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It is believed that at any point in time, a handful of small asteroids (TCO's) are temporarily orbiting the Sun-Earth Lagrange points 1 & 2. They are random samples from the Asteroid Belt and therefor represent that size distribution, mostly up to a couple of meters in diameter. They have irregular orbits which last about 9 months on average until they escape. (Btw, what are such orbits called, Lissajous although they are so short lived?)

I understand that it is really cheap to travel from LEO to Lagrange points. When I add up what I easily find online, going from LEO via an Earth-Moon L-point to a Sun-Earth L-point could require only 1 km/s. Is that reasonable? How long time would such a trip take? How much of an extra challenge would it be to rendezvous with an asteroid in a particular orbit around an L-point?

What would a long-term mission look like to redirect a handful such TCO's per year to LEO for studies by astronauts? I imagine one would like to have a small observatory in Lagrange orbit to detect the small candidates, and a mobile Solar electric tow vehicle to push them to LEO one by one.

In this very recent Keck talk the leading asteroid astronomer Dr. William Bottke mentions a mission to TCO's as an alternative to the controversial ARM. Here's a short news article and a paper about such asteroids/moons.

2006 RH120 is the only TCO yet observed, thanks to its large size of about 5 meters. That is about the size that the NASA Asteroid Redirect Mission aims to deal with. One of the advantages of going to a SEL point instead of to a NEO, is that one can go to SEL any day while a NEO has specific launch windows.

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  • $\begingroup$ Just came to think about that the Gaia telescope is at SEL-2. It will certainly observe this transient population very well during the coming years. $\endgroup$ – LocalFluff Aug 17 '14 at 15:33
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    $\begingroup$ They would be in tadpole or horseshoe orbits usually, if they're not more permanent Trojan or Hilda members. Also heard them referred to as "wanderers", if they don't have any stable orbit per se. This document might come handy listing required delta-v to match orbits of known NEA: echo.jpl.nasa.gov/~lance/delta_v/delta_v.rendezvous.html $\endgroup$ – TildalWave Aug 17 '14 at 16:48
  • $\begingroup$ @TidalWave, And here's a messy chart comparing delta-v and travel times for NEA and Mars missions and more nasa.gov/sites/default/files/… But where would a LEO-SEL2 mission end up there? $\endgroup$ – LocalFluff Aug 17 '14 at 20:44
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    $\begingroup$ @TildalWave - That's wikipedia for ya. A contradictory mix of too much and not enough information. Here that process is at work by having high thrust and low thrust tables with inconsistent entries. Think about where an impulse delta V of 7.4 km/s can get you. That article is chock full of errors and misrepresentations (LEO to ELM1 is only 0.77 km/s, and to EML2 it's 0.33 km/s??) And no, don't tell me to fix it. I don't do wikipedia. $\endgroup$ – David Hammen Aug 18 '14 at 12:33
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    $\begingroup$ @David Hammen Exactly! And it's not just Wikipedia. What HopDavid has written here and on his blog at hopsblog-hop.blogspot.se has discouraged me from trusting any delta-v tables. dv(LEO-SEL) should be constant, a value to be calculated once and for all. But confusion reigns on the net. What Gaia actually used, would be a reliable figure. $\endgroup$ – LocalFluff Aug 18 '14 at 12:41
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enter image description here

Above are 4 ellipses. They all have a 400 km altitude perigee, but widely varying apogees.

The blue ellipse has an ~1.5 million km apogee, about the distance to SEL1 or SEL2. The larger grey ellipse has an apogee at EML2 altitude, the smaller grey ellipse has an apogee at lunar altitude. The red ellipse has an apogee at EML1 altitude.

A striking thing about all these ellipses is they have very nearly the same perigee speed. The blue one has a perigee speed of 10.82 km/sec. The red one has a perigee velocity of 10.73 km/sec. They are all just a hair under escape velocity.

A 400 km LEO is about 7.7 km/s. So no matter which of these Lagrange points you're heading for, you need a LEO burn of about 3 or 3.1 km/s.

And the EML1, EML2, SEL1, SEL2 are all quite close to one another in terms of delta V. EML2, SEL1 and SEL2 all have C3 close to zero. Which makes them much closer to Mars, asteroids, or other destinations in our solar system.

If you wanted to park an extraterrestrial propellent source in the earth moon neighborhood, high lunar orbit is a more strategic location than LEO.

It can take take less than 1 km/s delta V to go from these places to LEO. This is because aerobraking can be used to shed that 3 to 3.1 km/s delta V at perigee. But aerobraking can only help you slow orbits. For speeding up from LEO to a big transfer ellipse, you need around 3 km/s worth of propellent plus some to park when you reach your apogee.

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  • $\begingroup$ That's funny. So, near escape velocity there are a wide range or elliptical orbits. What kind of ellipse would one get with a perigee speed of, say, 9 km/s? $\endgroup$ – LocalFluff Aug 19 '14 at 8:51
  • $\begingroup$ A 9 km/s perigee at 400 km altitude would give you a 8700 km apogee. $\endgroup$ – HopDavid Aug 19 '14 at 16:03
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    $\begingroup$ Do you have Excel? I often use this spreadsheet: www.clowder.net/hop/railroad/Hohmann.xls You can type in different altitudes for perigee or apogee into pink cells. 4 cells beneath apogee altitude is the perigee speed (cell F43). Also in that part of the spreadsheet is escape velocity at periapsis. $\endgroup$ – HopDavid Aug 19 '14 at 16:07
  • $\begingroup$ Your contribution to us the interested public is most outstanding! $\endgroup$ – LocalFluff Aug 19 '14 at 16:30

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