farthest moon orbit question

keermalec · May 7, 2007

Hi, what is the farthest orbit that is stable for a moon around its parent body? The gravitational Sphere of Influence around a planet, as defined on Wikipedia, has a radius of a*(m/M)^(2/5), where a is semi-major axis of planetary orbit, m is planetary mass, and M is sun's mass. This gives an SOI of 920'000 km for the Earth, almost 3x as far as the Moon. Is this the farthest orbit a satellite can have around the Earth? it seems pretty far. Is there another equation to determine the furthest stable satellite position around a given planet? many thanks <div class="Discussion_UserSignature"> “An error does not become a mistake until you refuse to correct it.” John F. Kennedy </div>

qso1 · May 8, 2007

In our system, Jupiter is the closest massive planet to earth and moon. The moon could be a million miles from earth and not be affected IMO because Jupiter at closest approach is still almost 500 times as far away. The moon at a million miles from earth would probably be in a bit more of an elliptical orbit however. <div class="Discussion_UserSignature"> My borrowed quote for the time being:There are three kinds of people in life. Those who make it happen, those who watch it happen...and those who do not know what happened. </div>

vogon13 · May 8, 2007

I would have a concern as the moon recedes from earth, at some point it's orbital period will become commensurate with something massive enough to pump up the perturbations dangerously. And it might be something seemingly innocuous, like Venus or Mercury or Saturn. For instance, at around a lunar orbital period of 44 days, it will repeat it's orientation to Mercury every other orbit. The resonance might be sufficient to 'upset the apple cart' regarding inclination or eccentricity. <div class="Discussion_UserSignature"> TPTB went to Dallas and all I got was Plucked !!So many people, so few recipes !!Let's clean up this stinkhole !! </div>

spacester · May 8, 2007

My understanding is that the Sphere of Influence is being somewhat mis-applied here. It's not completely off-base, just not what the SOI is about. The SOI is used to calculate interplanetary trajectories using the patched conic method. You plot a trajectory within a planet's gravitational field out to the distance given by the SOI. You then convert the velocity vector from planet-centric to heliocentric (relative to the Sun) and plot that trajectory in interplanetary space. When you reach the destination planet's SOI you convert the velocity vector from heliocentric to planet-centric and plot the trajectory from there. (In practice you do the interplanetary trajectory first, then fine-tune it for the planetary segments) The thing is that if you have the right formula for SOI, this method, while seemingly a very rough approximation, works amazing well. So in practice, the SOI formula gets tweaked to account for the effect of other planets, in particular Jupiter. (The effect of Jupiter on the other planets is much more profound than intuition would indicate.) So given that the SOI is specifically created for navigation, I do not think it is a terrific means of answering this question. Maybe a good first approximation. I apologize for not having a better answer. hth <div class="Discussion_UserSignature"> </div>

3488 · May 8, 2007

Hi Keermalec. You may be interested. Neptune has the furthest known & named moon from the parent planet. It is known as Neso, orbiting Neptune at a distance of 48.39 million kilometres, once every 9,374 days (25 years & 243 days) in a retrograde direction & appears moderately large at 60 km wide. It is likely a captured KBO. The other giants!!! Jupiter has Kore. Kore is a type C (Carbonaceous) object, barely 2 kilometres in diameter. Kore orbits Jupiter in a retrograde direction once every 779 Days (two years & 49 days) at a distance of about 24.573 Million Kilometres. Kore appears to cross orbits of its slightly inner neighbours at Perijove, Callirrhoe (a 7 km wide type C object) & Cyllene (a 2 km wide typre C object). Like Kore, they orbit Jupiter in a retrograde direction. Jupiter also has the UNNAMED moon: S/2003 J2. S/2003 J2 like Kore, is a type C (Carbonaceous) object, also 2 KM wide. S/2003 J2 orbits Jupiter in a retrograde direction at an average distance of 28.57 million kilometres, once every 983 days (2 years & 253 days). It is likely that either all of these including other members of the Carme & Pasiphae retrograde groups are one object that got smashed or are seperate objects that were captured after wandering from the Asteroid Belt. Saturn has Fornjot, orbiting in a retrograde direction once every 1,491 days (4 years & 30 days) @ a distance of 25.11 million kilometres & appears to be 6 km wide. It is likely to be a piece of Phoebe, or like Phoebe, a captured comet. Uranus has Ferdinand, orbiting at a distance of 20.10 million kilometres, once every 2,823 days (7 years & 266 days) in a PROGRADE direction!!! Ferdinand appears to be about 20 kilometres wide. Ferdinand is likely to be a captured comet. Andrew Brown. <div class="Discussion_UserSignature"> "I suddenly noticed an anomaly to the left of Io, just off the rim of that world. It was extremely large with respect to the overall size of Io and crescent shaped. It seemed unbelievable that something that big had not been visible before". Linda Morabito on discovering that the Jupiter moon Io was volcanically active. Friday 9th March 1979.http://www.launchphotography.com/ http://anthmartian.googlepages.com/thisislandearthhttp://web.me.com/meridianijournal </div>

qso1 · May 9, 2007

vogon13: The resonance might be sufficient to 'upset the apple cart' regarding inclination or eccentricity. Me: Possibly, and one reason I mentioned eccentricity effects but I tend to think the effects are not as much as some might think. For one thing, we pass close to mars every now and then...in 2003, as close as 35 million miles with no noticeable effect on the moon. Certainly nobody including the press and astronomers didn't mention any anticipated effects on the moon as a result of close passage to mars. Mars is larger and passes much closer to us than mercury but at 35 million miles, probably to far to have more than a minimal effect on the earth moon system. <div class="Discussion_UserSignature"> My borrowed quote for the time being:There are three kinds of people in life. Those who make it happen, those who watch it happen...and those who do not know what happened. </div>

tony873004 · May 9, 2007

Keermalec: "Hi, what is the farthest orbit that is stable for a moon around its parent body? " The farthest that an object can orbit from another object is given by the Hill Sphere. For the Earth, it is about 1.5 million kilometers. At the edge of the Hill Sphere, an object should be able to complete at least 1 retrograde orbit. To be stable, an object should be no more than roughly 1/3 of the way to the edge of the Hill Sphere, perhaps to about 2/3 for retrograde orbits, as retrograde orbits are more stable. You compute the Hill Sphere by multiplying an ojbect's distance from a perturber by the cube root of the object's mass divided by 3 times the mass of the perturber. For example, the Sun is by far the biggest perturber for objects orbiting Earth. The Sun is 150 billion meters from Earth. Earth is 5.97e24 kilograms. The Sun is 1.989e30 kilograms: 150000000000 * (5.97e24/(3*1.989e30)) ^(1/3)=1.5 billion meters, or 1.5 million kilometers. Here's a calculator that will do it for you. Many known solar system masses are included: http://orbitsimulator.com/gravity/articles/hillsphere.html qso1: "In our system, Jupiter is the closest massive planet to earth and moon. The moon at a million miles from earth would probably be in a bit more of an elliptical orbit however." The Moon at a million miles from Earth would instantly escape the Earth, and not because of Jupiter. It is the Sun's influence that would cause this to happen. A million miles exceeds Earth's Hill Sphere with respect to the Sun. But you are right that closer the Moon comes to the edge of the Hill Sphere, its orbit should become more elliptical on average. vogon13: "I would have a concern as the moon recedes from earth, at some point it's orbital period will become commensurate with something massive enough to pump up

qso1 · May 9, 2007

Excellent information. I always knew there had to be something that defined the farthest distance an object can maintain a stable orbit. I went to the link and tried toi use the formula but the fill ins don't register when I type a number in after selecting distance from the small square. One of the things I wanted to figure out is what distance can an object maintain a stable orbit around the sun. To see what it says about object suchs as the theorized Nemesis star, or Proxima Centauri from Alpha Centauri. <div class="Discussion_UserSignature"> My borrowed quote for the time being:There are three kinds of people in life. Those who make it happen, those who watch it happen...and those who do not know what happened. </div>

3488 · May 9, 2007

Hi there. I was taken aback by this too. When Neso was found in 2002, it was assusmed at first a KBO that was passing Neptune. Further observations showed that Neso was actually gravitaionally attached to Neptune, & a very slight retrograde orbital motion was detected. Neso appears quite large, about 60 km & appears very dark red. It would be worth a close approach if possible by a future Neptune craft. A long month isn't it. Nearly 26 years!!!!! Long time to wait for the next Pay Day. <img src="/images/icons/smile.gif" /> Neptune not only has the longest year of any of the planets, but the longest 'month' too!!!! Andrew Brown. <div class="Discussion_UserSignature"> "I suddenly noticed an anomaly to the left of Io, just off the rim of that world. It was extremely large with respect to the overall size of Io and crescent shaped. It seemed unbelievable that something that big had not been visible before". Linda Morabito on discovering that the Jupiter moon Io was volcanically active. Friday 9th March 1979.http://www.launchphotography.com/ http://anthmartian.googlepages.com/thisislandearthhttp://web.me.com/meridianijournal </div>

tony873004 · May 9, 2007

The Hill Sphere doesn't define the furthest stable orbit, just the furthest orbit. Stability is a gray area affected by lots of things, and you have to define stable for how long. Within the Hill Sphere, an object should be able to complete at least 1 retrograde orbit. Sorry the calc isn't working for you. What browser are you using? I've tested it on IE and Firefox, but I've had trouble with Konquestor and the Mac browser. It might be as simple as black text against a black background. If this is the case, maybe you can highlight your inputs or outputs. In the worse-case scenerio, you can always use a regular calculator with this formula, although then you'd have to look up the masses yourself. I think the Sun's Hill Sphere extends about halfway to Alpha Centauri. You can measure it against Alpha Centauri (use 4.5 light years and 2 solar masses) or against the galactic tide (if I recall correctly, use 27000 light years and 10^11 solar masses).

qso1 · May 9, 2007

Thanks for the info. I did use IE with the formula link. I'll mess around with it some more later. I'll highlight the background to see if any text shows. <div class="Discussion_UserSignature"> My borrowed quote for the time being:There are three kinds of people in life. Those who make it happen, those who watch it happen...and those who do not know what happened. </div>

3488 · May 9, 2007

You may be interested that Neptune has another moon, only slightly closer in than Neso. it is called Psamathe, orbits Neptune in a retrograde direction @ a distance of 46.70 million kilometres, once every 9,116 days (24 years & 15 days) It is 38 kilometres wide & like Neso, appears dark red. A common origin perhaps??? Psamathe was discovered in September 2003. Although Neptune is considerably less massive than Jupiter (about 5% @ 17 Earth masses as against Jupiter's 318 Earth masses), Neptune is very isolated, with no major objects near by & also being so far from the Sun. Andrew Brown. <div class="Discussion_UserSignature"> "I suddenly noticed an anomaly to the left of Io, just off the rim of that world. It was extremely large with respect to the overall size of Io and crescent shaped. It seemed unbelievable that something that big had not been visible before". Linda Morabito on discovering that the Jupiter moon Io was volcanically active. Friday 9th March 1979.http://www.launchphotography.com/ http://anthmartian.googlepages.com/thisislandearthhttp://web.me.com/meridianijournal </div>

3488 · May 9, 2007

Hi there. Would the Alpha Centauri pair (one G type & one K type main sequence stars) have a Hill Sphere 50 % larger than the Sun's? Would the Red Dwarf companion Proxima Centauri disrupt it? I think our Sun's Hill Sphere can be no larger than 1 light year radius (2 light years diameter), unless I am missing something!!! Also it cannot be a fixed figure, because as the Sun orbits the galactic centre, close encounters with other stars, must shrink the Sun's Hill Sphere at these times. If so, the Oort Cloud cannot exist as theorized, unless it is much closer in than is thought. Andrew Brown. <div class="Discussion_UserSignature"> "I suddenly noticed an anomaly to the left of Io, just off the rim of that world. It was extremely large with respect to the overall size of Io and crescent shaped. It seemed unbelievable that something that big had not been visible before". Linda Morabito on discovering that the Jupiter moon Io was volcanically active. Friday 9th March 1979.http://www.launchphotography.com/ http://anthmartian.googlepages.com/thisislandearthhttp://web.me.com/meridianijournal </div>

heyscottie · May 9, 2007

Great post, Tony ... I was not aware of the definition of the Hill Sphere. This seems like a useful rule of thumb kind of tool....

tony873004 · May 9, 2007

3488: :Also it cannot be a fixed figure, because as the Sun orbits the galactic centre, close encounters with other stars, must shrink the Sun's Hill Sphere at these times. If so, the Oort Cloud cannot exist as theorized, unless it is much closer in than is thought. That is correct. The size varies as the Sun approaches other stars. However, most stars that pass our Sun have relative velocities of 20 km/s or more, so they pass pretty quickly relative to the orbital period of an Oort Cloud object. Before the Oort Cloud object has a chance to escape the Sun, the perturbing star is gone, expanding the Sun's Hill Sphere once again to encompass the Oort Cloud. There's no doubt in my mind that numerous objects do escape in such incidents, but they are a small percentage of the entire population. In the Sun's lifetime, it is likely that thousands of other stars have passed closer than 60,000 AU, the distance to the edge of the Oort Cloud. Here's another fun calculator to play with: http://orbitsimulator.com/gravity/articles/cse.html It's a close stellar encounter calculator. Enter a distance, and a time, and it will tell you how many stars are expected to pass the Sun in this period of time. For example, enter 60000 AU and 1 billion years, and it will tell you that every billion years, 346 stars are expected to pass the Sun within 60 thousand AU, the distance to the edge of the Oort Cloud. Or for fun, enter 1 AU and 1 year, and you will see that every year, 8x10^-17 stars should pass the Sun closer than the Earth. This formula is for the Sun as it orbits the galaxy now. When the Sun formed, it was likely part of an open star cluster, and close stellar encounters would have been much more frequent.

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