Question about orbital precession of highly inclined orbits around Saturn

[ThreePounds]

I just posted this to reddit, but I figured you guys are even smarter so I expect to get even better answers here. So here it goes.

The title sounds awfully specific and rightfully so. I was watching an awe-inspiring talk about the cassini probe and it's mission around Saturn. One of the statements made by the awesome Dr. Linda Spilker confused me a little bit as I lack the proper understanding of advanced orbital mechanics to appreciate it fully. I was hoping someone out there smarter than me can shine some light on this issue and point me to the right direction.

Here is what she said.

I just want to point out one difference between Juno and Cassini, Juno is in a polar orbit, basically going over the poles. (With) Cassini we're only tipped at 63 degrees. And that's basically our optimum orbit to keep the periapses from precessing and putting us into the rings.

Source: https://youtu.be/YchCuFvyAZ4?t=3393 (at 56:37)

The first thing I am unfamiliar with is the relationship between inclination and apsis precession. Secondly, what does she mean by "putting us into the rings"? Does she talk about the orbital plane or the perichron? And how does precessing fit into any of this - I always thought it's just the argument of periapsis that changes.

Can someone explain?

[Green Baron]

Space battleships are easier to discuss ;-)

 

I see it like this but i don't pretend that this is right:

I assume that they wanted to keep the probe from diving through the rings during the mission to minimise risk of destruction through collision, so they had to choose orbits that are somehow synchronized with Saturn's rings and moons but nevertheless take the probe to the interesting spots. Since almost every orbit's apsides, in respect to the parent body (in this case that includes the rings), precess (that grammatically ok ?) the probe would have sooner or later ended up diving though the rings if (one of) the apsides had been lower than the rings' radius and the orbit wasn't changed (limited dV-wise).

 

I can't figure out why just 63° are a nice orbital inclination, and they don't tell whether this is toward Saturn's axis or its ecliptic around the sun (Saturn's axis has a tilt of 27° towards its ecliptic) to achieve that goal because i lack the math knowledge.

Guesses me, but maybe somebody with the right math background shows up and develops this better.

 

Edited August 17, 2017 by Green Baron

[ThreePounds]

5 minutes ago, Green Baron said:

Since almost every orbit's apsides, in respect to the parent body (in this case that includes the rings), precess (that grammatically ok ?) the probe would have sooner or later ended up diving though the rings if (one of) the apsides had been lower than the rings' radius and the orbit wasn't changed (limited dV-wise).

I always thought that apside precession essentially changes the argument of periapsis, not the periapsis itself. But I guess it has something to do specifically with Saturn.

[Green Baron]

Exactly, change the argument with the rate of Saturn's precession. Or, as long as Cassini stayed for a while in a specific orbit, to change the argument with a rate so that it would not dive through the rings before the next orbital change.

An inclination of 0 towards Saturn's axis would mean that the orbit is in the rings' ecliptic. No change necessary as long as both apsides are outside, but no nice pictures as well :-)

As soon as one apsis is below ring radius inclination must be chosen so that, as long as the probe stayed in a given orbit it would not precess into the rings.

Was that right ?

Edit: i hope i don't annoy you with this link

Edited August 17, 2017 by Green Baron

[YNM]

All orbits precess due to irregularity in the gravitational field. Even under General Relativity all orbits are unclosed, unperiodical; but they are usually close enough to be approximated so.

What I presume happens is a bit like Molniya / Sun-Synchronous orbit (surprise surprise, Molniya are inclined 63.4° !). Saturn's flattening is thirty times Earth's (figures vs figures), so inclined, eliptical orbits are going to precess, even more than back home. The guys at NASA must have worked out that to avoid having the Longitude of Apses precess, or at least to equalize / synchronize them to another figure (say, precession of Right Ascension of Nodes) they have to make the orbit *that* inclined and **that** ellipse and ***that*** big.

tl;dr it's because RL is complicated. Maybe you should try this mod in KSP. And could that mod emulates irregular / non-"spherical" gravitational field ?

Edited August 17, 2017 by YNM

[ThreePounds]

21 minutes ago, Green Baron said:

Exactly, change the argument with the rate of Saturn's precession. Or, as long as Cassini stayed for a while in a specific orbit, to change the argument with a rate so that it would not dive through the rings before the next orbital change.

An inclination of 0 towards Saturn's axis would mean that the orbit is in the rings' ecliptic. No change necessary as long as both apsides are outside, but no nice pictures as well :-)

As soon as one apsis is below ring radius inclination must be chosen so that, as long as the probe stayed in a given orbit it would not precess into the rings.

Was that right ?

Edit: i hope i don't annoy you with this link

The rings are rotationally symmetric, aren't they? So how would a changed argument of periapsis put the space craft into a collision orbit. Links are never annoying, even though I know of that perticular document already. What exactly is it that you want me to read again?

10 minutes ago, YNM said:

All orbit precess due to irregularity in the gravitational field. Even under General Relativity all orbits are unclosed, unperiodical; but they are usually close enough to be approximated so.

What I presume happens is a bit like Molniya / Sun-Synchronous orbit (surprise surprise, Molniya are inclined 63.4° !). Saturn's flattening is thirty times Earth's (figures vs figures), so inclined, eliptical orbits are going to precess, even more than back home. The guys at NASA must have worked out that to avoid having the Longitude of Apses precess, or at least to equalize them to another figure (say, precession of Right Ascension of Nodes) they have to make the orbit *that* inclined and **that** ellipse and ***that*** big.

tl;dr it's because RL is complicated. Maybe you should try this mod in KSP. And could that mod emulates irregular / non-"spherical" gravitational field ?

This is closer to the answer I expected, thanks for the input. But again, I don't see how Dr. Spilkers remark is related to that. As am amazing scientist as she is, her job is not trajectory design and I am starting to think what she said there might have been a bit imprecise and makes my head spin as a result.

Edited August 17, 2017 by Three_Pounds

[ThreePounds]

I'm starting to think this might have something to do with Titan. The trajectory designers used it extensively for plane changes in the several hundred flybys they've made over the years. Maybe you are right, @YNM and they use the precession actively to track Titan in it's orbit. So if they were in a higher inclination, the precession would slow or even stop and an encounter would somehow cause the periapsis to shift into the rings. I guess that's what the trajectory designers told the scientist, who obviously were asking for a higher inclination and this statement has come out as a result.

The only explanation I can see at this point.

Edited August 17, 2017 by Three_Pounds

[YNM]

@Three_Pounds Even without any gravitational assists, due to mass distribution irregularity, things will go away from what it was (AFAIK this isn't simulated in Principia yet). As I've said, people at NASA must have planned it. They have the knowledge, computing power and man hour to do whatever things they wanted to pull for their probes. So it could be so that they want it to aling with Titan every so often ? Be that it. So they want it to look over different parts of the ring without crashing through it ? Be that it. As long as the propellants and opportunity are there, they'll make it.

[ThreePounds]

5 minutes ago, YNM said:

@Three_Pounds Even without any gravitational assists, due to mass distribution irregularity, things will go away from what it was (AFAIK this isn't simulated in Principia yet). As I've said, people at NASA must have planned it. They have the knowledge, computing power and man hour to do whatever things they wanted to pull for their probes. So it could be so that they want it to aling with Titan every so often ? Be that it. So they want it to look over different parts of the ring without crashing through it ? Be that it. As long as the propellants and opportunity are there, they'll make it.

I see it this way. If someone tells you something you don't know anything about, it normally just flies over your head and you learn nothing from it. If someone says something you're very familiar with and it makes sense, fine. But if someone tells you something that should in theory make sense, but as you try to comprehend it, it makes less and less sense, you become intrigued. This is normally where you learn the most. As I try to understand the finer points of celestial mechanics and see the masterpiece the trajectory designers have created for the Cassini-Huygens mission, the visualization of which they affectionately call the yarn ball, my heart jumped. As KSP doesn't model anything beyond the very basics of orbital mechanics, I'm struggling to get an intuitive understanding for these kinds of things. I am looking at principia again as a learning tool.

[Green Baron]

29 minutes ago, Three_Pounds said:

The rings are rotationally symmetric, aren't they? So how would a changed argument of periapsis put the space craft into a collision orbit. Links are never annoying, even though I know of that perticular document already. What exactly is it that you want me to read again?

 

Sorry, i was just trying to be courteous because i expected you to know it. But it has paragraphs on the influence of inclination on precession and on those parts that @YNM mentioned.

[ThreePounds]

1 minute ago, Green Baron said:

Sorry, i was just trying to be courteous because i expected you to know it. But it has paragraphs on the influence of inclination on precession and on those parts that @YNM mentioned.

No actually, that's brilliant. I want to highlight this:

Quote

 

"The potential generated by the non-spherical Earth causes periodic variations in all the orbital elements. The dominant effects, however, are secular variations in longitude of the ascending node and argument of perigee because of the Earth's oblateness"

"Molniya orbits are designed so that the perturbations in argument of perigee are zero. This conditions occurs when the term 4-5sin²i is equal to zero or, that is, when the inclination is either 63.4 or 116.6 degrees."

 

That can't be a coincidence. The first sentence is actually new info. Thanks a lot. I think that even solved my question.

[Green Baron]

There you go :-)

[YNM]

1 hour ago, Three_Pounds said:

I see it this way. ... But if someone tells you something that should in theory make sense, but as you try to comprehend it, it makes less and less sense, you become intrigued. This is normally where you learn the most. As I try to understand the finer points of celestial mechanics and see the masterpiece the trajectory designers have created for the Cassini-Huygens mission, the visualization of which they affectionately call the yarn ball, my heart jumped. As KSP doesn't model anything beyond the very basics of orbital mechanics, I'm struggling to get an intuitive understanding for these kinds of things. I am looking at principia again as a learning tool.

I'm very, very sorry if my wording sounds too harsh. In truth I know nothing and I can't comprehend anything about their finer details either. My only knowing is that these things exist and are extensively exploited in polar orbits.

I found this Q&A which references... blew my mind to pieces. Even tidal forces are easier to do than them - but they are from near-antiquity ! Even getting Kepler Laws from Newton's Equation of Motion looks easier. I'm really sorry if this sounded like hoccus poccus to you, they sort of are mathematically at a glance, but intuitively they are to be expected. I mean, if you randomly orbit a rugby ball, there are going to be times where one of the more convex poles pulls you harder than the other - you're not always pulled to the center of mass of parent body. That's how the drift kicks in. The only question is whether it's only the nodes or the apsides - you might predict it should be both in some ways though, which it really is. There are just special states where it congregates in one.

Edited August 17, 2017 by YNM

[Green Baron]

Thanks @YNM ! I just found out that i mixed up axial and planar precession. Keep the links safe, i am surre we'll need them in the future ;-)

 

[ThreePounds]

41 minutes ago, YNM said:

I'm very, very sorry if my wording sounds too harsh. In truth I know nothing and I can't comprehend anything about their finer details either. My only knowing is that these things exist and are extensively exploited in polar orbits.

I found this Q&A which references... blew my mind to pieces. Even tidal forces are easier to do than them - but they are from near-antiquity ! Even getting Kepler Laws from Newton's Equation of Motion looks easier. I'm really sorry if this sounded like hoccus poccus to you, they sort of are mathematically at a glance, but intuitively they are to be expected. I mean, if you randomly orbit a rugby ball, there are going to be times where one of the more convex poles pulls you harder than the other - you're not always pulled to the center of mass of parent body. That's how the drift kicks in. The only question is whether it's only the nodes or the apsides - you might predict it should be both in some ways though, which it really is. There are just special states where it congregates in one.

There is an astronomy focused stack exchange? Oh well, there goes the rest of my free time. Thanks for the link.

Your wording wasn't harsh at all. I was just afraid you meant that "NASA does what it does and that's why it just works. No need to question it." After all, they also put their pants on one leg at a time. They might have the better tools, experience and better understanding of the maths behind it but at the end of the day, trajectory design isn't magic. It's just very, very complicated around Saturn because of the unbelievably complex orbital perturbations.