Asteroid Transit Map Thread 2

[mikelepage]

Pop quiz: (before scrolling down )  Can you name more asteroids than you can planets? 

There are quite a few of them... this should be easy... 

I'll start with that question, because hopefully by the end of this post, you will.  I'm starting a new thread for this, because even though this is the continuation of two older threads here and here, this is intended as a new starting point for anyone coming into this fresh (and honestly, this is the most amount of work I've ever done for a post on NSF!).

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When we talk about "the asteroids" as destinations for human exploration and settlement and/or mining, it's usually as opposed to the moon or Mars, but we tend to think of them just as the "main belt asteroids", or sometimes "Near Earth asteroids" (NEOs) or "potentially hazardous asteroids" (PHAs).  Aside from 1 Ceres or 4 Vesta, or perhaps 243 Ida and the other asteroids visited by space probes, we rarely know them by name.  Before doing this I would have struggled to name 9 asteroids in the question above, even though there are tens of thousands that have been named.

My aim with this exercise, was to see if there was a better way to present the asteroids... What they are called, where they are, and through that get a better feel for what the best strategy to explore them might be.  The transit map analogy comes in when you think about how the asteroids are moving around the solar system, all in their different orbits, almost like the buses, trains and trams in a city might move according to their own timetables.  If you've got the money, you might hire a car to go directly to your destination in a city, but if you need to travel cheaply in a city with good transit options, you can also get around pretty easily by "hopping" from bus to train to tram.  You might especially want to do this "hopping" style of travel with asteroids so that you can have near constant radiation protection, as well as access to resources you can mine, rather than spending months out in space en route to your destination, but without protection from solar flares or being able to actually do much of anything while you're on the way.  The only problem: to "hop" properly, you need a transit map so you can plan how you'll move from asteroid to asteroid.

Is there a better way of prioritising which asteroids we mine/settle? The obvious solution is to look at near Earth asteroids - those that pass close to Earth at relatively low Delta Vs, and explore those first.  That's an important first step, but choosing which NEO should be part of a larger strategy.  It's no good catching the first bus to come past the bus stand just because it's there.  Every single asteroid we do any detailed study on, let alone mine, can serve as a waypoint to those who follow. The key is to think about where we want to end up... solar system bodies with sufficient resources to support large numbers of people - so Mars, obviously, but also, the main belt asteroids. 

My idea was to generate a list of the biggest asteroids in the belt - the places humankind will want to end up - and filter them by which asteroids encounter each other more often (eventually leading allowing trade and travel).  That almost certainly means humankind will be concentrated on asteroids with lower inclinations close to the ecliptic, and of small absolute magnitude (remember smaller H => bigger asteroid).   Find those asteroids, then work backwards to the find the Near Earth Asteroids with similar orbital parameters that we explore first, such that we can that will allow us to "hop" from Earth to these main belt asteroids. 

So the idea is: define the main belt "anchor" asteroids where we want to end up, and then find the Apollo and Amor class asteroids we can use as "stepping stone" asteroids to get there.  Yes, most of these "stepping stone" asteroids will have higher deltaV requirements than the lowest possible deltaV NEOs, but they'll be part of a strategy, and also remember we can perform both Oberth maneuvers and aerobraking to achieve relatively high delta-V transits to and from Earth, but almost nowhere else.

Attachment 1:

I came up with a list of 118 "anchor" asteroids, and from the NASA Horizons database I downloaded their xyz co-ordinates for every week for 50 years (2030-2080), and used MS excel to compare positions when they came closest to each other (I also have the velocity data).  The reasoning behind choosing these 118 was as follows.  The first 91 were selected based simply on having an aphelion of less than 4 AU (don't want Hildas or Jupiter Trojans for now), an inclination of less than 4 degrees and an absolute magnitude (H) of <10 (~25km across or larger).  Then, because I wanted to include 1 Ceres, 4 Vesta, and 3 Juno (it would be a shame to go to all this work and not include the biggest asteroids), I decided somewhat arbitrarily that for inclinations up to 10 degrees they had to be at magnitude 8 or smaller, and for inclinations up to 13 degrees they had to be magnitude 6 or smaller.  That gave me an extra 27 higher inclination asteroids for the total of 118, plotted by longitude of ascending node in the first chart (note the two largest asteroids, Vesta and Ceres, have a similar longitude of ascending node, which allowed the Dawn probe to visit both).

With me so far? Great.

Attachment 2:

From here I started to calculate the relative positions of all 118 asteroids to each other every week during that time period (multiplied 2609 time points - Ouch!).  My laptop complained, but not before I generated the first couple of plots.  The second chart shows the close approaches of every anchor asteroid to 73 Klytia.  Which was first on the list because of having lowest longitude of ascending node, longitude of perihelion, and inclination, but coincidentally turned out to be the asteroid with the most close approaches below.

As you can see, it's not dissimilar to charts of the movement of the closest stars, except that some asteroids do stick around in relatively close proximity for a number of years (214 Aschera has 120-280m/s relative velocity with 73 Klytia from 2041-2044, 203 Pompeja is the close approach 2046-49), while another one whips past at high speed (77 Frigga, relative velocity ~4.4km/s) on a regular basis.

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Attachment 3:

Because of computing power limitations, calculating every single interaction was out of the question for me, and I hedged by only calculating the results for every 25th week in the 50 years (fairly sure this is representational).  For those 118x105 data points I then counted up the number of close interactions (<78 Lunar Distances = <0.2 AU) each asteroid has with the other 117 "anchors".  I've compiled this data in the final attachment.  I've just extracted the single sheet out of the whole workbook to keep file size down.

So without further ado, my top "anchor" asteroids (>=50, <78 LD interactions in 50 years) are:
73 Klytia, 37 Fides, 720 Bohlinia, 332 Siri, 215 Oenone, 21 Lutetia, 277 Elvira, 214 Aschera & 135 Hertha.

My plan is now to start looking for "stepping stone" asteroids that will have regular interactions with both Earth, and these "anchor" asteroids, making sure they have similar longitudes of ascending node, inclinations, etc.  I figured I'd done enough for now to start a new thread.

Anyone who wants to help is welcome.  Looking forward to comments/questions too.

[glennfish]

OK, you got me intrigued.  Unlike you, I'm not lap-top limited so in principle I could work with the entire database.  Plus, I've got some optimal routing software that could actually do trip planning based on various assumptions.

I'm assuming there is commercial value in what you've started, i.e. someone is going to want to do an optimal mining survey at some point.

So my first question is, how would you go about downloading the horizons database.  I browsed the JPL site and it wasn't obvious how to do a batch download.  More like 1 at a time?

[mikelepage]

OK, you got me intrigued.  Unlike you, I'm not lap-top limited so in principle I could work with the entire database.  Plus, I've got some optimal routing software that could actually do trip planning based on various assumptions.

I'm assuming there is commercial value in what you've started, i.e. someone is going to want to do an optimal mining survey at some point.

So my first question is, how would you go about downloading the horizons database.  I browsed the JPL site and it wasn't obvious how to do a batch download.  More like 1 at a time?

Hi and thanks for the interest.  I agree there will eventually be something in this, although I'm not sure precisely how it will come about.  I hope it will become more obvious as a result of doing this kind of exploratory analysis.  And computing power or no, I'd caution that the entire database is vast, so I think it's still worth limiting your objects of study by inclination and magnitude, since that's where foreseeable manned spacecraft will be sent to, anyway.

In answer to your question, yes the OP was done by downloading that data one-by one, because it wasn't obvious how to do a batch download, but I'm now pretty sure the best way to do batch downloads is via the email interface, where you can download up to 200 at a time (each of which generates a separate email back to you). 

It's a bit painful in that you have to make sure you're sending plaintext emails - which I've found is possible using the plaintext option in gmail.  I doubt it would do me much good to copy and paste anything here on the forum - but I have had had success by copying the instructions from the ftp link in on the page below directly into my email compose window, and modifying it manually to specify the numbers of the asteroids I want, what timeframe and frequency I want, that I want it as a VECTOR table, type 2 (which gives x, y, z, vx, vy, vz for each time point):

https://ssd.jpl.nasa.gov/?horizons#email

Obviously you want to get the same set of time points for every single small body, and I've actually come to the conclusion that querying the database for positions every week is a bit overkill.  Better to dedicate computing resources towards doing a greater number of small bodies, at less frequent timepoints.  3 times a year is enough that any encounters which are slow enough for for a probe/ship to transit (<3km/s) will be picked up. 

So if you want you could try replicating what I've done with the 118 "anchors" I put in the previous post, or you could try extracting your own set of asteroids from the web interface here:

https://ssd.jpl.nasa.gov/sbdb_query.cgi

For my next effort I was preparing to download data for a set of 1398 asteroids (Q<4, i<4, H<13), because I think the greater number of objects in low inclination will result in more frequent close approaches between large (>2km) bodies which last more than a year.  Those are the ones for which I can imagine BFR type spaceships going back and forth multiple times between city-state sized settlements.

[glennfish]

Holiday schedule is messing up my free time.

It would seem to me that if we were able to simply download the orbital equations for each object, we could calculate the position for any time (ignoring n-body gravity effects for now).

There are several algorithms that could calculate minimum separation of any two elliptical orbits and I haven't found it, but it should be feasible to sort the equations based on relative delta v and closest location spitting out the when as an output rather than in input.

I'd rather load the orbital parameters one time and calculate the position for a given time, than iterate through many times to find the position at that time.

Gotta noodle on this some more.

It looks like we can get all the orbital parameters at the page you posted:  https://ssd.jpl.nasa.gov/sbdb_query.cgi


I initially downloaded everything, and cancelled when it hit over 50 mb.

Then I tried NEO asteroids only, and it spit out 2,793

Definitely got to noodle this more.

[mikelepage]

Haven't had a chance to work on this either, same holiday schedule issues

Must admit, I'm not that interested in many of the objects classified as NEOs because most of them are scarcely more than large boulders, often in higher inclination orbits (which allows them to avoid perturbation by Earth's gravity over longer periods of time).  We want the low inclination, larger bodies that go further out and allow us to access the main belt asteroids.  If you limit your NEO search to H<17 and i<4 you'll see the 21 bodies I think are more interesting as far as the transit map goes.   

It would seem to me that if we were able to simply download the orbital equations for each object, we could calculate the position for any time (ignoring n-body gravity effects for now).

It would definitely be easier to just use the orbital elements and calculate it out, but my calculus is not that great and I found it easier to just download the more accurate data someone else had calculated.  It could be worth checking on a few bodies just to see how great the effect is of including n-body simulation or not just to see how much those effects multiply over time.  You would certainly expect the effect to be bigger on small bodies, although perhaps not great enough to change the frequency of the rendezvous opportunities we're interested in.

Ideally what I would like is to have a web-based interface that produced plots like attachment 2 above for any specific asteroid over a given time period.  That way you can start to plot a course from asteroid to asteroid the way future navigators may well do.

You could eventually game-ify the the whole scenario on an online platform: give each player a ship and allow them to hop from asteroid to asteroid - choosing from among the real transit opportunities we calculate - but constrain them into mining asteroids/performing ISRU at a particular rate, so they had to make sure they had enough fuel to make the next hop (while also selling any metal ores for ship upgrades, etc) as they did so. 

Incidentally, the reason I emphasise the low inclination asteroids is because in a future asteroid mining scenario where this kind of exploration is actually happening, you want to keep everyone pretty close to ecliptic plane, such that in any emergency scenario where a ship/crew needs rescue, there's more than a snowflake's chance in hell of there being someone nearby who can actually reach them to offer help.

[Eer]

I know this is probably obvious, but ...

https://ssd-api.jpl.nasa.gov/doc/sbdb.html

includes the APIs, and essentially the data design, of the Small Bodies DataBase, and at the bottom of the page provides a contact email for the curators / researchers working on it.

This seems like a better approach than excel downloads to pull orbital elements for the asteroids you're interested in, whether it comes to you in XML or CSV.

Just a thought.

[Greg Hullender]

I found a paper giving an algorithm to compute the minimum orbital intersection distance (MOID) between two Keplerian orbits in terms of their eccentric anomalies. Fast error–controlling MOID computation for confocal elliptic orbits. Best of all, they have a link to C++ code to compute this efficiently and controlling for numerical errors.

That means that for each asteroid, A, of interest, you can find the minimum possible approach to any other asteroid, B. That lets you eliminate pairs that have no hope of getting usefully close. Further, for each B, it tells you the point in A's orbit when they'll be closest. Those are the only points you need to test.

Obviously you'll need to recompute these values as the orbital parameters change over time, but that should still be vastly cheaper than computing distances between all the orbits at each instant of time.