along with the other orbital parameters, we can calculate almost everything else. (The exception is that the orbital data uses the parent body's equatorial plane as the reference plane, rather than the system's ecliptic plane, and so we're missing axial tilt directions for all parent objects, and the tilt itself for barycenters). If you want the actual current mean anomaly, it can be advanced by a number of degrees based on elapsed time and the orbital period (meanAnomaly += 360*days/period).

So starting with that Mean Anomaly, we have to first get the Eccentric Anomaly. This is the complicated part. There's no single equation to do this, but rather you have to iterate over it until the error is small enough for what you're doing. Here's my function:

sub EccentricAnomaly {
        my $e = shift;          # Orbital Eccentricity
        my $M = shift;          # Mean Anomaly (degrees)
        my $Mrad = $pi*$M/180;  # Mean Anomaly in Radians

        my $E = $M + ($e * sin($Mrad) * (1 + ($e * cos($Mrad))));
        my $error = 1;

        while ($error >= 0.00001) {
                my $F = $E - ($E - (sin($E*$pi/180) * $e * 180/$pi) - $M) / (1 - $e * cos($E*$pi/180));
                $error = abs($F-$E);
                $E = $F;
        }
        return $E;
}

I replicated the logic from this javascript code:

// From javascript example: view-source:https://theskylive.com/libjs/_lib_orbits.js?v=1624047523

var E = M + (e * Angle.SinDeg(M) * (1.0 + (e * Angle.CosDeg(M))));
for(;;) {
  var F = E - (E - (Angle.DEG_FROM_RAD * e * Angle.SinDeg (E)) - M) / (1 - e * Angle.CosDeg (E));
  var error = Math.abs (F - E);
  E = F;
  if (error < 1.0e-5) {
    break;  // the angle is good enough now for our purposes
}

And then we can easily gets its coordinates within the plane, the true anomaly, and current "radius" distance from parent:

X = semiMajorAxis * (cos(eccentricAnomaly * pi / 180) - eccentricity)
Y = semiMajorAxis * (sqrt(1 - eccentricity^2) * sin(eccentricAnomaly * pi / 180))

True Anomaly in radians, and radius/distance:

trueAnomaly = atan2(X,Y) * 180 / pi
distance = sqrt(X^2 + Y^2)

 

[CMDR Von Abrahart]

This is so cool - i wish i was decent at maths