IMFD From Europa to Earth

[ADSWNJ]

You are right to think that the slingshot program is the solution. I recorded a quick video showing you how to do it, but my mic was on "mute" :facepalm: (Not the first time this happens).

Still you will be able to see the setup. Try it and come back with any questions you might have.

Orbiter 2010 Europa to Earth with IMFD (Direct) - YouTube

Perform the first correction when you are outside of Jupiter's SOI.

I would really love to see you redo this video with your commentary. I have played with both TransX and IMFD in the past to do simple maneuvers and hops from one planet to another. Never done a slingshot or an aerobrake, etc. I would love to understand this tool through your commentary and see how you explain each of the values you are manipulating.

 

[C3PO]

My disagreement with Tommy is about a single burn solution for a Moon→Mars journey, where I claim that using one burn to drop to low perigee and escape wastes fuel.

That may be true for Europa --> Earth but I'm not convinced it's better for Earth -->Mars. Europa orbits deep in Jupiter's massive SOI, but that's not the case with the Moon. If you look at OrbitMFD when you are at Europa's Sma but not close to it, more than 99.5% of the gravity is from Jupiter. But if you do the same in Earth orbit, 67% of the gravity is from the Sun.

This means that you enter Earth's SOI as you drop in from lunar orbit. Relative to the Sun, the Moon's orbital speed isn't that much different to the Earth's, but the Earth's mass should give you a good slingshot as you arrive from (almost) outside it's gravity well. Additionally you can utilize the Oberth effect by doing a part of the burn at periapsis as you swing by the Earth.

 

[dgatsoulis]

That may be true for Europa --> Earth but I'm not convinced it's better for Earth -->Mars. Europa orbits deep in Jupiter's massive SOI, but that's not the case with the Moon. If you look at OrbitMFD when you are at Europa's Sma but not close to it, more than 99.5% of the gravity is from Jupiter. But if you do the same in Earth orbit, 67% of the gravity is from the Sun.

This means that you enter Earth's SOI as you drop in from lunar orbit. Relative to the Sun, the Moon's orbital speed isn't that much different to the Earth's, but the Earth's mass should give you a good slingshot as you arrive from (almost) outside it's gravity well. Additionally you can utilize the Oberth effect by doing a part of the burn at periapsis as you swing by the Earth.

Yes, but then we are not talking about a single burn solution.

Just to throw in some numbers:

For a heliocentric transfer orbit from Earth's orbital distance to Mars' orbital distance that costs 2.8 km/s (pretty close to a Hohmann transfer) the single burn solution for the Injection ΔV from a Low Lunar Orbit (10 km alt) is ~1.7 km/s


For the same transfer, the most efficient 2 burn solution is this:

1st burn from LLO ~0.85 km/s with the vector opposite of the moon's orbital path to drop to a perigee of ~150 km. (the Geocentric trajectory is still an elliptical orbit, with the apogee at the moon's distance and the perigee at 150km above the surface of the Earth).
At perigee the velocity of the ship would be ~10.9 km/s

The velocity needed for a 2.8 km/s heliocentric transfer orbit at 150 km alt above Earth's surface is the square root of the square of the escape velocity of that altitude plus the square of the transfer orbit ΔV.

So the ΔV for the second burn is Vinj - Vpe = 11.4-10.9=0.5 km/s

Total ΔV = 0.85+0.5=1.35 km/s saving ~0.35 km/s from the single burn solution.

In theory there is an even cheaper 3 burn solution, but it's not practical for the Earth Moon system, since the apogee of the first burn is higher than Earth's SOI.
The way to do it is to go to a high apoapsis in the first burn, there make a second retrograde burn to lower the periapsis and then the third burn at periapsis for the injection.

This kind of solution is better suited for more massive planets. It worked great for flytandem in a Titan→Saturn→Jupiter→Earth flight. You can find the thread here.

 

[C3PO]

You could add all the DV in the Lunar ejection burn. That would mean that the Geocentric transfer orbit would have a apogee higher than the Moon's orbit. But that would be less efficient then the 2 burn solution.

 

[dgatsoulis]

You could add all the DV in the Lunar ejection burn. That would mean that the Geocentric transfer orbit would have a apogee higher than the Moon's orbit. But that would be less efficient then the 2 burn solution.

Not only that. Even for single burn solutions, every single burn solution that doesn't have the moon's orbital altitude as the perigee of the Earth escape trajectory is going to be inefficient.

It's as simple as this: The best time to raise your apoapsis is when you are at periapsis. In this case we want to raise our apoapsis to a hyperbola, but the same rule applies.

 

[Max Pain]

Just to throw in some numbers:

For a heliocentric transfer orbit from Earth's orbital distance to Mars' orbital distance that costs 2.8 km/s (pretty close to a Hohmann transfer) the single burn solution for the Injection ΔV from a Low Lunar Orbit (10 km alt) is ~1.7 km/s


For the same transfer, the most efficient 2 burn solution is this:

1st burn from LLO ~0.85 km/s with the vector opposite of the moon's orbital path to drop to a perigee of ~150 km. (the Geocentric trajectory is still an elliptical orbit, with the apogee at the moon's distance and the perigee at 150km above the surface of the Earth).
At perigee the velocity of the ship would be ~10.9 km/s

The velocity needed for a 2.8 km/s heliocentric transfer orbit at 150 km alt above Earth's surface is the square root of the square of the escape velocity of that altitude plus the square of the transfer orbit ΔV.

So the ΔV for the second burn is Vinj - Vpe = 11.4-10.9=0.5 km/s

Total ΔV = 0.85+0.5=1.35 km/s saving ~0.35 km/s from the single burn solution.

Very nice! I think I have to learn TransX in order to do such maneuvers. Ever since I read the Rolling Stones, I wanted to do such a thing in Orbiter.

 

[Tommy]

Not only that. Even for single burn solutions, every single burn solution that doesn't have the moon's orbital altitude as the perigee of the Earth escape trajectory is going to be inefficient.

It's as simple as this: The best time to raise your apoapsis is when you are at periapsis. In this case we want to raise our apoapsis to a hyperbola, but the same rule applies.

Yes, the single burn plan is like in your diagram above (like used in the Moon - Mars tutorial. One thing to keep in mind is that when using a planetary swingby to leave one of it's moons, we aren't using a gravity assist to increase our velocity. It only changes the direction - not the magnitude. Also, the Earth - Moon combo is unique in this solar system, it is the the only moon that is a truly significant fraction of it's planets system mass. With the other planetary systems, none of the moons (or even all of the moons combined) account for any really significant part of the system's mass.

Now, I haven't tried with a Moon - Venus trip, so I can't say that your single burn "direct" solution isn't more efficient than a single burn "sling" solution. I have tried the Moon - Mars flight several times and can say that the sling solution is rarely more expensive and often less expensive. Wat I say from here applies ONLY to the Moon - Mars trip (but may apply for other trips from the Moon to other planets - haven't tried it yet).

I suspect there are two slight errors in your thinking. For one, any burn capable of escaping the moon with any noticeable residual velocity will provide enough dV to get to Mars. This is true for both direct and sling methods - so there is no difference in the dV for the Lunar Ejection - which also serves as the Transfer burn. While the Moon does have a small velocity (wrt the Sun compared to the Earth) this is actually excess velocity. It won't make the trip cheaper - but could make it faster (without increasing burntimes). At least on paper, which brings us to the second possible error.

From your remarks, you appear to be taking a two dimensional approach. This can cause some problems - especially with Mars as the target.

The Moon's plane is quite low inclination (wrt the ecliptic), while Mars has a fairly high RInc. So unless you are using a source plane transfer - or an offplane transfer that will intercept Mars very near a node (between the target plane and the ecliptic) any velocity you inherit from the Moon won't be aligned with the transfer plane.

You can get a bit of plane change (ecliptic) by using a high lunar inclination for your Lunar ejection plane, but not much. This will likely mean an expensive plane change (wrt Sun) component built into the ejection burn, or a plane change during the transfer. The first will make the Lunar ejection
much less efficient, and the second makes the MCC more expensive.

We can, however, use the sling around the Earth to provide the plane change for us, for free.

In short, adjusting the inclination of your Lunar Ejection plane will have very minor effect on your plane wrt the ecliptic, but can have a major effect on your sling plane wrt the Earth. Adjusting the inclination of the Earth Sling/Ejection Plane can have a much more significant effect on your plane wrt the ecliptic.

As with all flights, no single solution is ALWAYS best. Moon - Mars direct will be best once in a while, but Moon - Earth - Mars sling will be best most of the time.

And, of course, other multi burn solutions will almost always be even better!

 

[dgatsoulis]

@ Tommy

Please look at the pic again.

There is a fundamental flaw in the method you propose.
You are not thinking about the direction the excess velocity relative to the Moon is applied. There is no case that you go from the initial green orbit to the red "direct sling" trajectory and not waste fuel relative to the "direct" method. Period.

Yes my example was "two dimensional", but only to simplify the calculation. As you saw I used a 1.7 km/s example for the ΔV needed to eject from the Moon, which in itself embeds a typical large plane change (~30°). The ideal burn with no plane change is about 1.52 km/s from a 50 km circular orbit around the Moon.

The worst case scenario, where a 90° plane change is needed, requires an ~1.9 km/s ejection burn from the same (50 km) altitude lunar orbit. Comparing the worst "direct" case (90° plane change) to the best "direct sling" case (no plane change) and there is still a difference of at least 250 m/s for the ejection burn.

The numbers above are for a 2.8 km/s ΔV Earth-Mars transfer (oV in Course\Target intercept program).

As with all flights, no single solution is ALWAYS best. Moon - Mars direct will be best once in a while, but Moon - Earth - Mars sling will be best most of the time.

No, dropping to a low perigee -without using a two burn solution- will ALWAYS be worse than leaving directly from the Moon's orbital altitude.

I guess we could settle this with an IMFD scenario in Orbiter.

When you find the time, place a DG anywhere you want on the Moon, setup a Mars transfer and post the IMFD plan with your "direct sling" method, dropping to a low perigee and escaping Earth. (Left MFD course\target intercept program, right MFD Slingshot program).
According to you, it should look something like the pic above. Please also post the ΔV you needed to make the ejection burn from lunar orbit and the altitude of that orbit.

I submit to you that within the same lunar month from your ejection burn, (either a few days before of a few days after), there will be a much cheaper single burn solution that will leave directly from the Moon's orbital altitude, will have approximately the same TOF and will look similar to this: