An orbital period of one year?

[Kimberly]

For my own special reasons, I want to place a satellite (a telescope, to be precise) in such an orbit that its position relative to the sun is stationary. Specifically, I want Kerbin to permanently eclipse the sun, from the telescope's point of view.

I'm not great with this sort of thing, but intuition tells me that if I have an orbital period equal to one Kerbin year, then if I start facing away from the sun my orbit should never take me closer to the sun, due to Kerbin's own orbit. I've calculated that this would take an orbit at 195,820 kilometers (correct me if I'm wrong), which the wiki tells me is unfortunately outside of Kerbin's sphere of influence.

So, I guess that leaves me with two questions: is this kind of orbit possible, and if so, around which planets could I do it?

Edited June 30, 2013 by Kimberly

[J0hnsmine]

It is not possible, unless you edit files.

[falofonos]

I may be wrong but I believe the orbit you want is outside Kerbin's SoI anyway.

As the orbit is "higher" than Kerbin in Kerbol's gravity well, it would be slower and would require fairly regular correction to stay in Kerbin's shadow.

Haven't done the math but I don't think you could make the orbit stable while fulfilling your requirements.

[Kimberly]

Hm, but what about other planets, e.g. Jool? Is there a physical or game reason it can't be done, or are there simply no suitable planets?

[AceMgy]

You seem to want to put this telescope at Kerbin's L2 Lagrange point relative to the sun. While this is possible in real life, and in fact a telescope is planned for this specific orbit, it isn't in KSP. The reason is simple: KSP doesn't model more than one gravitational body acting on you at a time. You've probably noticed this when you switch sphere of influence to another planet / body that you're acted on by that object's gravity only. It's not likely to be possible to do for a long time, either. This is due to two reasons:

1. The L2 Lagrange point is unstable, it'd have to have frequent small corrections made to its orbit to keep it there just like in real life. This would require some sort of mechanism to automatically control craft when you're elsewhere, which is troublesome due to the on-rails nature of KSPs engine.

2. The most important reason is that increasing the number of gravitational bodies acting on your spacecraft would at least double the performance requirements of the physics engine. Even more importantly, it makes it so orbits aren't exactly predictable, so the on-rails system that saves so much performance power doesn't work again.

Sorry... =/

Does your telescope really have to have an eclipsing Kerbin?

Edited June 30, 2013 by AceMgy

[UmbralRaptor]

The necessary orbit would be at the Kerbin-Kerbol L2 point. Lagrange points are not simulated in KSP, so...

[Sirrobert]

Could you perhaps do the same thing with an orbit around the sun?

[Holo]

Could you perhaps do the same thing with an orbit around the sun?

No, because if you were behind Kerbin you would be orbiting slower than it.

[sgt_flyer]

Maybe you can simply add some kind of round 'shield' a bit in front of your telescope, to create an artificial eclipse, and send the telescope into a kerbol orbit, then you just need to turn to face the sun. (kinda like nasa did during the apollo - soyouz mission, they used the apollo csm as an artificial eclipse, in order to allow the soyouz to study the sun's coronna, except this time, the shield would be directly fixed to your telescope.

[Kimberly]

Maybe you can simply add some kind of round 'shield' a bit in front of your telescope, to create an artificial eclipse, and send the telescope into a kerbol orbit, then you just need to turn to face the sun. (kinda like nasa did during the apollo - soyouz mission, they used the apollo csm as an artificial eclipse, in order to allow the soyouz to study the sun's coronna, except this time, the shield would be directly fixed to your telescope.

...that's actually a much simpler idea. Not quite as scientific as placing the telescope in a really fancy orbit, but it might do the trick! Thanks for the suggestion. Though I just did the calculation for Jool, which has a much greater sphere of influence, and if my math is right then it should be possible to do there. Anyone willing to check?

I used the Kepler's Third Law calculator to solve for the orbital radius, using a mass of 4.2332635×10^24 kg and a year-length (synodic orbital period is what I need, right?) of 10091019 seconds; both values are from the wiki. That results in an orbital radius of 893890000 meters, which, minus Jool's radius, is still inside its sphere of influence 2.4559852×10^9 meters.

[stupid_chris]

...that's actually a much simpler idea. Not quite as scientific as placing the telescope in a really fancy orbit, but it might do the trick! Thanks for the suggestion. Though I just did the calculation for Jool, which has a much greater sphere of influence, and if my math is right then it should be possible to do there. Anyone willing to check?

I used the Kepler's Third Law calculator to solve for the orbital radius, using a mass of 4.2332635×10^24 kg and a year-length (synodic orbital period is what I need, right?) of 10091019 seconds; both values are from the wiki. That results in an orbital radius of 893890000 meters, which, minus Jool's radius, is still inside its sphere of influence 2.4559852×10^9 meters.

If you're inside Jool's SOI, you will be on a Jool orbit. As said above, KSP doesn't handle N-body physics, it works off patched conics, and as soon as you're in something's SOI, you're in orbit around it for KSP.

But to make it simple, to have the same orbital period as a body, you need to have the same semi major axis. So you either have exactly the same orbit, or you have an eccentric orbit meaning you will have a part of your orbit farther out than let's say Kerbin, and the other half closer to the sun than Kerbin.

[AceMgy]

I used the Kepler's Third Law calculator to solve for the orbital radius, using a mass of 4.2332635×10^24 kg and a year-length (synodic orbital period is what I need, right?) of 10091019 seconds; both values are from the wiki. That results in an orbital radius of 893890000 meters, which, minus Jool's radius, is still inside its sphere of influence 2.4559852×10^9 meters.

This feels so wrong, but I checked the math several ways and it seems to work... Perhaps you've found an inaccuracy in patched conics that you can exploit, but I'll leave it to an expert to say for sure, I merely took a class in Astrophysics (which I enjoyed immensely). I'm going to come at it from a different direction, using the definition of the hill sphere and Kepler's third law to see if this is true in general that you can't be stable at the L2 Lagrange point in patched conics.

In the meantime why don't you go ahead and launch a light-weight probe to Jool, and see if it's battery runs out due to no sunlight. I'm intrigued.

So far I've gotten the nice result that such an orbit would have a radius around the planet of r = R cuberoot( m / M ) where:

r = semimajor axis of satellite around planet (this is all assuming circular orbits)

R = semimajor axis of planet around sun

m = Mass of planet

M = Mass of sun

This looks nice and all, but is just wrong. Plugging in the definition of the hill sphere gives the result that this is possible for any planet which has a mass less than the sun, which is nonsense.

I'm gonna take a break for now.

Edited June 30, 2013 by AceMgy

[Geschosskopf]

...that's actually a much simpler idea. Not quite as scientific as placing the telescope in a really fancy orbit, but it might do the trick! Thanks for the suggestion. Though I just did the calculation for Jool, which has a much greater sphere of influence, and if my math is right then it should be possible to do there. Anyone willing to check?

I used the Kepler's Third Law calculator to solve for the orbital radius, using a mass of 4.2332635×10^24 kg and a year-length (synodic orbital period is what I need, right?) of 10091019 seconds; both values are from the wiki. That results in an orbital radius of 893890000 meters, which, minus Jool's radius, is still inside its sphere of influence 2.4559852×10^9 meters.

This (and all things like it) won't work, either. If you're staying inside a planet's SOI, then you're orbiting that planet just like one of its moons. Thus, necessarily you spend 1/2 the orbital period closer to Kerbol than the planet itself. You can't hide behind it.

[Kimberly]

This (and all things like it) won't work, either. If you're staying inside a planet's SOI, then you're orbiting that planet just like one of its moons. Thus, necessarily you spend 1/2 the orbital period closer to Kerbol than the planet itself. You can't hide behind it.

Sorry if I'm about to say something stupid, but...Jool itself moves around the sun, it doesn't stop doing so while I'm orbiting Jool (right?). If my angle to Jool changes at the same rate that Jool's angle to the sun changes, won't that mean it will continually block the sun? I will still move from apoapsis to periapsis, of course, but the apoapsis and periapsis change position (relative to the sun) due to Jool's own orbit. ...right?

I had a suspicion something was wrong with this idea when I came up with it, but if I think about it, I can't find any particular flaw (other than the sphere of influence problem, which seems to work for Jool).

[Jones-250]

That might work, in theory. However I do not belive that Jools SoI is vast enought to allow you orbit around it with a orbital cycle long enough.

[AceMgy]

Bah... I'm so silly. My equation is correct, I've just flipped an inequality when analyzing it. Turns out this can only work if the mass of your planet is bigger than the mass of the sun in KSP, which would never happen.

The problem you ran into (and myself, when I followed your math) is that you used the synodic orbital period, which is not what you want. You want the period of the orbit itself, without regard to the surface rotation of the planet. I had forgotten that siderial and synodic periods take the rotation of the planet into account, so it's the completely wrong number to use.

So, no. It's not possible in patched conics to achieve this orbit, and therefore impossible in KSP sadly..

[stupid_chris]

Actually, what you need is an orbital period the exact same length as a Joolian year, and that is about 29072h. And for that you would need an orbit of 4.2798x10^9m, which is almost twice the lenght of Jool's SOI. That woun't really work :l

[Kimberly]

D'oh, there we are...I wasn't sure which figure to use, and a lack of attention to detail caused me to overlook the fact that the sidereal period is over 1000 days longer, so that maybe it made a significant difference. I guess it's not possible, then.

That said, is my understanding of the way orbital mechanics work in the game still correct in this regard, or...?

[stupid_chris]

D'oh, there we are...I wasn't sure which figure to use, and a lack of attention to detail caused me to overlook the fact that the sidereal period is over 1000 days longer, so that maybe it made a significant difference. I guess it's not possible, then.

That said, is my understanding of the way orbital mechanics work in the game still correct in this regard, or...?

Doesn't seem like you were assuming you would be held in place by anything, so I guess you're fine. You just miscalculated your needed orbital period. Happens to everyone

[AceMgy]

Since I always believe in posting my work, I've meticulously typed out my proof twice. The forums deleted the first draft

Values:

M = mass of sun

m = mass of planet

R = semimajor axis of planet

r = semimajor axis of satellite

T = period of planet

t = period of satellite

G = gravitational constant

Kepler's Third: 4 pi^2 / T^2 = G M / R^3

Finding period of planet: T^2 = 4 pi^2 R^3 / G M

T = 2 pi ( R^3 / G M )^(1/2)

Finding period of satelitte same way: t = 2 pi ( r^3 / G m )^(1/2)

Now equating these, as that's the only way you get such an eclipsing orbit:

2 pi ( r^3 / G m )^(1/2) = 2 pi ( R^3 / G M )^(1/2)

r^3 / G m = R^3 / G M

r^3 / m = R^3 / M

So the axis of the orbit is: r = R ( m / M )^(1/3)

The definition of the sphere of influence radius, or Hill sphere: R(soi) = R ( m / M )^(2/5)

We want this value bigger than r to work:

R ( m / M )^(2/5) > R ( m / M )^(1/3)

( m / M )^(2/5) > ( m / M )^(1/3)

( m / M )^(6/5) > 1

( m / M ) > 1

m > M

So you see, the mass of the planet would have to be greater than the mass of the sun for this to ever work in KSP. Not likely...

[Kimberly]

Thanks for all the help, guys. It's a shame the idea isn't feasible, though I will definitely try to implement sgt_flyer's suggestion.

[AceMgy]

Hey, it's an exciting idea. So exciting that a mistake in my math made me want to fly to Jool immediately and try it out.

I'd name your telescope the James Kerbin space telescope, since the James Webb space telescope is essentially what you were trying to recreate whether you knew it or not. I'd give it a slightly larger solar shield to account for the fact that you'll get the full heat of the sun, and plenty solar panels on the sun side to power the cyrogenics aboard. It'd certainly still be possible to do it that way in real life if you had to, just expensive, and Kerbals don't care about money when it comes to space exploration.

[Kimberly]

I was indeed inspired by the James Webb space telescope, after reading up on Hubble and deciding that its orbit was far too simple.

I think what I'll do now is simply orbit the sun, so that like the Webb telescope I can have a shield with solar panels, and I'll simply keep the craft pointing away from the sun.

Edited June 30, 2013 by Kimberly