Can a high inclination minimize dark time for an elliptical orbit?

[fallingphoenix]

Specifically a highly elliptical orbit with a period of one Kerbin day (6 hours). It seems like worst-case would be when the 'sides' (ascending and descending nodes) of the orbit are on the dark side. Would this be less dark time than a kerbosynchronous orbit with 0 inclination and eccentricity?

Related question: Is there an orbit or dark time calculator that takes into account inclination, or can someone help me out with the math to sort it out?

Thanks in advance!

[Geschosskopf]

The dark time for any inclined orbit will vary throughout the course of the year.  This is because the orbit's plane is fixed relative to the sun whle Kerbin carries it around the sun.  So take a polar orbit.  If you launch when the orbit's plane is tangent to Kerbin's orbital path, then there will be zero dark time.  But as Kerbin moves around the sun, the angle of the orbit's plane to incoming sunlight will change.  1/4 of the year later, the orbit will be edge-on to the sun so will be in the dark on the back side of Kerbin.  Lesser inclinations will always have some dark time and it will vary more throughout the year, unless the Pe is high enough always to be in sunlight.

If you're worried about battery duration in the dark, what you need is to build for the worst-case scenario, the longerst period of dark.  This is fairly easy to determine with a calculator, at least if you're in a circular orbit so your ship has a constant speed.  What you do is figure out the maximum fraction of the orbit is in the dark based on Kerbin's angular size as seen from the sun, the worst possible alignment of the orbit's plane to the sunlight, and the ship's orbital speed.  Once you know what fraction of the orbit is in the dark, and you know the orbital period of your ship, you'll know how many seconds you'll be in the dark.  Given the amount of EC/sec the ship consumes, that will tell you how much battery you need.  The rest of the time is in daylight, which tells you how miuch solar panel juice you need to recharge the batteries before you go dark again (although this is seldome a problem).

With eccentric orbits, it's rather more complicated because the ship's speed varies over the course of its orbit.  But there's an easy fix.  Determine the orbital velocity for a circular orbit at your Pe and use that to determine your dark time.  This will provide a bit of safety because your ship will be a bit faster than this.

[FancyMouse]

IRL we have a better option of Sun synchronous orbit which has zero night time 365/24, but KSP doesn't model planet oblateness so we don't have this...

Then highly eccentric orbit - the best option I can think of is when periapsis/apoapsis is over the pole, in which case the worst case is two arcs near the periapsis which should spend minimal amount of time, which I hope due to higher orbital velocity thus higher angular momentum, swipe the same angle much faster than circular case.

Exact number? I don't know - probably start with Kepler's second law (which is essentially just conservation of angular momentum anyway) and do some calculation there? Finding the area of a sector of an ellipse is the more difficult part, which I don't know on top of my head how to do it by hand.

[purpletarget]

Basically your worst case (at whatever the worst time of year is) for an inclined orbit won't be any different than you'd see on an equatorial orbit, as the size of kerbin will cast a shadow across the same angular distance for any other orbit on that altitude. IIRC, the KEOSYNC dark time is only about 20 minutes for a circular orbit.

The only variance that you might see with a Elliptical orbit, is that the hang time near the Ap could result in a longer period of darkness, where the Ap was positioned roughly centre over the darkside equator... but again, inclination will not affect how often that comes into play, nor for how long.

[Geschosskopf]

38 minutes ago, purpletarget said:

Basically your worst case (at whatever the worst time of year is) for an inclined orbit won't be any different than you'd see on an equatorial orbit, as the size of kerbin will cast a shadow across the same angular distance for any other orbit on that altitude. IIRC, the KEOSYNC dark time is only about 20 minutes for a circular orbit.

Actually, the worst case is a little bit either side of the new moon.  Here you have Mun and Kerbin blocking the sun in series.  This is more of a problem with an equitorlal orbit, not so much with inclined orbits, however.

[Snark]

Going back to the OP'S question, can you explain why you care about the length of the dark period? It's only a few minutes long in the worst case, unless you have a deliberately photophobic elliptical orbit with Ap lined up on the dark side equator (and even that would only last a little while until the planet's orbital motion moved the Ap out of the dark). And in any case, the game only tracks your ship's electric consumption while you're flying it.

I ask because, for those reasons, I've never had a problem where I've needed to minimize dark time of an orbit in KSP. I've needed to minimize occlusion time for RemoteTech comsats, but that's a slightly different problem. And dealing with dark time for a surface base can be hard, since the dark is hours long. And an inconveniently placed planetary shadow can be a pain for ion ships trying to eject or capture, but that doesn't appear to be what the OP is asking.

Therefore, it would be very helpful to know exactly what the OP is trying to accomplish, in order to be able to give helpful advice.

[purpletarget]

20 hours ago, Geschosskopf said:

Actually, the worst case is a little bit either side of the new moon.  Here you have Mun and Kerbin blocking the sun in series.  This is more of a problem with an equitorlal orbit, not so much with inclined orbits, however.

Missed ya Ges,

Rhetorical question for your niche case though....the OP specified a 6h orbit. So, can you get an Ap past the Mun in that situation to cause this issue? 

(On larger orbits, sure, hang time for a highly eliptical where the Ap is just inside the SOI and an atmo scraping Pe....could happen. But it's a minutia that I personally wouldn't design on.)

 

 

If the OP Is interested specifically in the Math, there's a vid here that explains the process of figuring it out.

 

Snark: I'm not sure if the OP had a specific design issue in mind, or if there's just an innate curiosity. However, the charge and designing for operation of a solar powered craft in dark periods can be a consideration for players who have particular power needs, are using mods which require powered craft to be in operation for scanning and the like, or if they want to be able to maintain some kind of orbital effects during actual flight. Especially if someone is trying to shave funds off their missions...then why pay for more batteries than you need??

 

[fallingphoenix]

On 12/14/2015, 7:15:37, FancyMouse said:

On 12/14/2015, 7:15:37, FancyMouse said:

Then highly eccentric orbit - the best option I can think of is when periapsis/apoapsis is over the pole, in which case the worst case is two arcs near the periapsis which should spend minimal amount of time, which I hope due to higher orbital velocity thus higher angular momentum, swipe the same angle much faster than circular case.

Exact number? I don't know - probably start with Kepler's second law (which is essentially just conservation of angular momentum anyway) and do some calculation there? Finding the area of a sector of an ellipse is the more difficult part, which I don't know on top of my head how to do it by hand.

That's exactly what I was hoping to find out once I'd thought about it and some of the answers people offered. Would the two arcs near periapsis give you a shorter worst case than a circular equatorial orbit?

2 hours ago, purpletarget said:

If the OP Is interested specifically in the Math, there's a vid here that explains the process of figuring it out.

 

Snark: I'm not sure if the OP had a specific design issue in mind, or if there's just an innate curiosity. However, the charge and designing for operation of a solar powered craft in dark periods can be a consideration for players who have particular power needs, are using mods which require powered craft to be in operation for scanning and the like, or if they want to be able to maintain some kind of orbital effects during actual flight. Especially if someone is trying to shave funds off their missions...then why pay for more batteries than you need??

 

 

The question started out because I've started using Remote Tech and needed to set up a solid base comm network near Kerbin. The tutorial I was looking at tried to design for worst case for a flat equatorial orbit and needed something like 8 or 9 1k batteries, if I remember right. Then I started to realize that the likelihood of having things actually drain power in my network after I set them up (due to not actually flying them after that) meant that I probably didn't need to be too concerned about it and the question became more one of curiosity.

So...thanks for the math links and suggestions. I'm really interested to find out if a highly inclined orbit with Pe and Ap always in sunlight would have a shorter worst case than a flat, circular orbit with the same period!

[Snark]

13 hours ago, fallingphoenix said:

The question started out because I've started using Remote Tech and needed to set up a solid base comm network near Kerbin. The tutorial I was looking at tried to design for worst case for a flat equatorial orbit and needed something like 8 or 9 1k batteries, if I remember right. Then I started to realize that the likelihood of having things actually drain power in my network after I set them up (due to not actually flying them after that) meant that I probably didn't need to be too concerned about it and the question became more one of curiosity.

So...thanks for the math links and suggestions. I'm really interested to find out if a highly inclined orbit with Pe and Ap always in sunlight would have a shorter worst case than a flat, circular orbit with the same period!

Okay, so you're doing this for RemoteTech, that clarifies matters.

There are two issues I could imagine your being concerned about.

1. Interruption of your interplanetary communications network due to planetary occlusion (e.g. your Duna probe loses contact because your relay satellite in Kerbin orbit is hiding behind Kerbin).
2. Communications satellite runs out of electrical power while in the dark.

For issue #1, what you want to minimize is not maximum length of dark time, but percentage of dark time (where "dark" means "blocked from your communications target" rather than "blocked from the Sun").  For that, the solution is to stay as far away from the planet as possible; the best, most reliable relay would be one that's in a polar circular orbit at the highest altitude possible.

For issue #2, I don't think you need to worry about it at all.  KSP doesn't track electrical consumption of ships that are running "on rails".  I assume that once you set up a communications relay satellite, you don't really have any further reason to switch to it and control it directly for extended periods of time-- you put it in place and go fly other ships.  Therefore, it doesn't matter how much time it spends in the dark, since it will never run out of electricity as long as you're not flying it yourself.