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Space Forum / Astronomy / July 2008Gravity assist to Mars by retrograde comets?
I'm thinking in regards to shortening the travel time for a manned Mars mission. There is a nice article here on gravity assist or the gravitational slingshot effect: Gravity assist. http://en.wikipedia.org/wiki/Gravity_assist#Explanation This show the greatest effect is when the spacecraft is traveling in an opposite direction to the gravitating body. You get twice the velocity of the body added to the spacecraft's velocity, both measured with respect to the Sun. Then this could be especially useful if a retrograde comet near its perihelion is rendezvoused by the spacecraft. You would make the rendezvous when the comet is near Earth's orbit to cut the travel time to the comet. If we can get an initial velocity off the Earth of say 30 km/sec, and added to the Earth's orbital velocity of 30 km/sec, this would result in a tangential velocity of 60 km/sec. The problem of just using this tangential velocity to get to Mars is that it turns out the increased distance of the tangential direction to intersect Mars orbit over just the radial direction cancels out the improvement of the increased speed. And even traveling at an optimal angle only shortens the travel time slightly.(*) However, when a comet is close to the Earth's orbit it will have an orbital velocity close to that of the Earth, about 30 km/sec. Then when the slingshot effect is applied to the spacecraft on close flyby of the comet, its speed will be increased from 60 km/sec to 60 + 2*(30) = 120 km/sec. Now this would result in a significant reduction in the travel time to Mars even with an increased tangential distance. A key problem though would be finding a retrograde comet that is close to the Earth when Mars is also near its perihelion, not a trivial matter. After a web search I found this sci.astro.amateur post that discusses retrograde comets: ====================================== Newsgroups: sci.astro.amateur From: pau...@electra.saaf.se (Paul Schlyter) Date: 1997/04/18 Subject: Re: Why no retrograde asteroid orbits? ... Not one single asteroid has been found in a retrograde orbit around the Sun. Therefore not merely "most" asteroids move in prograde orbits, but ALL known asteroids do. Of course there may be some unknown asteroid moving in a retrograde orbit, but since not a single one has been found so far, they must be very few - if they exist at all. > another line of evidence that they all came from the same source in the > solar nebula that formed the solar system, if you don't believe in the > planet explosion theory. Another thing to consider: any asteroid in a retrograde orbit would run a much much greater risk of colliding with other asteroids. Therefore their lifetimes would probably be quite short -- and this may have wiped all of them out by now. The only known celestial objects in retrograde orbits are comets, and almost all retrograde comets are long-period comets. Almost all short- period comets move in prograde orbits: of all the 124 short-period comets catalogued so far, only three move in a retrograde orbit: 1P Halley, 55P Tempel-Tuttle, and 109P Swift-Tuttle. A few additional ones have quite high inclinations (122P de Vico 85 degrees, 12P Pons- Borrks 75 degrees, 35P Herschel-Rigollett 64 degrees, 96P Machholz 1 60 degrees, 8P Tuttle 55 degrees, 13P Olbers 44 degrees) - but all the remaining 115 short-period comets have inclinations lower than 32 degrees. ========================================= So according to this there are only three (!) short-period retrograde comets. Tempel-Tuttle is the only one that has its next perihelion at a reasonably close to time now, on May 20, 2031. I don't know if its perihelion corresponds to a close approach of Mars. However, it turns out most long period comets have retrograde orbits. So it may be possible out of this large population to find one whose perihelion occurs near the time when Mars is at its closest approach. Another key fact to consider is that for using the comet gravity assist for shortening the Mars travel time, the optimal angle might not be tangential. This is because of the shortness of the radial distance to Mars and to the comet. In this case as shown in the "Gravity assist" article you would still get an increase in velocity though a smaller one from using vector addition of the velocities. Note in this case you might not even need the comet to be retrograde which would greatly increase the population of comets that might be used such their closest approach and Mars closest approach are near the same time. Bob Clark (*)Newsgroups: sci.astro, sci.physics, sci.space.policy, sci.math From: Robert Clark <rgregorycl...@yahoo.com> Date: Wed, 9 Jul 2008 13:29:06 -0700 (PDT) Local: Wed, Jul 9 2008 4:29 pm Subject: Re: Short Mars travel times at high speed. http://groups.google.com/group/sci.astro/msg/132aa4c9666ef2ef You've said it all in this one sentence: "A key problem though would be finding a retrograde comet that is close to the Earth when Mars is also near its perihelion, not a trivial matter." What would you do, wait a thousand years for the right comet to come by through happenstance, or travel to Mars the slow way and get there in a human lifetime? Where I live there is a bus every 10 minutes except on Sundays when there is a bus every hour. Given that I have to find somewhere to park in town, I drive on Sundays and get to town much faster than the bus - if I wait a week. But when I'm hungry for ham and eggs on Wednesday and the fridge is empty I take the slow bus. | I'm thinking in regards to shortening the travel time for a manned | Mars mission. There is a nice article here on gravity assist or the [quoted text clipped - 90 lines] | Subject: Re: Short Mars travel times at high speed. | http://groups.google.com/group/sci.astro/msg/132aa4c9666ef2ef A couple of "peanut gallery" questions on using gravity assist from a comet: *) Is the ratio of the mass of the comet to that of the spacecraft still such that the effect on the comet's orbit is epsilon? *) How much extra shielding if any might be required to protect the spacecraft's vital bits from the stuff spewing from the comet? rick jones  SignatureWisdom Teeth are impacted, people are affected by the effects of events. these opinions are mine, all mine; HP might not want them anyway... :) feel free to post, OR email to rick.jones2 in hp.com but NOT BOTH... > A couple of "peanut gallery" questions on using gravity assist from a > comet: [quoted text clipped - 10 lines] > these opinions are mine, all mine; HP might not want them anyway... :) > feel free to post, OR email to rick.jones2 in hp.com but NOT BOTH... Both good questions. For massive manned craft you might not want to use the same comet repeatedly for the perturbation they might have on the comet. However comets are such long period anyway I don't think you could even if you wanted to. About protecting the craft from ejected matter from the comet perhaps the Deep Impact and Stardust missions could give an idea of how much dust we could expect to encounter on close approach to the comet. Bob Clark > Both good questions. For massive manned craft you might not want to >use the same comet repeatedly for the perturbation they might have on >the comet. However comets are such long period anyway I don't think >you could even if you wanted to. I don't think you need to worry much about even the most massive craft we're likely to build having much effect on a body a few kilometers across. > About protecting the craft from ejected matter from the comet perhaps >the Deep Impact and Stardust missions could give an idea of how much >dust we could expect to encounter on close approach to the comet. They did. Lots of dust, and lots of damage. Optics got pitted, and there was always concern about a chunk large enough to do fatal damage. These craft employed special shielding. You could do the same for a manned mission, but I think we'd be a lot more conservative about safety- enough that this wouldn't be attempted. BTW, Stardust demonstrates something else (mentioned elsewhere in this discussion): a comet doesn't have enough mass to be useful for providing a gravity assist. The probe, massing just a few hundred kilograms, and passing only 240 km from the nucleus of Comet Wild, was barely deflected. It continued on in nearly the same orbit it had previously been following. _________________________________________________ Chris L Peterson Cloudbait Observatory http://www.cloudbait.com > On Mon, 14 Jul 2008 19:14:12 -0700 (PDT), Robert Clark > [quoted text clipped - 28 lines] > Chris L Peterson > Cloudbait Observatoryhttp://www.cloudbait.com Yeah, this won't work. Here's a mathematical analysis: Gravitational Slingshot. http://www.mathpages.com/home/kmath114.htm It shows the spacecraft receding from the gravitating body at the same angle it approached, at which point you would get the high increase in speed. It doesn't say so, but this *assumes* the gravity is strong enough to bend the spacecraft around into going in the reverse direction. It would be true if the body was a point particle then you could get close enough to it you wanted to get the high enough gravitational field. But not for a real sized body. Bob Clark > Yeah, this won't work. Here's a mathematical analysis: > >Gravitational Slingshot. >http://www.mathpages.com/home/kmath114.htm That's an incomplete treatment. A full analysis needs to include the planetary mass and the slingshot radius (hyperbolic focus). I'm pretty sure that the equations will simplify to just including a term for the escape velocity, which scales with the square root of the mass and the inverse square root of the radius. Of course, it's a good thing that a gravitational assist is dependent on escape velocity. Otherwise, we'd never get to any other planet, since our probes would be slingshotting all over the place off of cosmic dust! _________________________________________________ Chris L Peterson Cloudbait Observatory http://www.cloudbait.com >> Yeah, this won't work. Here's a mathematical analysis: >>Gravitational Slingshot. >>http://www.mathpages.com/home/kmath114.htm > >That's an incomplete treatment. A full analysis needs to include the >planetary mass and the slingshot radius (hyperbolic focus). As I read it, the mass of the planet IS included in that web page analysis, and then at the end it is simplified by noting that the mass of the space probe is negligibly small compared with the mass of a planet. Also it points out that the "radius" of the hyperbolic orbit doesn't matter, provided the planet's radius is small enough that you can pass close enough to get the desired angular deflection. As it says on that page, the only limitation is the density of the planet (and its atmosphere), which determines how closely you can loop around the planet. > I'm pretty sure that the equations will simplify to just including a term for > the escape velocity... What do you mean by this? What would equations look like if they "just included a term for the escape velocity"? >As I read it, the mass of the planet IS included in that web page >analysis, and then at the end it is simplified by noting that the mass >of the space probe is negligibly small compared with the mass of a >planet. I think what they do is an oversimplification. The mass of a small probe is also negligible compared with the mass of a comet. You need to consider both the mass and the radius. >Also it points out that the "radius" of the hyperbolic orbit >doesn't matter, provided the planet's radius is small enough that you >can pass close enough to get the desired angular deflection. As it >says on that page, the only limitation is the density of the planet >(and its atmosphere), which determines how closely you can loop around >the planet. Yes, but they failed to provide any rigorous analysis of that. My point was only that a more complete analysis would- in its final form- contain mass and radius terms, or that those terms would be encapsulated in a term for escape velocity. >What do you mean by this? What would equations look like if they "just >included a term for the escape velocity"? I'm not sure- I haven't tried working it out. But it seems intuitively obvious (to me, anyway <g>) that mass and radius need to be considered. The article said more or less the same thing (without analysis). Escape velocity is a function only of mass and radius. It wouldn't surprise me if the problem could be framed largely in terms of escape velocity. As you get closer to the CG, the escape velocity increases, as does the deflection. _________________________________________________ Chris L Peterson Cloudbait Observatory http://www.cloudbait.com >I think what they do is an oversimplification. The mass of a small probe >is also negligible compared with the mass of a comet. You need to >consider both the mass and the radius. The mass must certainly be considered if the objective is to determine the radius necessary to give a certain amount of deflection, but we can achieve any deflection we want by choosing a suitable radius (until bumping into the planet or its atmosphere), so this has nothing to do with determining the slingshot effect for the probe as a function of the relative speeds and angles. > My point was only that a more complete analysis would- in its final > form- contain mass and radius terms, or that those terms would be > encapsulated in a term for escape velocity. If someone wants to know what hyperbolic radius would be needed to achieve a given amount of deflection for a given mass of the body, they would naturally have to consider the radius and the mass of the body, but the slingshot effect itself depends only on the relative speeds and angular deflection, which we can freely choose (until the planet's surface or its atmosphere prevent us from passing any closer). > it seems intuitively obvious (to me, anyway <g>) that mass and radius > need to be considered. The article said more or less the same thing > (without analysis). Hmmm... I'd say the article DID give the analysis for why mass and radius do NOT need to be considered, and gave the explicit solution which does not depend on mass or radius. But aside from that, we're in complete agreement! > It wouldn't surprise me if the problem could be framed largely in terms > of escape velocity. I guess it depends on what problem you're trying to solve. The deflection angle for a given hyperbolic radius is well known and given by a simple formula, but I've never seen it expressed in terms of "escape velocity". > I'm thinking in regards to shortening the travel time for a manned >Mars mission. There is a nice article here on gravity assist or the [quoted text clipped - 13 lines] >30 km/sec, and added to the Earth's orbital velocity of 30 km/sec, >this would result in a tangential velocity of 60 km/sec... There is a problem with this. A comet simply doesn't have enough mass to significantly slingshot a probe. At 30 km/s, even if you graze the surface of the nucleus, you're only going to get a tiny deflection. You aren't going to swing around at all. And if a comet is near the Earth, it's probably active, so getting close is very risky. _________________________________________________ Chris L Peterson Cloudbait Observatory http://www.cloudbait.com [...] Well thought out, but is unfortunately DOA given that comets simply do not mass enough to give the impulse you require. |
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