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Space Science

Relativistic Navigation Needed For Solar Sails 185

Posted by Soulskill
from the i'd-rather-be-sailing dept.
KentuckyFC writes "Last year, physicists calculated that a solar sail about a kilometer across with a mass of 300 kg (including 150 kg of payload) would have a peak acceleration of roughly 0.6g if released about 0.1AU from the Sun, where the radiation pressure is highest. That kind of acceleration could take it to the heliopause — the boundary between the Solar System and interstellar space — in only 2.5 years; a distance of 200 AU. In 30 years, it could travel 2500AU, far enough to explore the Oort Cloud. But the team has discovered a problem. Ordinary Newtonian physics just doesn't cut it for the kind of navigational calculations needed for this journey. Because the sail has to be released so close to the Sun, it becomes subject to the effects of general relativity. And although the errors these introduce are small, they become magnified over the course of a long journey, sending the sail roughly 1 million kilometers off course by the time it reaches the Oort Cloud. What these guys are saying is that if ever such a sail is launched (and the earliest estimate is 2040), the navigators will have to be proficient in a new discipline of relativistic navigation."
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Relativistic Navigation Needed For Solar Sails

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  • by Anonymous Coward on Wednesday August 19, 2009 @12:24PM (#29120209)

    You mean one part in 370,000, but on the whole you're right. The unfolding speed of the solar sail, or its random deformation during travel will have a higher impact. What a stupid article.

  • by djcinsb (169909) on Wednesday August 19, 2009 @12:28PM (#29120259) Homepage

    It's more likely that the flight engineers would just add course corrections in (i.e. change the sail orientation to redirect the force) if they had a specific target in the Oort cloud in mind.

    Just as small errors due to GR get magnified over the long trajectory, so do small corrections get magnified if made early enough. And, as one earlier commenter noted, a million km isn't much of anything at these distances.

  • by clintp (5169) on Wednesday August 19, 2009 @12:28PM (#29120261)

    And isn't starting at the Sun and aiming for a point in the Oort cloud complicated by the N-body problem anyway? Course corrections will have to be done for the entire trip because of all of those large chunks of rock and gas floating around. Gravity's a bitch, man.

  • by djcinsb (169909) on Wednesday August 19, 2009 @12:42PM (#29120495) Homepage

    On a "good" sail the surface is very reflective. The force that propels the spacecraft is the sum of two vectors; one pointing from the sun to the spacecraft, and a second for the reflected radiation leaving the sail. So you can steer the spacecraft by shortening one side and lengthening the other side of the says attaching the sail to the spacecraft, redirecting the outgoing vector. Or do something similar (e.g. reorient segments rather than the whole sail).

  • by John_Booty (149925) <johnbooty@b[ ]yp ... g ['oot' in gap]> on Wednesday August 19, 2009 @12:52PM (#29120641) Homepage

    Right. There's (almost) no friction in space, so your craft isn't going to slow down just because it's no longer receiving enough power from the sun to accelerate. But after a certain point it won't receive enough solar power to power onboard navigation and communications systems. Those would likely be powered by a wee bit o' radioactive power like today's deep space probes.

  • Re:Computers? (Score:3, Informative)

    by maxwell demon (590494) on Wednesday August 19, 2009 @01:03PM (#29120763) Journal

    Probably you are trying to say that the computers will have to be proficient in this new discipline.

    It's not that hard, either. Just math. We have the equations. They're well-understood. Some physics grad students could probably write the basic engine for such an endeavour. I'd worry more about $UNKNOWN_EXOTIC_EFFECT pushing something off-course.

    You mean, something like the Pioneer anomaly? [wikipedia.org]

  • by jeffb (2.718) (1189693) on Wednesday August 19, 2009 @01:06PM (#29120805)

    There are ways [wikipedia.org].

  • by Minwee (522556) <dcr@neverwhen.org> on Wednesday August 19, 2009 @01:20PM (#29121051) Homepage

    So...um...how do you miss it? You go straight out in any direction. When you see a lot of icy chunks floating around, you're there.

    I think that watching The Empire Strikes Back may have given you the wrong idea about just how densely packed objects like asteroids and comets are in our solar system.

    Consider this. Get your own envelope and pencil if you want to follow along at home. The inner boundary of the Oort cloud is at about 5,000 AU, or 750 billion km from the Sun. The outer boundary is expected to be somewhere around 100,000 AU or 1500 billion km. Inside that volume are an estimated twelve billion objects. Nobody has been able to count them, but Jan Oort guessed that there would be that many and no astronomer has been able to contradict him yet.

    That gives us a total volume on the order of 10^28 km^3, with just 12,000,000,000 objects in it. That's 10^18 km^3 for each object, giving you an average distance between objects of at least a million kilometers. A million km is three times the distance from the Earth to the Moon, and the size of a cometary nucleus is on the order of ten km. You'd be lucky just to see a 10 km object at that distance, let alone see it well enough to justify the trip out there.

    That means that if you're aiming for an object in the Oort cloud but miss by up to a million km, you're going to sail right through empty space. You won't narrowly dodge between densely packed cometary bodies, rolling and weaving to avoid laser blasts, and then have to hide inside the belly of a giant space worm while the Empire searches for you. You'll just pass on by and miss everything.

    Real astronomy isn't nearly as exciting as Star Wars, but that's probably good news for everyone who lives in our galaxy.

  • by mbone (558574) on Wednesday August 19, 2009 @01:23PM (#29121119)

    The JPL ODP (Orbit Determination Program) has incorporated relativity since the 1960's and uses the proper Einstein Infeld Hoffmann (EIH) equations of motion for the harmonic gauge.

     

  • by WhiteDragon (4556) on Wednesday August 19, 2009 @01:32PM (#29121325) Homepage Journal

    It can't work like a sailboat does... steering partly into the wind, or changing the sail angle to alter the thrust exerted. There's no resistive force to work against, so it just kind of goes where it is taken.

    However, tacking [caltech.edu] with the solar sail is still possible.

  • by peter303 (12292) on Wednesday August 19, 2009 @01:44PM (#29121593)
    There is slowing of the clock onboard GPS satellites both due to the orbital speed (special relativity) and lower gravity (general relativity). This paper [google.com] says special relativity errors accumlate about 7 microseconds a day and general relativity 46 microseconds. Radio signals move a thousand feet per microsecond, so the effect significant.
  • Re:Computers? (Score:3, Informative)

    by OwnedByTwoCats (124103) on Wednesday August 19, 2009 @02:11PM (#29122091)

    That's what I get for posting before whipping out the calculator. The acceleration needed to go 200 AUs in 2.5 years is only 9.5 E-3 meters/second. Or around .001g. I don't trust my calculus any more, but integrating the acceleration over that time is in the ballpark.

  • by Idarubicin (579475) <allsquiet.hotmail@com> on Wednesday August 19, 2009 @04:32PM (#29124715) Journal

    And with essentially unlimited ability to maneuver, course-corrections aren't going to be an issue, really.

    I agree with the posts which note that the relative magnitude of the navigational error is trivial (a million kilometers in 2500 AU is the same relative error as one kilometer on a trip to the Moon). I also fully agree that any expedition to the Oort would be a random crapshoot anyway.

    I do have to quibble with the notion of 'essentially unlimited ability to maneuver', however. The amount of thrust available decreases with increasing distance from the sun. (Indeed, it falls off as the inverse square of the distance.) If our hypothetical sail starts off at 0.1 AU from the sun for maximum thrust, its acceleration will be down to 1% of its original value as it crosses the Earth's orbit, and less than 0.04% when it crosses Jupiter's orbit. At Pluto's orbit, the probe will be able to call on less than a hundred-thousandth the amount of sunlight it saw when it started. In other words, errors in course selection which take place early will accumulate for the longest, and will be most apparent when the least thrust is available for correction.

  • by Crookdotter (1297179) on Wednesday August 19, 2009 @04:36PM (#29124789)
    Why is this a suprise at all? GPS satellites have to include relativistic calculations. This isn't difficult for anyone involved. It's hardly rocket science.....
  • by Ungrounded Lightning (62228) on Wednesday August 19, 2009 @05:02PM (#29125185) Journal

    Wrong.

    The solar wind force is essentially outward (in the solar wind direction) only. (The particles initially stick to the sail and then are released, if at all, by a different mechanism such as electrostatic repulsion.) And the portion of the light that is absorbed by the sail also produces an outward force.

    But for a mirror-finished solar sail the portion of the light that is reflected (most of it) gives the vector sum of the momenta of its arrival and the recoil of its departure. So tilting the sail to reflect sunlight forward along the direction of orbit gives a strong deceleration and lowers the orbit.

  • Re:Computers? (Score:3, Informative)

    by HTH NE1 (675604) on Wednesday August 19, 2009 @06:40PM (#29126479)

    (Damn summary.) G is acceleration. g is grams.

    1G is acceleration due to gravity at the surface of the Earth, 9.8 m/s^2.

    An object in motion will stay in motion unless acted on by an outside force.
    An object in acceleration will cease to be in acceleration when the outside force is removed. As the force reduces, the acceleration reduces.

    0.6G means if you stand with your head in the direction of acceleration, you'll weigh 3/5ths your weight on Earth.
    0.6c means you're moving 3/5ths the speed of light.

  • Re:Computers? (Score:4, Informative)

    by Antique Geekmeister (740220) on Wednesday August 19, 2009 @06:47PM (#29126561)

    It's a solar sail. Without significant solar thrust, it _will_ drag against the interstellar gas, and it's likely to gain mass as it does so.

  • by khallow (566160) on Wednesday August 19, 2009 @09:21PM (#29127825)

    Of course there's resistive force. It's called gravity and most people, when they think about space travel, vastly underestimate it's strength.

    Gravity is not a resistive force. A resistive force is a force that acts opposite the motion of a moving object. Gravity is an attractive force between masses independent (in the Newtonian model in which it exists) of the motion of the masses. I think GR has an extremely weak resistive force in that gravity waves carry away some energy from masses moving near one another.

  • by khallow (566160) on Wednesday August 19, 2009 @09:32PM (#29127925)

    Unless we have some specific target in the Oort Cloud that we aim for at the beginning of the trip, with no course-corrections, this is pretty much meaningless.

    Why call it the "Oort Cloud" if there's nothing in it? My view is that such solar sails would be first used for Kuiper Belt targets and the heliopause (the latter not needing trajectory accuracy aside from making sure the probe heads away from the Sun). Later as we discover targets in the Oort cloud to investigate, probes could be sent out in this way. It's also good for interstellar missions. These velocities provide a good first stage boost. Accurate trajectories might greatly reduce the propellant consumed to correct the trajectory to another star.

  • Re:one more stat (Score:3, Informative)

    by jeffb (2.718) (1189693) on Thursday August 20, 2009 @11:38PM (#29142845)

    <deep sigh/>

    What happens if you shoot a bullet at a sailboat's sail? You get a tiny hole in the sail. Now imagine the bullet is a million times less massive, and traveling a thousand times as fast. Same kinetic energy, but it's going to punch a much smaller and neater hole.

    Any space debris at the relative velocity of a solar sail will punch right through any imaginable sail material, vaporizing the tiny bit that it contacts. The surrounding material won't even feel a tug.

Your code should be more efficient!

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