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limit to possible asteroids at Earth-Sun L4 and L5?
I know that there are no large asteroids to be found at the L4 or L5
points of the Earth-Sun system. But what I don't know is: how large is "large"? In other words, how big could an object at these points be and still have escaped detection? Is it possible there's a small but still useful cache of resources here that we simply haven't spotted yet? Thanks, - Joe |
#2
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limit to possible asteroids at Earth-Sun L4 and L5?
Joe Strout wrote:
I know that there are no large asteroids to be found at the L4 or L5 points of the Earth-Sun system. But what I don't know is: how large is "large"? In other words, how big could an object at these points be and still have escaped detection? Is it possible there's a small but still useful cache of resources here that we simply haven't spotted yet? Thanks, - Joe I was hoping someone more knowledgeable than I would answer since it's an interesting question. The phase angle would be good: Their terminator plane would be tilted 30 degrees wrt to an earth viewer. So Earth Sun trojans would be 3/4 illuminated from our point of view. They'd be 1 A.U. distant. I believe most NEOs are detected when they're somewhat closer than 1 A.U. As I understand it, NEAT, LINEAR and other asteroid hunters like to point their telescopes up, avoiding the horizons. There'd be 60 degrees of separation between the sun and an earth Trojan, so it could get as far as 60 degrees above the horizon before sunrise or after sunset. Somewhat better than Venus or Mercury. I believe the Earth-Sun L4 and L5 would be good spots to put communication satellites. L4 & L5 relays could facilitate communication with locations on the far side of the sun. Hop |
#3
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limit to possible asteroids at Earth-Sun L4 and L5?
In article ,
Hop David wrote: I know that there are no large asteroids to be found at the L4 or L5 points of the Earth-Sun system. But what I don't know is: how large is "large"? In other words, how big could an object at these points be and still have escaped detection? ... The phase angle would be good... They'd be 1 A.U. distant. I believe most NEOs are detected when they're somewhat closer than 1 A.U. I took a quick look and couldn't find any solid data on this. People *have* looked. One fundamental difficulty is that most Trojan asteroids don't sit *at* the L4 or L5 point -- they librate around it, and that is sometimes a euphemism for quite large wanderings in the very general vicinity. So there's potentially a lot of sky for them to be found in, with the further complication that the background is full of main-belt asteroids to confuse identification. As a vague indication, 5261 Eureka -- the first Mars Trojan discovered -- is thought to be maybe 2-4km across. My gut feeling is that something of that size at or near one of the Earth Trojan points would have been noticed by now. Something substantially smaller... maybe not. As I understand it, NEAT, LINEAR and other asteroid hunters like to point their telescopes up, avoiding the horizons. You can't work too close to the horizon, because the atmosphere messes things up. Traditionally, near-Earth-asteroid hunting was done by looking mostly around the antisunward direction, because most asteroids are substantially brighter when the light's more or less exactly behind the observer. However, there are a few searchers who systematically look in other directions, e.g. looking for asteroids with orbits partly or totally inside Earth's. I believe the Earth-Sun L4 and L5 would be good spots to put communication satellites. L4 & L5 relays could facilitate communication with locations on the far side of the sun. The main problem is that you'd need very large comsats to come anywhere close to the communications capabilities of good Earth stations. It's usually easy enough to just accept that there'll be a week or two every year or so when communications are difficult or impossible. You'd need either some purpose for which continuous communication was very important, or dramatically lowered costs and expanded space activities, to make it worthwhile. Also, going maybe 10-15 million km from Earth along Earth's orbit (in either direction) is enough to let you communicate past the Sun. Such a position isn't stable in the long run, but the stationkeeping costs are small enough that they'd probably be acceptable, and the shorter speed-of-light lag might well be worth it. One thing a position farther from Earth might be useful for is to watch for long-period comets hazardous to Earth. You'd watch from Earth (or Earth orbit) too, but there is an unfortunate possibility of a long-period comet that basically approaches from the other side of the Sun -- given the right/wrong general orbit, it can stay quite close to the Sun in our sky for most of its approach. Sun-observing satellites like SOHO will see it as it rounds the Sun, but at that point there isn't a lot of time left. Watching for such unfortunately-placed comets is best done from a location *well* away from Earth, so the Sun is well away from the telescope field of view; this is a much more demanding requirement than communications, because you're looking for faint objects of unknown position. -- spsystems.net is temporarily off the air; | Henry Spencer mail to henry at zoo.utoronto.ca instead. | |
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limit to possible asteroids at Earth-Sun L4 and L5?
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#5
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limit to possible asteroids at Earth-Sun L4 and L5?
Joe Strout wrote:
In article , (Henry Spencer) wrote: I took a quick look and couldn't find any solid data on this. People *have* looked. ... As a vague indication, 5261 Eureka -- the first Mars Trojan discovered -- is thought to be maybe 2-4km across. Henry, do you know if 5261 Eureka was discovered at opposition? At opposition it would've been fully illuminated, quite high in the sky at midnight, and about half an A.U. distant, somewhat more favorable conditions than an earth trojan. Hop |
#6
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limit to possible asteroids at Earth-Sun L4 and L5?
Joe Strout wrote:
However, computing the delta-V to EL4 or EL5 is beyond me, and I haven't been able to find this in my usual references. I suppose it may be a complex question, depending on whether you use the Moon for an assist. Is mining an object at EL4 or EL5 completely ridiculous, or (assuming such an object exists) a sensible idea? For minimum delta vee, you'd want velocity vectors parallel to the Trojan's. This means a one A.U. perihelion or apohelion. Space ship to leading trojan would have a 5/6 year period. Apohelion velocity is 27.8 km/sec vs Earth's 29.8 km/sec. The delta vee is 2 km/s. Ship to a trailing Trojan would have a period of 7/6 year. The difference between earth's velocity and ship perihelion velocity is about 1.4 km/sec. Unlike Hohmann orbits, the transfer path would be over 360 degrees instead of 180. So this means a trip time of about a year, instead of the approximate half year for Hohmann trips to neighbors. Of course you could make shorter trips but the delta vee would increase substantially. I believe help from lunar gravity assists would be 1 km/sec or less and trips relying on lunar assists could use 12 windows a year. Hop |
#7
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limit to possible asteroids at Earth-Sun L4 and L5?
In article ,
Hop David wrote: For minimum delta vee, you'd want velocity vectors parallel to the Trojan's. This means a one A.U. perihelion or apohelion. Space ship to leading trojan would have a 5/6 year period. Apohelion velocity is 27.8 km/sec vs Earth's 29.8 km/sec. The delta vee is 2 km/s. Ship to a trailing Trojan would have a period of 7/6 year. The difference between earth's velocity and ship perihelion velocity is about 1.4 km/sec. Unlike Hohmann orbits, the transfer path would be over 360 degrees instead of 180. So this means a trip time of about a year, instead of the approximate half year for Hohmann trips to neighbors. Of course you could make shorter trips but the delta vee would increase substantially. I believe help from lunar gravity assists would be 1 km/sec or less and trips relying on lunar assists could use 12 windows a year. Thanks, Hop. That's not too terrible. Still a pretty long mission, but not too bad for an unmanned craft. And the frequent windows could be a significant advantage over other NEOs. Well, here's hoping somebody finds something useful there! Best, - Joe |
#8
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limit to possible asteroids at Earth-Sun L4 and L5?
In article ,
Joe Strout wrote: However, computing the delta-V to EL4 or EL5 is beyond me, and I haven't been able to find this in my usual references. I suppose it may be a complex question, depending on whether you use the Moon for an assist. To a first approximation it's actually very simple: the delta-V can be arbitrarily small if you're willing to wait an arbitrarily long time. Just set up an orbit that's nearly identical to Earth's except with a slightly different period. The slightly-different period means that you slowly move ahead of, or slowly fall behind, Earth. You simply wait until you've moved ahead or fallen behind by 60deg, and you're there. Arranging a slightly different period requires part of the orbit being inward or outward from Earth's, but you can just juggle the numbers so that at arrival time, you've done an integer number of orbits and are therefore at 1AU. Trouble is, doing an integer number of orbits takes roughly an integer number of years. And the cost rises as the integer gets smaller (to the limit of the numbers Hop cited, for n=1). Is mining an object at EL4 or EL5 completely ridiculous, or (assuming such an object exists) a sensible idea? It's not ridiculous, but it's not clear that it has big advantages over choosing some other convenient near-Earth asteroid. (And the fact that we don't currently know of any Earth Trojans is definitely a disadvantage!) -- spsystems.net is temporarily off the air; | Henry Spencer mail to henry at zoo.utoronto.ca instead. | |
#9
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limit to possible asteroids at Earth-Sun L4 and L5?
In article ,
Hop David wrote: As a vague indication, 5261 Eureka -- the first Mars Trojan discovered -- is thought to be maybe 2-4km across. Henry, do you know if 5261 Eureka was discovered at opposition? At opposition it would've been fully illuminated, quite high in the sky at midnight, and about half an A.U. distant, somewhat more favorable conditions than an earth trojan. Indeed so. No, I don't know the details of its discovery, which is one reason why I wasn't very definite in my comments. :-) It was found by an organized search, and it might well have been an opposition search. -- spsystems.net is temporarily off the air; | Henry Spencer mail to henry at zoo.utoronto.ca instead. | |
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