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Old 19th January 2019, 07:31 AM   #121
dasmiller
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Originally Posted by Roboramma View Post
When it comes to energy concerns far from the sun you might get some use out of carrying a low mass but high surface area reflector. Use that to focus the low intensity sunlight on your relatively small solar panels.
This will add considerable complexity to the design, though, which might not be worth it.
It's possible. Solar concentrators were a mixed success on GEO commsats and were dropped from later models, but for cruising around the asteroid belt, concentrators might be much more attractive.
For GEO commsats, one of the big issues was solar panel temperature. Solar cells (the kind we use, anyway) get less efficient as they get hotter, and of course reflecting more sunlight onto them makes them hotter. But out in the asteroid belt, where it's ******* cold and we're getting only 1/10 of the sunlight, panel temperature shouldn't be an issue even with big concentrators.

Not sure how that would work out during the mining operation, though, with the mining bot sitting on a rotating rock. Of course, that concern is there with or without the concentrators.

ETA: A nice picture and an actual in-flight photo
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Old 19th January 2019, 11:00 AM   #122
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Originally Posted by GlennB View Post
I think theprestige is still being sarcastic, but heading towards meta.
In that case, I'd say heading towards trolling.

Hans
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Old 25th January 2019, 08:36 AM   #123
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Originally Posted by dasmiller View Post
I took what I thought would be the average delta-Vs needed for inclination changes (including node), eccentricity changes, SMA changes, and RSSed them on the theory that you'd usually be able to combine burns. Again, my numbers were pretty coarse.

The numbers don't look that small to me. Again, I will look deeper into this.
This post is all about the needed delta-V. For orbital dynamics, the available delta-V is closely analogous to the driving range available in a car, except that it's a 6-dimensional problem instead of a 2D problem, and the 6 dimensions are not entirely independent.

Anyway, I did a deeper dive, and the numbers are somewhat lower than I'd expected.

I used some basic orbitology to look at the energy needed to correct the 6 keplerian orbit elements, spoilered for brevity.
First, I found the delta-V to correct the 6 elements in 4 pieces requiring a total of 6 burns:
Piece 1 is 1 burn for combined inclination & node,
Piece 2 is 2 burns to simultaneously correct semi-major axis and eccentricity (Hohmann transfer), it tries two different sequences and chooses the more efficient of the two because with elliptical orbits, it's not always most efficient to do the apogee burn to correct perigee first. For ellipticals, there's the third possibility of doing an apogee burn to raise perigee to match the target orbit's apogee (flipping the xfer orbit's arg-peri by 10 deg), and sometimes that might be advantageous, but I haven't added that to my code yet.
Piece 3 is one burn for argument of perigee correction,
Piece 4 is two burns (start & stop) to correct anomaly. It turns out that you can't really rephase to match anomaly without specifying the date. I simply had the code rephase to get the anomaly-at-epoch to match, which is arbitrary-but-straightforward and should give a realistic distribution of delta-Vs, although in a case-by-case basis they aren't accurate.

Usually there's some benefit (sometimes a LOT of benefit, sometimes none) to combining maneuvers, but finding the actual combinations can be very involved, and my attention span is limited, so I assumed I'd get half of the benefit of RSSing rather than straight-adding the 4 pieces.

I ignored the gravity of the asteroids themselves; with few exceptions, they're pretty negligible.

I also assumed that we wouldn't be able to do any clever slingshot or gravity-assist maneuvers. Within the main belt, at least, there's not much to slingshot around.

The calculations do not include losses due to non-impulsive burns ("arc losses"). First, I was estimating burn durations on the order of a few weeks, and on a 4 year orbit, that's not too much arc so I'd expect the losses to be small (<5%). Second, I don't know any easy way to estimate arc losses.

I assumed minimum-energy maneuvers for everything but the anomaly correction, and the anomaly correction used whatever fuel was needed to stay under the 10 year limit assuming roughly one full orbit was needed for the ecc/sma correction. That's why some asteroids are unreachable regardless of the available delta-V; it simply takes more than 10 years for a minimum-energy transfer to get there even without rephasing the anomaly. Of course, if we weren't limited to minimum-energy transfers, we could do things faster, but my code isn't that clever.

I limited each trip to 10 years; reducing that to, say, 6 years would dramatically reduce the targets in range for a given delta-V.

I downloaded a ******* huge asteroid database, estimated (see spoilered stuff) how much delta-V it took to go from each of the first few hundred asteroids to any of the first 100,000, and binned the results. The first few lines are pasted below. I apologize for the underscores but I haven't figured out the "table" thing yet.

The columns represent the number of other asteroids in-range for the available delta-V. For example, if your spacecraft had 2 km/s total delta-V, starting from Ceres, it would have 541 other asteroids in range.

________________________max_delta-V,_km/sec
______________________0.50____1.00____2.00____4.00 ____8.00___20.00___50.00___80.00
_____1_Ceres_____________0_______6_____541___22747 ___96953___99840___99879___99879
_____2_Pallas____________0_______0_______2______87 ___55237___99234___99879___99879
_____3_Juno______________0_______0______71____5753 ___94393___99426___99879___99879
_____4_Vesta_____________2______39____1361___32336 ___92147___99835___99879___99879
_____5_Astraea___________1_______8_____367___24073 ___96287___99837___99879___99879
_____6_Hebe______________0_______0_____102___11511 ___90257___99404___99879___99879
_____7_Iris______________0_______5_____348___16968 ___91638___99450___99879___99879
_____8_Flora_____________0______15_____826___21385 ___78239___99724___99879___99879
_____9_Metis_____________0______34____1490___34486 ___92782___99859___99879___99879
____10_Hygiea____________0______15_____600___14667 ___92596___99672___99878___99879
____11_Parthenope________0______18____1744___39459 ___95852___99856___99879___99879


The table assumes an actual rendezvous with the target asteroid, not just a flyby. Flybys require much less delta-V but I really don't know how to calculate them.

Based on this, you could certainly design a viable system with 2 km/s. Ideally, I'd design the spacecraft for 4 km/s and then do hops that require no more than 2 km/s. That way, if it arrived at an asteroid and, for whatever reason, couldn't refuel there, it could move on to another asteroid. A 4 km/s system also makes it easier to get to the asteroid belt in the first place (and even easier if you have about 7; I don't think there's much benefit beyond 7 unless you're in a hurry).

I think the calculations are good to about +/-25% and I don't think there's much overall bias; more rigorous calculations will make some numbers higher and some lower.

It was an interesting exercise and I'd been meaning to write some orbital mechanics tools for quite some time now.
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Old 25th January 2019, 08:54 AM   #124
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Originally Posted by dasmiller View Post
This post is all about the needed delta-V. For orbital dynamics, the available delta-V is closely analogous to the driving range available in a car, except that it's a 6-dimensional problem instead of a 2D problem, and the 6 dimensions are not entirely independent.

Anyway, I did a deeper dive, and the numbers are somewhat lower than I'd expected.

I used some basic orbitology to look at the energy needed to correct the 6 keplerian orbit elements, spoilered for brevity.
First, I found the delta-V to correct the 6 elements in 4 pieces requiring a total of 6 burns:
Piece 1 is 1 burn for combined inclination & node,
Piece 2 is 2 burns to simultaneously correct semi-major axis and eccentricity (Hohmann transfer), it tries two different sequences and chooses the more efficient of the two because with elliptical orbits, it's not always most efficient to do the apogee burn to correct perigee first. For ellipticals, there's the third possibility of doing an apogee burn to raise perigee to match the target orbit's apogee (flipping the xfer orbit's arg-peri by 10 deg), and sometimes that might be advantageous, but I haven't added that to my code yet.
Piece 3 is one burn for argument of perigee correction,
Piece 4 is two burns (start & stop) to correct anomaly.

Usually there's some benefit (sometimes a LOT of benefit, sometimes none) to combining maneuvers, but finding the actual combinations can be very involved, and my attention span is limited, so I assumed I'd get half of the benefit of RSSing rather than straight-adding the 4 pieces.

I ignored the gravity of the asteroids themselves; with few exceptions, they're pretty negligible.

I also assumed that we wouldn't be able to do any clever slingshot or gravity-assist maneuvers. Within the main belt, at least, there's not much to slingshot around.

The calculations do not include losses due to non-impulsive burns ("arc losses"). First, I was estimating burn durations on the order of a few weeks, and on a 4 year orbit, that's not too much arc so I'd expect the losses to be small (<5%). Second, I don't know any easy way to estimate arc losses.

I assumed minimum-energy maneuvers for everything but the anomaly correction, and the anomaly correction used whatever fuel was needed to stay under the 10 year limit assuming roughly one full orbit was needed for the ecc/sma correction. That's why some asteroids are unreachable regardless of the available delta-V; it simply takes more than 10 years for a minimum-energy transfer to get there even without rephasing the anomaly. Of course, if we weren't limited to minimum-energy transfers, we could do things faster, but my code isn't that clever.

I limited each trip to 10 years; reducing that to, say, 6 years would dramatically reduce the targets in range for a given delta-V.

I downloaded a ******* huge asteroid database, estimated (see spoilered stuff) how much delta-V it took to go from each of the first few hundred asteroids to any of the first 100,000, and binned the results. The first few lines are pasted below. I apologize for the underscores but I haven't figured out the "table" thing yet.

The columns represent the number of other asteroids in-range for the available delta-V. For example, if your spacecraft had 2 km/s total delta-V, starting from Ceres, it would have 541 other asteroids in range.

________________________max_delta-V,_km/sec
______________________0.50____1.00____2.00____4.00 ____8.00___20.00___50.00___80.00
_____1_Ceres_____________0_______6_____541___22747 ___96953___99840___99879___99879
_____2_Pallas____________0_______0_______2______87 ___55237___99234___99879___99879
_____3_Juno______________0_______0______71____5753 ___94393___99426___99879___99879
_____4_Vesta_____________2______39____1361___32336 ___92147___99835___99879___99879
_____5_Astraea___________1_______8_____367___24073 ___96287___99837___99879___99879
_____6_Hebe______________0_______0_____102___11511 ___90257___99404___99879___99879
_____7_Iris______________0_______5_____348___16968 ___91638___99450___99879___99879
_____8_Flora_____________0______15_____826___21385 ___78239___99724___99879___99879
_____9_Metis_____________0______34____1490___34486 ___92782___99859___99879___99879
____10_Hygiea____________0______15_____600___14667 ___92596___99672___99878___99879
____11_Parthenope________0______18____1744___39459 ___95852___99856___99879___99879


Based on this, you could certainly design a viable system with 2 km/s. Ideally, I'd design the spacecraft for 4 km/s and then do hops that require no more than 2 km/s. That way, if it arrived at an asteroid and, for whatever reason, couldn't refuel there, it could move on to another asteroid. A 4 km/s system also makes it easier to get to the asteroid belt in the first place (and even easier if you have about 7; I don't think there's much benefit beyond 7 unless you're in a hurry).

I think the calculations are good to about +/-25% and I don't think there's much overall bias; more rigorous calculations will make some numbers higher and some lower.

It was an interesting exercise and I'd been meaning to write some orbital mechanics tools for quite some time now.
Wow, thank you for this! It's a very generous effort on your part. I really appreciate it.

I like your thinking about a 4 km/s system with a 2 km/s mission profile.

I wonder if it wouldn't make more sense to use a much more powerful one-time rocket to carry the probe to the asteroid belt, and then let the probe's own engine take over from there.
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Old 25th January 2019, 09:06 AM   #125
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Very nice work, dasmiller.

Originally Posted by theprestige View Post

I wonder if it wouldn't make more sense to use a much more powerful one-time rocket to carry the probe to the asteroid belt, and then let the probe's own engine take over from there.
We'd need more than a guess at what the actual engine performance is to answer that accurately. With assumptions being made lately in this thread the answer would likely be yes, use a traditional upper stage to get to the belt (or wherever). My assumption, however, is that this will never fly as is. To me there seem to be other engine designs in the works that would be a much better fit for this.
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Old 25th January 2019, 09:54 AM   #126
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Originally Posted by RecoveringYuppy View Post
Very nice work, dasmiller.
Thirded.


Could delta V be saved by some sort of harpoon for rendezvous, rather than expending propellant? Or is that just plain mental and would rip the probe apart/weigh too much/ be unable to fix to the asteroid/other obvious terminal problem that I haven't thought of?
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Old 25th January 2019, 10:06 AM   #127
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Originally Posted by 3point14 View Post
Thirded.


Could delta V be saved by some sort of harpoon for rendezvous, rather than expending propellant? Or is that just plain mental and would rip the probe apart/weigh too much/ be unable to fix to the asteroid/other obvious terminal problem that I haven't thought of?
Keep in mind the size of delta-v we're looking at. For example, to get 100 meters/second (which would make very little difference in the table), the harpoon will have to stop the spacecraft from ~200 mph, so it's a pretty substantial yank. Not necessarily impossible . . . long reel, big springs (yeah, yeah, you wouldn't actually use springs), but not pretty. And if the harpoon didn't 'take,' the satellite would still be going by at 200 mph so it probably wouldn't get a 2nd shot.

But less-ambitious harpoons may be the only way to keep you from simply drifting off some of the smaller asteroids.
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Old 25th January 2019, 10:13 AM   #128
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Some kind of grapple as a stationkeeping aid while in situ probably makes sense.
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Old 25th January 2019, 10:14 AM   #129
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Originally Posted by RecoveringYuppy View Post
Very nice work, dasmiller.
Thanks.

Quote:
We'd need more than a guess at what the actual engine performance is to answer that accurately. With assumptions being made lately in this thread the answer would likely be yes, use a traditional upper stage to get to the belt (or wherever). My assumption, however, is that this will never fly as is. To me there seem to be other engine designs in the works that would be a much better fit for this.
Yeah, any mission concept is going to be heavily dependent on what capabilities you assume and what mission you're trying to accomplish. In this case, the capabilities are extremely vague; I think one could plausibly argue for an Isp anywhere from 30 (demonstrated steam rockets) to well over 400 (if we consider the shuttle main engines to be 'steam' because they burn hydrogen with oxygen), and if we extend it to "what could we do with H20 as a reaction mass?" we might be able to get Isp much higher yet. And that's coupled with a vague mission, so the possibilities and possible constraints are all over the map.
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Old 29th January 2019, 09:55 AM   #130
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Originally Posted by dasmiller View Post
...and if we extend it to "what could we do with H20 as a reaction mass?" we might be able to get Isp much higher yet.
Someone go find Solomon Epstein and tell him to get off his lazy butt.
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