guest blogger john hare

When posting about capturing an asteroid using a Lunar gravity turn, I realized that there is a very useful orbit there that I had not heard of. A station in retrograde orbit at altitudes similar to the moon but just different enough not to impact has a number of very attractive features.

A vehicle coming in from Mars, Venus, an NEO, or any other point in the inner solar system can use a Lunar gravity turn to rendezvous with the station without burning propellant. Clever use of the incoming direction and angle of gravity turn can capture a vehicle with an Earth relative velocity between 1 and 3km/sec inbound. A vehicle coming in at 3km/sec times the approach to chase the moon in its’ orbit. The closing rate on the moon becomes 2 km/sec. With a 180 degree gravity turn, the vehicle is in a 1km/sec orbit Earth relative at Lunar altitude.

A vehicle coming in at 2km/sec Earth relative approaches the moon at 90 degrees to its’ direction of travel and uses a 90 degree Lunar gravity turn to reach the same retrograde orbit. Other incoming velocities will need other angles of approach to get the same result. The big penalty is that Earth approach must be done at exactly the right time of the Lunar month with very precise angles of approach.

Earth to Retro Station is a matter of using a TLI that will allow a 300m/s burn at perilune to put it into the retrograde orbit with the station.

The advantages to returning this way are that no heat shield is needed for the returning vehicles, the vehicles never see the high gee environment of a reentry, and that the complete vehicles are in a parking orbit that retains much of the energy for another mission. Heat shields can be attached at the station if the vehicle is to be sent on to Earth anyway, or just the crew and samples can be returned in a dedicated taxi vehicle.

The heat shield that is left behind is a massive payload boost when you do the numbers. 15% seems to be a common number thrown out for heatshield mass. A ton of vehicle returning from Mars will have 150 kg of heat shield. Propellant must be provided in Mars orbit to put the vehicle on TEI. Depending on the propellants and trajectories chosen, that propellant can mass twice that of the article being accelerated. In this case, that is 300 kg of propellant just to push the heat shield. That propellant must come from Mars, or even Earth itself if in situ propellants are not available. If from Earth, the heatshield and its’ Mars departure propellant mass 45% as much as the ship. Give any mission an additional 45% mass budget and serious value has been added. Or a launch tonnage 70% of the baseline mission for the same job.

For NEO sample return missions the gain is much higher. They must use propellant to rendezvous with the NEO as well as the Earth return boost. If it is a storable propellant and 5km/sec delta V, then a 65% gain is possible, or a ship 60% of the initial mass.

Since the Earth return vehicle need never see high gees, it can be built much lighter for zero gee work only, or have a tether based artificial gravity that doesn’t have to be discarded before reentry. If manned, the vehicle doesn’t need to be able to protect the crew from acceleration with special couches and whatnot.

With the vehicle stopped in a parking orbit with the station, it can be refueled and retasked and sent again. There is no need to build another vehicle and lift it out of Earths’ gravity well for the next job. These vehicles could fly dozens of operational missions for decades with a little maintenance, propellant, and upgrades as the technology requires. Voyagers and Pioneers have lasted a while with no hands on in space.

Leaving the station has some interesting characteristics also. A small burn sends a vehicle toward the Lunar intercept point where a gravity turn can send the vehicle to Earth or an interplanetary trajectory with only stationkeeping propellant. The interplanetary trajectory starts with 3km/sec Earth relative, which should get the vehicle to Mars, Venus, or several other interesting places, again with just stationkeeping propellant.

If these numbers are right, then this would be a path more useful for an interplanetary cycler for convenience and ability to support it than the orbits normally suggested.

#### johnhare

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Can you actually get that much of a trajectory change without impacting the surface? I don’t have time to model typical trajectories to check, but a 3 km/s nearly-180 degree turn seems a bit on the high side, unless the moon were a superdense object. Escape velocity from the surface is only 2.4 km/s after all.

Does this manoeuvre work with low thrust spacecraft, such as those powered by electric propulsion and solar thermal rockets?

Doug,

All the trajectory changes are at 2 km/s, though sometimes that will be 3 km/s Earth relative. I don’t know for absolute certain that I am right. I think that the implications of this idea, if I am right, make it worthwhile for me to find out. Next time I have enough free time, I am going to dig more references out of storage so I can nail this down.

This thought series is interesting enough to me that I think I will look for a reference on orbital mechanics. Right now I am going by half remembered scenerios by others. Any suggestions on a reference that a semiliterate redneck could understand?

A_M_,

With the reservations brought up by Doug, it should work with vehicles with just enough propulsion to maintain some very precise trajectories. So yes, providing that your navigation is nearly perfect.

Sorry for the intrusion, as this is somewhat OT:

Glenn Reynolds at Instapundit gives propellant depot/orbital infrastructure a plug (via Rand Simberg).

http://pajamasmedia.com/instapundit/85211/

I was going to reply to this yesterday, but I thought I better check my references to be sure. It is not possible to get a full 180 degree gravity turn from a hyperbolic trajectory. The basic relationship is this: sin(delta/2) = 1/e, where e is the eccentricity of the orbit, and delta is the turn angle (angular separation between the incoming and outgoing asymptotes). Solving for delta gives: 2*arcsin(1/e). A parabolic trajectory (e=1) would theoretically give a full 180 degree turn, but to pull that off your incoming spacecraft would have to be approaching at a velocity which exactly matches the heliocentric velocity of the moon. For a hyperbolic trajectory: e = 1+(r[per] v[inf]^2)/mu^2, where r[per] is the radius of perapsis, v[inf] is the incoming/outgoing velocity (i.e. far away), and mu = G*M is the standard gravitational parameter.

So, you will still need some form of propulsive braking to get a body to swing into your retrograde orbit. I’m not certain at the moment, but I think doing so would actually cost you more propellant than just trying to capture into a prograde orbit. If I get some time, I’ll see if I can work through a couple of permutations on this idea to see how much heliocentric delta-v can be extracted from a spacecraft by doing a lunar flyby.

This is very cool, if it is indeed workable. The economic implications of it are much bigger than just saving some mass/fuel. I’ve long believed that an incremental building of infrastructure, gradually going from LEO to L1 or LLO and then to Luna, and incorporating space stations and cyclers along the way as profit centers, learning opportunities, waystations, and stepping-off points for the next expansion.

Building a chain of space stations & cyclers to the Moon before going to Mars makes much more economic sense given the scenario outlined above. I’m going to presume there is an orbit or set of orbits wherein this proposed retro-orbiting station can be made to synchronize (at low delta-v) with a cycler to earth. Unfortunately I am not enough of an orbital mechanician to know what those might be. Anyone see a reason such things might not be feasible?

Eric,

You are right about the 180 not working. About mid-morning I suddenly realized that an escape orbit cannot possibly close to less than 180 because then it would be an orbit instead. Construction people look at you funny when you mention orbits while pouring concrete. The potential mission architecture improvement, if something along these lines can be done, is downright useful. I will find some numbers on the possibilities, for this is information that could be used in the near term without a lot of hardware development. If we can get even 135 degrees of turn, it would help a lot.

It will take some number games to find out if we could use an Earth gravity turn at any Lunar cycle point to line up a Lunar 90 degree to retrograde capture. I intend to look at other numbers to see about tiny peregee burns during that manuever to get the energy down.

If this general concept of leaving the heatshield and its’required propellant at home can be developed, then some really tiny cubesat NEO explorers would be a good place to test the technology.

This manoeuvre will need a name.

Having to make 2 or 3 turns to get the delta-v is not a major problem, it will just require skilled navigation.

On trips from Mars there are several weeks to get the speed right so high levels of accuracy are available.

For naming, if this manuever is actually useful, experts on three continents probably have it calculated to twenty decimal points already. I won’t get time for serious numbers for a while, but in the meantime I am quite sure that a 2.3 km/s capture can be done with a slightly modified scenerio. I’m going to look for some sort of Mars mission plan to see what effect this all would have.

One thing against it is that Mars propellany could be used during a perigee burn to capture to an eccentric Earth orbit. Mass of propellant appears to be similar to mass of heatshield, except that the propellant wouldn’t have to be carried both ways.

I’ve run this a couple of times, and I’m getting very small turn angles for the lunar flyby. I still have a couple of permutations to try out though. Perhaps it would help to include a LEO flyby as well.

If the returning spacecraft using propellant rendezvous with an Earth lander like the Orion or Dragon capsule at L1/L2 it can be made reusable by refuelling the spacecraft. We do not have the technology to make high orbit heatshields reusable without major repairs.

How small are the turn angles at what velocity? An LEO flyby would certainly help navigation and timing and would reduce required Lunar angles to 90 degrees. Obviously I still haven’t done any hard numbers yet.

The propellant rendezvois with LEO flyby offers an alternative that might be more feasible than the orriginal concept. I’m thinking on it.

This manoeuvre will need a name.

Having to make 2 or 3 turns to get the delta-v is not a major oroblem, it will just require skilled navigation.

On trips from Mars there are several weeks to get the speed rifht so high levels of accuracy are available.;

From solar orbits smaller than Earth’s orbit, a 1AU aphelion means Earth overtakes them, and a 180 turn puts them into a prograde orbit.

It is only from solar orbits bigger than Earth, where approaching orbits are at perihelion, overtaking Earth. Then a 180 turn puts them in a retrograde orbit.

We were looking at Earth/moon retrograde. Everything would still be solar prograde.

The 180 turns out to be wrong, still trying to see how much of the concept is valid, if any.

I’m getting turn angles much smaller than one degree for incoming velocity of 2km/s and perilune distances of 2000km. Unfortunately, no small changes in these numbers make much of a difference. I’ll try to put up a Google spreadsheet later with my calculations if anyone cares to check my results.

I’m amazed that turn angles could be that small. I’m going to go into denial here and try to game some part of the idea to try to salvage something. The only thing I can think of offhand is closing the perilune to 2,000m instead of 2,000km, though very small mistakes lead to a higher crater supply.

While I accept that you are usually right, and probably are again, I’m still looking for a way out. It would be so danged useful, though possibly like antigravity.

@Abramian

In comment #13 your point appears to have got lost. You have simply ended up reproducing my comment #8 with spelling mistakes.

Just checking – are the turn angles genuinely small? Or does the spacecraft go into a very long ellipse?

A 2000 m perilune will definitely increase the crater count since the mean radius of the moon is 1738 km.

The reasons for the small turn angle is that: a) the moon’s gravity well is fairly shallow, and b) you are passing through that gravity well very quickly. A satellite in a 2000 km orbit around the moon would only have an orbital velocity of about 1.5 km/s relative to the moon. An incoming spacecraft on a Hohmann transfer from Mars would have a relative velocity of about 3500 km/s relative to the Earth. Even if you timed it with the full moon, the velocity of the spacecraft with respect to the moon would still be about 2500 km/s. And that’s just the initial closing speed. Keep in mind that the spacecraft will also be accelerating under the influence of the moon’s gravity as it approaches perilune.

I think you have dropped a decimal point or two

3,500Km/sec is about 1% of lightspeed

we are talking about a Mars return not extrasolar!

What if you had a form of propellentless propulsion. That only needed solar power to operate.

Paul

Other than solar or laser sail, I’m not sure that exists.