When does Minmus cross Kerbin equatorial plane?

[Cooper42]

Minmus will cross Kerbin's equatorial plane twice in one orbit; at the ascending and descending nodes for the planet.

 

This is a useful time to leave Minmus orbit, if the plan is to rendezvous with something in an equatorial orbit of Kerbin.

 

I've searched, but I can't find a list of times that Minmus passes its own ascending and descending nodes.

Or even just the first time (i.e. UT + hh:mm.ss) from which I could calculate the rest...

 

Does anyone know if this information has been calculated anywhere?

 

Alternatively: I think this can be calculated from the velocity, Arg. of Pe. and Mean Anomaly at UT zero (both of which are on the wiki).

If it's not already been posted somewhere, I may sit down later and try to work it out, so any pointers on doing this would also be welcome.

[Zhetaan]

From the wiki, Minmus has an argument of periapsis of 38° and a mean anomaly at zero of .9 radians exactly.  The argument of periapsis is measured from the ascending node, in the direction of motion, and centred on the primary, whereas the mean anomaly is measured about the centre of the ellipse (it's technically a circle for mean anomaly, but the centres coincide), so for most cases, you'd need Kepler's equation to translate between the two.

However, Minmus's orbit is circular; there is no difference between the mean anomaly and the true anomaly.  It's not a complete simplification, but it is made astronomically easier, to use exactly the right metaphor.

Since true anomaly conventionally measures from the periapsis at zero, but argument of periapsis conventionally measures from the ascending node at zero, the first thing to do is to convert the argument of periapsis into a true anomaly of the ascending node, which in this case would be 360° - 38° = 322°.  The descending node is 180° away from that or at 142°.  Conversion of .9 radians to degrees gives a mean anomaly for Minmus of 51.57° at time t = 0 seconds.  Minmus's orbital period (we want the sidereal period, not the synodic period) is 1,077,311 seconds, so from t = 0 to the descending node is equivalent to the time to travel 142° - 51.57° = 90.43°, which is (90.43° / 360°) * 1077311 = 270614.5 seconds, or 12 days, 3 hours, 10 minutes, and 14.5 seconds.  After that, Minmus passes through a node every 24 days, 5 hours, 37 minutes, and 35.5 seconds.

Edited May 4, 2020 by Zhetaan

[RoninFrog]

If you got a craft in an equatorial orbit, switching to the craft and setting Minmus as target will display ascending and descending nodes.

Edited May 5, 2020 by RoninFrog