### Author Topic: Orbital mechanics: Delta-vee vs. Mission duration  (Read 8948 times)

#### JohnFornaro

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##### Orbital mechanics: Delta-vee vs. Mission duration
« on: 12/15/2010 03:01 PM »
Over on the Appropriations thread was an interesting sidetrack on a subject which interests me a great deal:

BTW, it has been said, and quite correctly, that once you are docked at EML-2, you are literally halfway to nearly any location in the solar system. It is the perfect location for earth departure and arrival spacecraft on interplanetary missions.

That's not what I learnt from orbital mechanics. You want departure and arrival for interplanetary missions to have as low a perigee to Earth as possible, not way up there at EML-1 or EML-2.

From Zubrin's presentation to the Augustine Committee.

First, the civilities:  To Steven.  Ahhhh.  So that's what you meant when you said "From Zubrin's presentation".  [Inside joke, very lame.]

The first thing which interests me a great deal is mission duration.  One of the quiet assumptions of the HEFT presentation is that the six month space trip is actually doable.  What is it that astros do do on their trip?  Play video games?  Watch the stars?  [Alpha Centauri just moved a tenth of an arcsecond...]  I've suggested one working alternative:  A six month orbiting mission to thouroughly map every square inch of the Moon's surface.

The other thing is delta vee.  A subject near and dear to my heart, but one which I have not yet gone out on a date with.  [If I can switch similies.]  I've taken the liberty of parsing out the interesting sidetrack on delta vee here:

That map doesn't show EML-1 or 2. They're about 3.8 & 3.5 km/s from LEO respectively, and about 0.75 from either to Mars orbit.

Sure it's slightly more delta-v than from LEO (0.35 km/s), but you get to assemble &/or fuel much closer (in delta-v) to your destination, and have much more frequent departure windows.

Obviously, I don't quite get orbital mechanics:

From:
http://en.wikipedia.org/wiki/Delta-v_budget#Interplanetary

From LEO to Mars Transfer Orbit: 4.3 km/sec
LEO to EML-1: 3.77 km/sec

Steven's chart seems to indicate LEO to Mars surface at 3.9 km/sec?  What is it that I'm not getting here?

Part of it [my confustion] is that orbital mechanics is too complex to be expressed as a simple table, and part of it is that neither really define their terms. So, they are likely talking about two very different initial LEO orbits (with different inclinations and/or altitudes), and two different transfer trajectories (with different transfer times)...

That's not what I learnt from orbital mechanics. You want departure and arrival for interplanetary missions to have as low a perigee to Earth as possible, not way up there at EML-1 or EML-2.

To get from EML1 to a circular LEO orbit takes ~4 km/sec. About .7 km/sec to drop and then a 3.2 circularization burn at perigee.

But with no circularization burn, you're moving 10.8 km/sec at perigee, just under escape. From this speed another .5 km/sec suffices for Trans Mars Insertion.

The path from EML1or2 does exploit the Oberth effect and EML1or2 is much, much closer to Mars than LEO.

Here is a EML1 to LEO:

See how the orbit with an EML1 apogee is moving ~3 km/sec faster than LEO?

Here is LEO to Mars:

and here is EML1 to Mars:

My models (as well as some other models) assume circular, coplanar orbits. So they ignore the plane changes mandated by inclined orbits. However, plane changes are less expensive when apogee is high, another argument for EML1 and EML2.

One advantage of EML assembly for BEO missions is that hardware can be accumulated at the EML over time, using lower delta -v slow boat trajectories from LEO to the EML point. Solar ion is one option however single impulse ballistic trajectories would not require new propulsion technologies.

A Mars departure from EML-2 would also see a double gravity assist, first via lunar fly-by then an Earth fly-by then on to Mars.

Couldn't a returning trip from Mars also employ an Earth fly-by (combined with a touch of aerobraking?) to slow the transit habitat before arrival at EML-2?

Yes. Only .5 km/sec burn and/or aerobraking would suffice to drop the hyperbolic to an eccentric elliptic with an EML1 or 2 apogee. Then a .65  burn to circularize at EML1 -- but this apogee burn can't be aided by aerobraking. I still haven't grokked paths to EML2 so I won't comment on that.

Sure it's slightly more delta-v than from LEO (0.35 km/s), but you get to assemble &/or fuel much closer (in delta-v) to your destination, and have much more frequent departure windows.

How is it more frequent? You're in a 28 day orbit around Earth which means you are restricted to launch in a window of 18 hours every 28 days (assuming you've budgeted for a 10 degree difference in launch angle). In LEO, your launch opportunity is once every 90 minutes over a period of 10 days for the same 10 degree angle.

Steven's chart seems to indicate LEO to Mars surface at 3.9 km/sec?  What is it that I'm not getting here?

That chart is by Zubrin, not by me. The delta-V from LEO to Mars varies with the launch opportunity (due to Mars being in quite an elliptical orbit) and the required transit time and entry speed at Mars. For example, a minimum delta-V of 3.5 km/s is available in 2033 with a 180 day transit and 6.2 km/s entry speed. In 2024 the delta-V is 4.1 km/s for a 180 day transit and 7.8 km/s entry speed. Read the paper Trajectory Options for Human Mars Missions for more information.

To get from EML1 to a circular LEO orbit takes ~4 km/sec. About .7 km/sec to drop and then a 3.2 circularization burn at perigee.

But with no circularization burn, you're moving 10.8 km/sec at perigee, just under escape. From this speed another .5 km/sec suffices for Trans Mars Insertion.

The path from EML1or2 does exploit the Oberth effect and EML1or2 is much, much closer to Mars than LEO.

You're assuming that the Mars hardware appears at EML-1 for free, when in fact the Mars hardware will appear first at LEO. From your figures:

LEO to Mars: 3.6 km/s
LEO to EML-1 to Mars: 3.1+0.65+0.65+0.5 = 4.9 km/s

No.

Reinserting context:

BTW, it has been said, and quite correctly, that once you are docked at EML-2, you are literally halfway to nearly any location in the solar system. It is the perfect location for earth departure and arrival spacecraft on interplanetary missions.

That's not what I learnt from orbital mechanics. You want departure and arrival for interplanetary missions to have as low a perigee to Earth as possible, not way up there at EML-1 or EML-2.

Clongton correctly noted that once you're at EML-1 or 2, you're much closer to nearly any location in the solar system. You differed with this noting perigee burns deep in a gravity well are advantageous for interplanetary trips.

You seemed to be assuming that interplanetary routes from EML1 would do their perigee burns at EML1. This is wrong.

How you get to EML1 is irrelevant to Clongton's assertion. Once again:

BTW, it has been said, and quite correctly, that once you are docked at EML-2, you are literally halfway to nearly any location in the solar system. It is the perfect location for earth departure and arrival spacecraft on interplanetary missions.

Bolded the part you seemed to have missed.

Actually Clongton is underestimating the advantage of EML 1 or 2. Earth's surface is 14 km/sec from Trans Mars Insertion. EML1 or 2 is 1.2 km/sec from Trans Mars Insertion. Given that propellent fraction rises exponentially with delta V budget, I would say EML1 or 2 is 95% of the way there.

As for where propellent and consumables come from? Lunar volatiles are much closer to LEO and EML1 than earth's surface.

Red lines indicate possible one way aerobraking paths that save propellent.

If propellent and consumables come from the moon, you need only loft the dry mass of the MTV from earth's surface. You wouldn't need a 188 tonne to LEO HLV (Ares V). Nor would you need a 130 tonne to LEO HLV (the current pork frenzy). A 70 tonne to LEO HLV would do quite nicely.

LEO to Mars transfer orbit has a delta v requirement of 4.3 km/s.

LEO to EML1 to C3 to Mars transfer orbit has a delta v requirement of 4.51 km/s (3.77+0.14+0.6)

Not that much of a difference.

If you have a single propellent source, you don't get to break the delta V budget in chunks. Since all your propellent must be lifted on or above the first stage, all the parts must be summed to a total delta V budget. As your total delta V budget rises, your total mass at lift off rises exponentially

Total mass/dry mass = e^(dV/Ve)

This rises exponentially with dV.

There is a story of a Krishna who made a wager with a king over a chess game. Should the king lose he would give Krishna one grain of rice on the 1st square, two grains on the second, four grains on the third and doubling each subsequent square.  [King lost because of exponential growth.  Illustration parsed out.]

Now if your propellent is oxygen and hydrogen, each 3 km/sec is a square on the chess board.  Say you need 9 km/sec to reach orbit and then another 6 km/sec to reach a moon.

With no propellent depots, all the propellent must be carried aboard at lift off. Your delta V budget would be 15 km/sec. Your total mass to dry mass ratio would be 2^5.

Now, given a depot in orbit, that's propellent that doesn't need to be carried at lift off. This breaks the exponent in the rocket equation. Instead of 2^5, you have two legs, one 2^3 and other leg is 2^2.

32 vs 8 and 4.

A propellent source on your chess board square lets you start over with 1 grain of rice.

The object is not to save propellent but to simplify the rocket. As dry mass fraction shrinks, it becomes harder and harder to make the rocket engine and other components light enough. So dry mass must be discarded along the way. This is expendable stages. More stages means more complexity and failure modes.

red lines are possible one way aerobraking paths that save propellent.

As you can see the moon is much closer to LEO than earth. The ships transporting lunar propellent to LEO and EML1 could be much simpler than ships from earth's surface.

Given propellent depots in LEO, this vastly changes interplanetary trips. Instead of a 14 km/sec trip, you have 10 km/sec hop and a 4 km/sec hop.

It's about 4 km/sec from LEO to EML1. It's also about 4 km/sec to Mars. So what's the point in stopping at EML1? If your Mars Transfer Vehicle (MTV) is making a one way trip, there is no point.

However Mars Semi Direct (MSD) calls for an Mars Transfer Vehicle/Earth Return Vehicle (MTV/ERV) that carries earth propellent aboard for the return trip.

From earth's surface it's total delta V budget is around 16 km/sec.  A propellent depot in LEO would make this 10 and 6.  A propellent depot in LEO and EML1 would make it 10, 4 and 3.

A naive person might conclude a 4 km/sec hop and 3 km/sec hop is worse than one 6 km/sec trip. But these two hops give a propellent fraction that enables a much less ambitious ship than a 6 km/sec vehicle.

It is also worth noting the possibility an MTV can load up on consumables as well as propellent at EML1. Air to breathe, water to drink as well as water for radiation shielding. This could be 30 tonnes for the MSD MTV.

Sorry for continuing this off-topic discussion. This will be my last post on the subject.  [No, no.  Say more.  Please?]

You seemed to be assuming that interplanetary routes from EML1 would do their perigee burns at EML1.

No, I did not make that assumption, as you would see from the calculation I presented previously.

LEO to EML-1 to Mars: 3.1+0.65+0.65+0.5 = 4.9 km/s

LEO to TLI:    3.1  km/s
TLI to EML-1:  0.65 km/s
EML-1 to TEI:  0.65 km/s
TEI to TMI:    0.5  km/s <-- Burn is at 185 km altitude above Earth.

Quote
How you get to EML1 is irrelevant to Clongton's assertion.

I disagree. How you get to EML-1 is completely relevent. The Mars hardware for the forseeable future will orginate on Earth and not from any other place. That means you need 3.75 km/s to go from LEO to EML-1, compared to 3.5 to 4.1 km/s to go to directly to Mars from LEO. For Mars missions where TMI is less than 3.75 km/s, there is no advantage in going to EML-1.

Quote
Actually Clongton is underestimating the advantage of EML 1 or 2. Earth's surface is 14 km/sec from Trans Mars Insertion. EML1 or 2 is 1.2 km/sec from Trans Mars Insertion. Given that propellent fraction rises exponentially with delta V budget, I would say EML1 or 2 is 95% of the way there.

Assuming a TMI delta-V from LEO of 3.5 to 4.1 km/s (depending in window), then I calculate 1.0 to 1.6 km/s from EML-1 and 0.6 to 1.2 km/s from EML-2 using a Lunar flyby.

Quote
If propellent and consumables come from the moon, you need only loft the dry mass of the MTV from earth's surface. You wouldn't need a 188 tonne to LEO HLV (Ares V). Nor would you need a 130 tonne to LEO HLV (the current pork frenzy). A 70 tonne to LEO HLV would do quite nicely.

How do you figure that? I have done an analysis of a reusable system of sending propellant from the Moon to LEO. It unfortunately did not work (I got negative stage masses) as you need 3.1 km/s from the Moon, a heavy re-entry shield and then 6.3 km/s back to the Moon (and that was leaving the re-entry vehicle in LLO). I expect an expendable system may work, but that will require both propellant and stage manufacture on the Moon, which is way way out in the future.

You need 3.55 km/s to get to EML-2. That's only a 0.55 km/s saving for a worst case TMI delta-v of 4.1 km/s. For a 61 t payload at 4.1 km/s, I get an initial mass of 180.6 t (4531 m/s exhaust speed, 0.233*mp^0.844 stage mass model). At 3.55 km/s, the initial mass is 155.0 t, a reduction of only 14% plus you then need to build up all the infrastructure on the Moon to carry the remaining propellant to EML-2. How much is all that going to cost?
Sometimes I just flat out don't get it.

#### MikeAtkinson

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##### Re: Orbital mechanics: Delta-vee vs. Mission duration
« Reply #1 on: 12/15/2010 03:49 PM »
How do you figure that? I have done an analysis of a reusable system of sending propellant from the Moon to LEO. It unfortunately did not work (I got negative stage masses) as you need 3.1 km/s from the Moon, a heavy re-entry shield and then 6.3 km/s back to the Moon (and that was leaving the re-entry vehicle in LLO). I expect an expendable system may work, but that will require both propellant and stage manufacture on the Moon, which is way way out in the future.

Assume a stage which can do 7.3km/s (hard but doable) with 10 tonnes of payload. Start at L1, fully fuelled + 10 tonnes extra fuel, do powered insertion into LEO, offload the 10 tonnes of fuel and pick up 10 tonnes of payload, return to L1. From L1 to the lunar surface use a similar scheme. This works but is hopelessly uneconomic (unless you assume that fuel on the lunar surface is free and the lunar lander can make thousands of trips without replacement).

#### MikeAtkinson

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##### Re: Orbital mechanics: Delta-vee vs. Mission duration
« Reply #2 on: 12/15/2010 03:58 PM »
The first thing which interests me a great deal is mission duration.  One of the quiet assumptions of the HEFT presentation is that the six month space trip is actually doable.  What is it that astros do do on their trip?  Play video games?  Watch the stars?  [Alpha Centauri just moved a tenth of an arcsecond...]  I've suggested one working alternative:  A six month orbiting mission to thouroughly map every square inch of the Moon's surface.

You do not need astros to babysit a camera system, you don't need any at all. They would be just as bored (the view would soon get tiring), and are doing it for no useful purpose. A high resolution mapping satellite is probably 1% of the cost of a manned mission and would be more effective because it would be a more stable platform.

#### Jorge

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##### Re: Orbital mechanics: Delta-vee vs. Mission duration
« Reply #3 on: 12/15/2010 04:33 PM »

The first thing which interests me a great deal is mission duration.  One of the quiet assumptions of the HEFT presentation is that the six month space trip is actually doable.  What is it that astros do do on their trip?  Play video games?  Watch the stars?  [Alpha Centauri just moved a tenth of an arcsecond...]

The working assumption at NASA is that the crew would spend the outbound leg doing most of their mission training, and the return leg doing debriefs, mission analyses, and reports.
JRF

#### MikeAtkinson

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##### Re: Orbital mechanics: Delta-vee vs. Mission duration
« Reply #4 on: 12/15/2010 04:44 PM »
Missions from L1/L2 can make sense, but the reason is not delta-v.

Imagine this thought experiment. Suppose the best trajectory from LEO to Mars goes through L2 (it doesn't in the general case but just for the sake of argument assume it does). Then stopping at L2 takes extra delta-v for manoeuvring and station-keeping at L2 (not much but greater than zero), therefore the delta-v is always going to be more staging at L2.

So why stage at L2.

Firstly, you can stage and leave some of your mass behind (which can be reused).

Secondly, if you are doing powered flight to Mars and back (no areocapture) then returning to L2 means that you don't need to go back into the Earth's gravity well for the trans-hab and rocket stage. They can then be reused more easily (at least in terms of IMLEO).

If NTR is being used you may not want to bring a NTR stage back to LEO.

Nuclear electric and solar electric propulsion have too low a thrust to be used manned from LEO. You need to stage somewhere so the crew can come aboard.

Potentially lunar derived fuel can be used. In my opinion it is going to be very difficult to produce fuel on the Moon and deliver it to L2 at a cheaper price than it can be delivered from the Earth. For it to make a material difference either the cost of developing and manufacturing space hardware has to fall considerably compared to launch costs or there are large increases in total budget.

Getting back to the title of this thread. If it is desired to reduce the mission duration then the advantages of L2 are generally diminished because of the greater total delta-v. The one exception I can see is where electric propulsion is used, then it still makes sense to stage at L2.

#### mmeijeri

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##### Re: Orbital mechanics: Delta-vee vs. Mission duration
« Reply #5 on: 12/15/2010 04:49 PM »
Another advantage of Lagrange points is that you can use smaller transfer stages as well as prepositioning cargo and propellant by SEP. This would reduce IMLEO, not increase it. This is part of what the Huntress IAA study advocates.
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#### JohnFornaro

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##### Re: Orbital mechanics: Delta-vee vs. Mission duration
« Reply #6 on: 12/15/2010 04:53 PM »
You do not need astros to babysit a camera system, you don't need any at all.

Sometimes I just flat out don't get it.

#### Cog_in_the_machine

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##### Re: Orbital mechanics: Delta-vee vs. Mission duration
« Reply #7 on: 12/15/2010 04:55 PM »
The first thing which interests me a great deal is mission duration.  One of the quiet assumptions of the HEFT presentation is that the six month space trip is actually doable. What is it that astros do do on their trip?  Play video games?  Watch the stars?  [Alpha Centauri just moved a tenth of an arcsecond...]

Try sample return from the target, also testing radiation protection, life support and other necessities for 6 month missions in space, that aren't close enough to Earth for resuply. Oh wait, it doesn't involve the moon in any way, so naturally this means it's not worth it. And it's not that easy to make fun of it, so naturally you don't bring it up.

Quote
I've suggested one working alternative:  A six month orbiting mission to thouroughly map every square inch of the Moon's surface.

There are no samples to be gained from this mission, there is no incentive to build a spacecraft capable of surviving 6 months in space with minimal or no resupply and the astros would just be dead weight. An orbital satellite doesn't need a crew to scan the surface for 6 months.
Isn't LRO already scanning for resources anyway? According to wikipedia, it has two instruments designed to do the manned mission you propose:
- LAMP—The Lyman-Alpha Mapping Project will peer into permanently shadowed craters in search of water ice, seeing by the ultraviolet light from stars and the interplanetary medium.
- LEND—The Lunar Exploration Neutron Detector will provide measurements, create maps, and detect possible near-surface water ice deposits.

Unless a more thorough analysis is needed, I don't see why this mission is necessary, much less why it should be manned.
^^ Warning! Contains opinions. ^^

#### JohnFornaro

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##### Re: Orbital mechanics: Delta-vee vs. Mission duration
« Reply #8 on: 12/15/2010 04:59 PM »
But there's another thing: If six months in space is an option on the table, then six months in space should be an option for any BEO mission.  Spend six months building that EML1 or EML2 station.  This pushes the question to:  What are we getting for that six months?

As to the training/debriefing workloads; fine in principle.  But those details sound pretty sketchy to me, at least today.

And backing up to the mapping mission.  The astros would also determine which areas require more human attention.
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#### JohnFornaro

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##### Re: Orbital mechanics: Delta-vee vs. Mission duration
« Reply #9 on: 12/15/2010 05:15 PM »
(1) Try sample return from the target, also testing radiation protection, life support and other necessities for 6 month missions in space, that aren't close enough to Earth for resuply. Oh wait, it doesn't involve the moon in any way, so naturally this means it's not worth it.

(2) And it's not that easy to make fun of it, so naturally you don't bring it up.

Quote
I've suggested one working alternative:

(1) There are no samples to be gained from this mission,

(3) there is no incentive to build a spacecraft capable of surviving 6 months in space with minimal or no resupply and the astros would just be dead weight.

(4) An orbital satellite doesn't need a crew to scan the surface for 6 months.

(5) Isn't LRO already scanning for resources anyway?

(6) Unless a more thorough analysis is needed, I don't see why this mission is necessary, much less why it should be manned.

(1) The map is "news you can use" to for outpost planning.  Sample return would require a lunar lander, which I arbitarily left out of the initial suggestion.  The manned mission could feature a small re-usable lander which would bring the astros samples from areas that they determined to be interesting.  Trades, trades, trades.  The mission certainly would test radiation, life support, etc.  My initial idea was to compare as many apples to apples as is possible for the two missions.  Thus, I set equal the time component.

(2) Wrong, wrong, wrong.  We already know it's made of cheese.  Who cares if it's camembert or wensleydale?  Besides it's just a big rock.  And we already use terrrestrial ice for our drinks.

(3) The mission is the incentive, in both cases.

(4) Already smacked forehead.  Different misson.  The way I would proceed is to consider the lunar mission trades first as equivalents in mission duration and expected cost.  Cost would be the driver, and the lunar mission could be shorter in the first approximation.  What is the value of either mission, after as much as can be made equal is made equal?

(5) Up to a point.

(6) Same holds true in spades, clubs, hearts, and diamonds for HEFT.
Sometimes I just flat out don't get it.

#### Jorge

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##### Re: Orbital mechanics: Delta-vee vs. Mission duration
« Reply #10 on: 12/15/2010 05:54 PM »
But there's another thing: If six months in space is an option on the table, then six months in space should be an option for any BEO mission.  Spend six months building that EML1 or EML2 station.  This pushes the question to:  What are we getting for that six months?

As to the training/debriefing workloads; fine in principle.  But those details sound pretty sketchy to me, at least today.

I don't have time to write a dissertation for you, so it will necessarily be sketchy. Onboard training technology is being developed and used extensively for ISS, both to reduce the duration of the ground training flow and to keep crewmembers current on knowledge and skills they may not have practiced since launch. It will be a mature technology by the time we start BEO missions. Crews will be doing self-study and group simulations onboard.
JRF

#### mmeijeri

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##### Re: Orbital mechanics: Delta-vee vs. Mission duration
« Reply #11 on: 12/15/2010 05:57 PM »
By the way, isn't that exactly what happens on an aircraft carrier or submarine?
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#### Cog_in_the_machine

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##### Re: Orbital mechanics: Delta-vee vs. Mission duration
« Reply #12 on: 12/15/2010 05:59 PM »
(1) The map is "news you can use" to for outpost planning.  Sample return would require a lunar lander,

Not if you're going to a NEO, which is what the HEFT mission is suggesting and what I was referring to. I wasn't talking about sample return from the Moon.

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The manned mission could feature a small re-usable lander which would bring the astros samples from areas that they determined to be interesting.

So it went from "orbital resource mapping" to "landing people on the surface" "orbital resource mapping + sample return" all of a sudden? I'm confused. Sample return was already done from the Moon anyway, so developing a small lander just for this seems redundant. The space scientists would place more value on samples returned from a NEO.

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(2) Wrong, wrong, wrong.  We already know it's made of cheese.  Who cares if it's camembert or wensleydale?  Besides it's just a big rock.  And we already use terrrestrial ice for our drinks.

Again, wasn't referring to sample return from the Moon.

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(3) The mission is the incentive, in both cases.

Not in the case of the one that would orbit the Moon. Resupply via craft from Earth would be easier, because a ship orbiting the Moon would be more accessible than one that would be sent to that NEO (I forgot which one they chose). I.e. you can overcome potential technological limitations, with logistics solutions (resupply of the lunar orbiting craft) instead of technological solutions.
I'm not sure if I'm explaining my reasoning on this clearly.

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(6) Same holds true in spades, clubs, hearts, and diamonds for HEFT.

It doesn't. If LRO is indeed already mapping lunar resources, the justification for another lunar resource mapping mission is non-existent. Further, even if LRO's resource mapping data isn't satisfactory, any further mission would likely be another robotic probe with better instruments, not a crewed probe. Manned recon satellites are antiquated concepts nowadays, remnants from the days when electronics and computing were faultier. Remember one time you asked if Moore's law is a load of hooey? It isn't. No mission planner would propose a manned data gathering orbiter today, because robotic ones have become better at the task.

HEFT on the other hand outlines a mission that has never been done before. I'll elaborate in my reply to these points:

But there's another thing: If six months in space is an option on the table, then six months in space should be an option for any BEO mission.

BEO missions that last that long haven't been done yet, that's why this kind of duration isn't an option for every BEO mission yet. There needs to actually be a mission that establishes what it takes to last that long in space, before planning missions with such durations becomes more routine. This is NASA after all, we know how big they are on safety.

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Spend six months building that EML1 or EML2 station.  This pushes the question to:  What are we getting for that six months?

This is a policy issue.
Right now it's not clear what exactly it would take to pull off a mission with such duration in the first place, which is a technological issue.

Zubrin and others think there are no issues that are show stoppers, but far as I can tell, NASA planners are not convinced.

Current policy seems to be pushing for this 6 month mission, in the hopes that potential technological uncertainties will be addressed, i.e. what could be gained from the 6 month mission, is the ability do a 6 month mission in the first place.

That's my understanding anyway. I'm not sure I can explain the reasoning better.

Edit to correct spelling error and a misunderstanding on my part.

Final edit:
I figured out why I keep misunderstanding you. You're attempting to make a mission to a NEO and a mission to the Moon seem as similar as possible and as a result, coming up with these really baffling ideas. Developing a small lander, just for a token sample return mission from the Moon and coupling it with a manned resource mapping probe, orbiting the Moon for 6 months? This just makes no sense. No such mission will ever fly. You've created this entire unworkable scenario, just so you can "compare apples to apples", except of course you assert that in your scenario the astronauts would be doing something more productive. Sorry, this is just wrong. Like it or not, a mission to the Moon and a mission to a NEO will ultimately be different, both in execution, drawbacks and benefits.
Serves me right for thinking you might be trying to propose a sensible mission to the Moon, as opposed to just creating Moon first rationalizations again. I won't bother any more. Promote your so called mission all you want.
« Last Edit: 12/15/2010 10:01 PM by Cog_in_the_machine »
^^ Warning! Contains opinions. ^^

#### Jorge

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##### Re: Orbital mechanics: Delta-vee vs. Mission duration
« Reply #13 on: 12/15/2010 06:27 PM »
By the way, isn't that exactly what happens on an aircraft carrier or submarine?

Yes. The Navy knows how to keep its crews sharp at sea; NASA can use the same techniques.
JRF

#### Hop_David

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##### Re: Orbital mechanics: Delta-vee vs. Mission duration
« Reply #14 on: 12/15/2010 06:52 PM »

Assume a stage which can do 7.3km/s (hard but doable) with 10 tonnes of payload. Start at L1, fully fuelled + 10 tonnes extra fuel, do powered insertion into LEO, offload the 10 tonnes of fuel and pick up 10 tonnes of payload,

Depending on how much aerobraking you can get way with, up to 3.2 km/sec can be shaved off the down trip. So round trip may be as low as 4.2 km/sec.

I envision unmanned ACES 71 propellent tankers. Dry mass 5.5 tonnes, 71 tonnes propellent, if I remember right. And going back up empty for the trip back to EML1. If aerobraking is used, an ablation shield should be added to that 5.5 tonne dry mass.

return to L1. From L1 to the lunar surface use a similar scheme. This works but is hopelessly uneconomic (unless you assume that fuel on the lunar surface is free and the lunar lander can make thousands of trips without replacement).

I'll have to revisit how much propellent it takes to deliver lunar reaction mass to LEO. I don't believe thousands of trips are needed.

#### Hop_David

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##### Re: Orbital mechanics: Delta-vee vs. Mission duration
« Reply #15 on: 12/15/2010 07:41 PM »
You seemed to be assuming that interplanetary routes from EML1 would do their perigee burns at EML1.

No, I did not make that assumption, as you would see from the calculation I presented previously.

LEO to EML-1 to Mars: 3.1+0.65+0.65+0.5 = 4.9 km/s

LEO to TLI:    3.1  km/s
TLI to EML-1:  0.65 km/s
EML-1 to TEI:  0.65 km/s
TEI to TMI:    0.5  km/s <-- Burn is at 185 km altitude above Earth.

While the above is correct, you also made this statement:
That's not what I learnt from orbital mechanics. You want departure and arrival for interplanetary missions to have as low a perigee to Earth as possible, not way up there at EML-1 or EML-2.

I guess you could get pedantic and say a drop from EML2 burn precedes an earth departure burn. But Clongton's assertion remains essentially correct. (except he's underestimating the advantages of EML1-2)

How you get to EML1 is irrelevant to Clongton's assertion.

I disagree. How you get to EML-1 is completely relevent.

This is the statement you were disagreeing with:
BTW, it has been said, and quite correctly, that once you are docked at EML-2, you are literally halfway to nearly any location in the solar system. It is the perfect location for earth departure and arrival spacecraft on interplanetary missions.

This statement you were disagreeing with stipulates you're already there. Once you're there it's easier to get other places. Is this correct or not?

The Mars hardware for the forseeable future will orginate on Earth and not from any other place. That means you need 3.75 km/s to go from LEO to EML-1, compared to 3.5 to 4.1 km/s to go to directly to Mars from LEO. For Mars missions where TMI is less than 3.75 km/s, there is no advantage in going to EML-1.

Assuming no delta V past TMI is needed.

If propellent is needed for EDL, or if the MTV loiters in LMO and then returns to earth using onboard propellent, there is a large advantage.

Additionally, it's possible consumables of lunar origin can be provided at EML2. Air to breathe. Water to drink. Water for radiation shielding. This could easily be 30 tonnes.

Quote
Actually Clongton is underestimating the advantage of EML 1 or 2. Earth's surface is 14 km/sec from Trans Mars Insertion. EML1 or 2 is 1.2 km/sec from Trans Mars Insertion. Given that propellent fraction rises exponentially with delta V budget, I would say EML1 or 2 is 95% of the way there.

Assuming a TMI delta-V from LEO of 3.5 to 4.1 km/s (depending in window), then I calculate 1.0 to 1.6 km/s from EML-1 and 0.6 to 1.2 km/s from EML-2 using a Lunar flyby.

Yeah, that sounds right.

Quote
If propellent and consumables come from the moon, you need only loft the dry mass of the MTV from earth's surface. You wouldn't need a 188 tonne to LEO HLV (Ares V). Nor would you need a 130 tonne to LEO HLV (the current pork frenzy). A 70 tonne to LEO HLV would do quite nicely.

How do you figure that? I have done an analysis of a reusable system of sending propellant from the Moon to LEO. It unfortunately did not work (I got negative stage masses) as you need 3.1 km/s from the Moon, a heavy re-entry shield and then 6.3 km/s back to the Moon (and that was leaving the re-entry vehicle in LLO). I expect an expendable system may work, but that will require both propellant and stage manufacture on the Moon, which is way way out in the future.

Using EML1 or EML2 as midway stopping points, total delta V budget is busted into smaller hops.

Round trip delta V to EML1 is 5 km/sec. For the full tanker portion of this round trip, only 2.5 km/sec is needed. After delivery to EML1, some would be left at EML1 and some would go on to LEO.

For round trip delta V between EML1 and LEO, I get 7.6 km/sec. Up to 3.2 km/sec of that may be done with aerobraking. Aerobraking would save using propellent for the heavy tanker down leg portion. Then the 3.8 up leg need only be for an empty tanker.
« Last Edit: 12/15/2010 07:46 PM by Hop_David »

#### Steven Pietrobon

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##### Re: Orbital mechanics: Delta-vee vs. Mission duration
« Reply #16 on: 12/16/2010 04:24 AM »
This statement you were disagreeing with stipulates you're already there. Once you're there it's easier to get other places. Is this correct or not?

It depends. If you're bringing your own propellant its definitely not easier (since the total delta-V is higher). If bringing propellant from the Moon, especially for use at Mars, then it might be easier (since you need to develop the archicture for delivering propellant from the Moon).

Quote
Assuming no delta V past TMI is needed.

If propellent is needed for EDL, or if the MTV loiters in LMO and then returns to earth using onboard propellent, there is a large advantage.

I hadn't thought of that! I think perhaps a better profile is to assemble the Mars spacecraft and EDS in LEO and fire the EDS so that its apogee is below the Moon's orbit. That way, only a 3.1 km/s inital EDS burn is required. We're not wasting delta-v going into EML-1 or EML-2 and then back out again on the large Mars spacecraft. Around the same time the reusable Lunar tanker takes off from the Moon and goes into the same elliptical Earth orbit as the Mars spacecraft. The Lunar tanker delivers LOX from the Moon for use in TMI at perigee, Mars landing, Mars liftoff (if ISRU is not used) and TEI. The EDS transfers LH2 so the tanker can return to the Moon and lift-off again (assuming that H2O is too difficult to extract).

I studied something similar called Lunar orbit propellant transfer.

Quote
Using EML1 or EML2 as midway stopping points, total delta V budget is busted into smaller hops.

Round trip delta V to EML1 is 5 km/sec. For the full tanker portion of this round trip, only 2.5 km/sec is needed. After delivery to EML1, some would be left at EML1 and some would go on to LEO.

For round trip delta V between EML1 and LEO, I get 7.6 km/sec. Up to 3.2 km/sec of that may be done with aerobraking. Aerobraking would save using propellent for the heavy tanker down leg portion. Then the 3.8 up leg need only be for an empty tanker.

Crunch the numbers and let me know what you find out.
« Last Edit: 12/16/2010 04:26 AM by Steven Pietrobon »
Akin's Laws of Spacecraft Design #1:  Engineering is done with numbers.  Analysis without numbers is only an opinion.

#### JohnFornaro

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##### Re: Orbital mechanics: Delta-vee vs. Mission duration
« Reply #17 on: 12/16/2010 03:14 PM »
From Thunderdome:  Two men enter.  One man leaves.  We have two missions of the same duration and the same cost.  One mission is more useful than the other.

And it's not that easy to make fun of it [the Moon, that is], so naturally you don't bring it up.

Wrong, wrong, wrong.  We already know it [the Moon, that is] is made of cheese.

Again, wasn't referring to sample return from the Moon.

I submit that you're self-confusing.

Quote
So it went from "orbital resource mapping" to "landing people on the surface" "orbital resource mapping + sample return" all of a sudden? I'm confused.

I know.  I'm not going to compel you to understand what I'm talking about.  But there's hope:

Quote
You're attempting to make a mission to a NEO and a mission to the Moon seem as similar as possible and as a result, coming up with these really baffling ideas.

That's correct.  If the concept of six months in space, without the need for resupply is feasible to consider at all, then it can be considered for any BEO mission.  "Any" mission is not "all" missions.  Think "vacation", for a moment.  If one wanted to visit Pago Pago for six months, one would take everything with one that one would need for the stay.  If one wanted to visit Newyork Newyork for six months, one would take everything with one that one would need for the stay.  The "distance" between the two destinations is relatively independent of the supplies one would need at either of the two destinations in order to survive the specified vacation time.

In this vacation/mission comparison, if one wanted to argue that toothpaste was available in Newyork but not in Pago, and point to that as some sort of justification for preferring one vacation/mission to another, it would be a mistaken justification.  Unless the toothpaste were a type of unobtanium, absolutely necessary to any vacation/mission.  That is not the case.  Either destination, the asteroid or the Moon, over the time frame suggested, would require the same amount of Tang and T-shirts and Toothpaste and other comnsumables.

This thread has, if I have my way, two purposes:  A thorough discussion of orbital mechanics (OM).  A thorough discussion of mission duration (MD) and how best to utilize that duration.

As a part of MD, Jorge's observation that the journey should not be a problem with either mission, rings true.  Submarine experience and ISS experience are existential proofs of the ability to deal with that duration of journey, given a habitable environment.

Certainly, the astros would have to train on the way to the NEO.  I would suppose some sort of immersive 3D virtual experience, designed to test the landing and sampling techniques as thoroughly as is practicable, realizing that the actual experience will differ in unknown ways.  So I can readily grant that the outboard trip to the NEO might very well have more work, less idle time.

Whatever the line item costs of this virtual training soft and hard ware is, will be subsumed in the total NEO mission costs.  The two missions would be compared dollar for dollar.  It's not clear to me that the three month return would be completely taken up by debriefing.  Would they have an on board lab to assay the several kilos of samples?  How much work could they do in that lab?

On the OM side: How you get to EML-1 or EML-2 is relevant, as Steven points out, but there is a time component to the relevancy.  Today's way [from Earth] is the only way.  But tomorrow's way [from Moon] certainly seems to be the better way.

Wherever one is going from either of these departure points, one is tanked up and ready to go.  The hydrogen filled Macey's gorilla in the room is, where did that propellant come from, the Earth or the Moon?  Assuming plenty of manufacturing and launch services from either propellant origin for the moment; by the delta vee numbers alone; the Moon would make a better source of propellant for that Mars mothership.

Since today, we can safely assume plenty of earthside manufacturing of propellant, and some ability to launch that propellant, this is the only available source.  The delta vee component of the comparison, how the propellant gets to either L point is relatively unimportant.  Today.

Tomorrow's way of say, getting to Mars, is the subject currently at hand.  Steven is discussing, and I sorta get, some of this.  But I think the delta vee component isn't completely accounted for.  Assuming that the Lunar Orbit Propellant Transfer (LOPT) can be made to happen:  What is the delta vee budget for developing that architecture?  That should be compared to the delta vee budget for bringing up every gallon of prop from the Earth's surface.

At first, it probably makes sense to bring it from Earth.  But where's the crossover point in the delta vee amortization curve of the two scenarios of fueling that Mars mothership?  And where exactly is it assembled?  And where is it tanked up?  And where does it depart from?
Sometimes I just flat out don't get it.

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