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limit to possible asteroids at Earth-Sun L4 and L5?



 
 
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  #1  
Old January 11th 07, 10:32 PM posted to sci.space.policy
Joe Strout
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Default 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  
Old January 14th 07, 09:20 PM posted to sci.space.policy
Hop David
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Default 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  
Old January 15th 07, 01:27 AM posted to sci.space.policy
Henry Spencer
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Posts: 2,170
Default 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. |
  #6  
Old January 15th 07, 04:37 PM posted to sci.space.policy
Hop David
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Default 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  
Old January 15th 07, 06:07 PM posted to sci.space.policy
Joe Strout
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Posts: 972
Default 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  
Old January 15th 07, 08:44 PM posted to sci.space.policy
Henry Spencer
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Posts: 2,170
Default 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  
Old January 15th 07, 08:47 PM posted to sci.space.policy
Henry Spencer
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Posts: 2,170
Default 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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