Moon resonant orbits

Hop · 2005-04-03 21:03:27

It takes much less delta vee to capture incoming cargo to a long elliptical orbit than it takes to capture to a circular orbit. If the apogee is high enough, the perigee velocity is darn near escape velocity.

For capture the apogee needs to be within Earth's sphere of influence (SOI) which is about 922000 km altitude. But the apogee also needs to be low enough to avoid having the orbit destroyed by lunar perturbations. I've seen 1/2 lunar distance (LD) suggested for maximum apogee.

I don't like this limitation. Perhaps there are stable moon resonant orbits with higher apogees. The Hilda asteroids are in stable orbits resonant with Jupiter and Pluto is in a stable orbit resonant with Neptune. (Although some resonant orbits are decidedly unstable as evidenced by the Kirkwood gaps in the asteroid belt and also the gaps in Saturn's rings)

Here is a moon resonant orbit I like a lot but don't know if it's stable or unstable:
Period: 1/3 moon's period (about 9 days)
perigee: 300 km altitude
apogee: 356544 km altitude

The apogee would come close to the L3, L4 and L5 points, cycling through all three over a lunar period. So it could be a ferry between LEO and high orbital colonies. Fuel would be saved if radiation shielding, air, water, etc. don't need to be boosted each trip through the Van Allen belt.

But here's the best part: Capturing cargo and passengers incoming from Mars to this orbit at perigee would take only .49 km/sec delta vee. Ditto for sending stuff to Mars.

If near earth asteroids are mined for volatiles, metals, etc., these would be a good place to send these resources since they could be captured at perigee with relatively little delta vee.

If they served the L3, L4 and L5 points as I mentioned earlier, there could be three of them, spaced 120 degrees apart. So there are more launch windows.

But I don't known how stable this orbit it. If it's one of the decidedly unstable resonant orbits, then station keeping might well be too expensive. But I'm hoping it's a stable resonant orbit.

Martian Republic · 2005-04-04 09:07:41

We have had discussion over these topic before. The L1, L2, L3, L4, L5 points are supposedly the only really stable orbits in the immediate space around the Earth. Anything that is put in those places will stay there virtually forever, but they will drift out of those orbit eventually. I also understand that there are two more L points of 120 degrees ahead of the Earth and 120 degrees behind the Earth in it orbit around the sun too. That in relationship to the sun and the Earth orbit. I have not read this, but Mars probably has a 120 degree before and behind L points in it orbit around the sun too, that you could work with also. I’m sure there are other L points beside these too to work with in the solar system.

It was just an idea.

Larry,

Hop · 2005-04-04 10:30:06

Mars has Trojans
http://www.aas.org/publications/baas/v3 … 004/65.htm

The L points are the best known stable orbits but there are others. I've already given examples.

Although the L point orbits need little or no station keeping, they do not suit my purposes. To exploit the Oberth effect for delta v savings, the orbit should be fairly eccentric with perigee deep in Earth's gravity well.

RobS · 2005-04-04 10:44:39

Actually, L1 is NOT stable; objects placed at it (between the Earth and moon) will slowly drift away from it. However, I once saw somewhere that a delta-v of 30 meters per second is sufficient, as small bursts scatterred throughout the year, to keep something at the L1 point. That's only 60 miles per hour.

Hop, even if the orbits you propose are not perfectly stable--nothing is forever, anyway--perhaps they only require a low delta-v to cancel out orbital perturbations. That's the better question to ask. But I don't know how one would answer such questions!

-- RobS

Hop · 2005-04-04 13:26:20

Don't need an eternal orbit. An orbit with high apogee and low perigee that doesn't require a lot of delta vee to correct for perturbations would fill the bill.

BWhite · 2005-04-04 14:57:38

Can you suggest on-line research links for the "Oberth effect?"

Hop · 2005-04-04 17:45:05

Googling . . . huge pile of irrelevant stuff. Hmmm some interesting biographies of Hermann Oberth, rocketry pioneer . . . dammit.

Well I'll try to describe it. You get more bang for your buck if do your burn deep in a gravity well. Burns at periapsis are recommended.

Without earth's gravity, 3 km/sec a second is needed to leave for Mars from earth orbit. This 3 km/sec is called Vinfinity.

But 3 km/sec isn't your burn if you're leaving from Earth's gravity well. The burn is sqrt(Vinfinity^2 + Vescape^2) .

Concrete examples:

A burn for mars from LEO 300 km up:
Escape velocity's about 10.9 km/sec.
sqrt(3^2 + 10.9^2) = sqrt(9+118.8)=sqrt(130)=11.3 km/sec
Only .4 km/sec is needed in addition to escape velocity

A burn for Mars from GEO 36000 km up:
Escape velocity's about 4.3 km/sec
sqrt(3^2 + 4.3^2) = sqrt(9 + 18.5) = 5.2 km/sec
.9 km/sec is needed in addition to escape velocity.

A burn from 1 Lunar Distance, about 380,000 km
Escape is about 1.4 km sec
sqrt(9+1.96)=3.3 km/sec
Which is 1.9 km/sec past escape velocity.

If your apogee is really high and perigee very low, you'll be going almost escape velocity at perigee. For example the moon resonant orbit I was talking about with LEO perigee and apogee almost as high as the moon is moving 10.8 km/sec at perigee. Add .1 km/sec to get to 10.9 km/sec escape velocity and then with another .4 km/sec and you're on your way to Mars with a .5 km/sec burn.

BWhite · 2005-04-04 21:34:52

Aren't highly elliptical orbits also known as high energy orbits? Or did I pick that up wrong, somewhere?

Zubrin writes about a manuever known as the perigee kick with the orbit becoming more and more elliptical after every burn.

If your apogee is really high and perigee very low, you'll be going almost escape velocity at perigee. For example the moon resonant orbit I was talking about with LEO perigee and apogee almost as high as the moon is moving 10.8 km/sec at perigee. Add .1 km/sec to get to 10.9 km/sec escape velocity and then with another .4 km/sec and you're on your way to Mars with a .5 km/sec burn.

This seems to be the same idea.

The ingenious aspect of your idea is to look for a stable high energy orbit that passes through useful locations like L3, L4 and L5 and deploy a large station in that orbit. Tethers would allow you to snag low mass crew taxis rather like US Mail bags were once snagged by speeding locomotives.

Edited By BWhite on 1112672288

SpaceNut · 2005-04-05 05:43:19

And the momentum of the space mail bag would then be transferred up the tether to the station anchor point either breaking the anchor form the station or breaking the tether rope if the station is stationary. Now if one could store the energy on transfer of motion by spinning the station picking up small amounts of energy to keep it spinning then it might not break the tether or its anchor point. But you would need to match the station spinning speed.

Hop · 2005-04-05 15:39:04

Aren't highly elliptical orbits also known as high energy orbits? Or did I pick that up wrong, somewhere?
Zubrin writes about a manuever known as the perigee kick with the orbit becoming more and more elliptical after every burn.

Orbital energy is -Gm/2a

G is gravitational constant
m mass of central body
2a is the major axis of the ellipse.

So you see energy relies on length of ellipse and not it's shape. A circle orbit having radius a would have the same energy as a skinny ellipse having semi major axis a. It doesn't depend on eccentricity.

If you want to raise the apogee of an elliptical orbit, perigee burns are the best way to do it.

However if HEEO (highly elliptical Earth Orbit) ferries are possible, I don't propose they be built from Earth materials. Mined Asteroidal resources coming in on a hyperbolic trajectory with a near earth periapsis could be captured with very little delta vee to a HEEO.

BWhite · 2005-04-05 15:56:07

And the momentum of the space mail bag would then be transfered up the tether to the station anchor point either breaking the anchor form the station or breaking the tether rope if the station is stationary. Now if one could store the energy on transfer of motion by spinning the station picking up small amounts of energy to keep it spinning then it might not break the tether or its anchor point. But you would need to match the station spinning speed.

Bah! That is merely engineering.

Using 1960s technology fighter jets are arrested on aircraft carriers every day. We stop F-18s over distances measured in feet, or at least yards. With a 100 km tether there are lots of tricks to minimize shock loading.

Why would this be harder than building a space elevator? A lunar elevator (by the way) might not need carbon nanotubes to stay up.

However if HEEO (highly elliptical Earth Orbit) ferries are possible, I don't propose they be built from Earth materials. Mined Asteroidal resources coming in on a hyperbolic trajectory with a near earth periapsis could be captured with very little delta vee to a HEEO.

Suppose we move a nickel iron asteroid into a HEEO.

Deploy tethers to accelerate crew taxis and cargo to the HEEO and simultaneously deccelerate the Ni-Fe NEO to a lower orbit for easier mining and delivery to Earth.

If the Ni-Fe is headed for Earth anyway, so what if you subtract momentum from the NEO?

= = =

There is a whole Sci-Fi universe here, with the value of a Ni-Fe NEO augmented by its ability to transfer momentum to spacecraft in LEO, before slowed to a lower orbit and mined into oblivion. Then move a new Ni-Fe NEO into a HEEO.

Buy and sell momentum rights on the commodities market.

Edited By BWhite on 1112738426

Hop · 2005-04-05 18:52:02

Suppose we move a nickel iron asteroid into a HEEO.
Deploy tethers to accelerate crew taxis and cargo to the HEEO and simultaneously deccelerate the Ni-Fe NEO to a lower orbit for easier mining and delivery to Earth.
If the Ni-Fe is headed for Earth anyway, so what if you subtract momentum from the NEO?
= = =
There is a whole Sci-Fi universe here, with the value of a Ni-Fe NEO augmented by its ability to transfer momentum to spacecraft in LEO, before slowed to a lower orbit and mined into oblivion. Then move a new Ni-Fe NEO into a HEEO.
Buy and sell momentum rights on the commodities market.

If we moved a nickel iron asteroid into HEEO, I'd leave most of in HEEO. It'd be used to make the crew taxi that ferries crew from Low Earth Orbit to High orbital colonies like L4, L5 (and back again). The chief virtue of this metal, in my opinion, is that it's high on the slopes of Earth's gravity well, you don't have to pay a fortune to haul this up from earth's surface.

Same for volatiles mined from asteroids, sent to near earth space and caught in HEEO. Leave it in HEEO.

When it comes time to leave for Mars or elsewhere, send a crewed vehicle from the HEEO facility at perigee. All the fuel, metal, water, etc. in the vehicle would already have most the momentum it needs and a little kick from a tether would send it on it's way.

This would shed some of the HEEO ferry's momentum bringing down it's apogee. But you could compensate by tossing mass in the opposite direction to slow it down to a low earth orbit. There will be folks wanting to return to Earth as well as leave for Mars.

BWhite · 2005-04-05 19:30:14

I find this persuasive.

Currently 80% of a crewed Mars mission is fuel. 100MT in LEO means a 20MT lander to Mars per MarsDirect. Thus, an NEO in this HEEO has the potential to reduce Earth to Mars transit costs by somewhat less than 80%.

Cool!

= = =

Edit: Mine the NEO for PGMs using the carbonyl process and simply leave the Ni-Fe on the NEO to maintain momentum and mass.

= = =

Edit #2 - - Use an equatorial HEEO (close to zero inclination) that will assure the northern hemisphere nations (USA, Russia etc. . ) that there is no danger of a large NEO smashing into a city.

Edited By BWhite on 1112751209

Hop · 2005-04-09 13:21:43

Edit #2 - - Use an equatorial HEEO (close to zero inclination) that will assure the northern hemisphere nations (USA, Russia etc. . ) that there is no danger of a large NEO smashing into a city.

Some argue an increased awareness of NEOs combined with space travel abilities would drasticly reduce the chances of Chicxulub or even Tunguska class impacts.

This would be the case if humans were sane. But, IMO, exactly the opposite is true.

Here's a scenario: Al Queda Space Enterprises Ltd. is contracted to capture a nickel-iron NEO to Earth orbit. The accepted plan is to have a very near earth perigee to exploit aerobraking and the Oberth effect to shed velocity. But at the last minute the trajectory is somehow off by a fraction of a degree and aerobraking becomes lithobraking.

I advocate ceilings on the sizes of imports to near Earth space.

RobS · 2005-04-09 14:48:31

I doubt anyone will be allowed to aerobrake anything larger than, say, thirty meters across, and doubt even that will be allowed for a LONG time. I'd start people out aerobraking with Venus! Then mistakes don't hurt anyone, and Venus gets a small moon (very useful, since no one will ever walk on its surface; it'll be explored from orbit). If I want to put anything into Earth orbit I'd use Venus to slow the thing down and a gravity assist with the moon to put something into a very high orbit around Earth. I don't think elliptical orbits are stable long-term; no moons are in such orbits.

-- RobS

Hop · 2005-04-10 17:59:42

It depends on what the incoming cargo is. If it is a solid nickel iron shipment, maybe that's too high. If it's a loose, and airy it might be low. I believe we've already deorbited some structures larger than 50 meters, but they were hollow.

Tunguska was thought to be about 100 meters across.

If it's something that will burn up easily, the ceiling could be higher.

We've already practiced aerobraking in the earth's atmosphere with the Challengers. & we've used Mars' atmosphere to slow some of the spacecraft we've sent there. It is still a good idea to practice more aerobraking with Mars and Venus, maybe Titan.

The perigee of the ellipse needs to be above the atmosphere or it'll crash and burn after a few passes through earth's atmosphere at perigee. If aerobraking is used to capture an incoming load, another burn should be done at apogee to lift the perigee out of the atmosphere.

Whether or not all HEEOs are unstable to the point of requiring prohibitive delta vee station keeping expense is something I still don't know.

BWhite · 2005-04-10 18:50:44

Equatorial orbits mean the developed world is pretty much safe. It also means that equatorial nations would stand to benefit from their location as asteroids are digested and their materials returned to Earth.

If a large Ni-Fe asteroid were inbound for an equatorial orbit, to plane change away would require quite a substantial burn, no?

RobS · 2005-04-11 15:27:35

Hop, I agree; we would need different aerobraking regulations for different objects, depending on their density and intrenal strength.

-- RobS

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#1 2005-04-03 21:03:27

Re: Moon resonant orbits

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Re: Moon resonant orbits

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Re: Moon resonant orbits

#4 2005-04-04 10:44:39

Re: Moon resonant orbits

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Re: Moon resonant orbits

#6 2005-04-04 14:57:38

Re: Moon resonant orbits

#7 2005-04-04 17:45:05

Re: Moon resonant orbits

#8 2005-04-04 21:34:52

Re: Moon resonant orbits

#9 2005-04-05 05:43:19

Re: Moon resonant orbits

#10 2005-04-05 15:39:04

Re: Moon resonant orbits

#11 2005-04-05 15:56:07

Re: Moon resonant orbits

#12 2005-04-05 18:52:02

Re: Moon resonant orbits

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#14 2005-04-09 13:21:43

Re: Moon resonant orbits

#15 2005-04-09 14:48:31

Re: Moon resonant orbits

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