Moon to Mars trip, beneficial to perform TMI burn in LEO?

[Marijn]

On a Dutch forum, I got myself into a discussion about the question whether it is a good idea to travel to LEO from the moon on a trip to Mars. The alternative is a direct trajectory from the moon to Mars. Which of these is the most efficient?

The idea for a detour to a low earth orbit is that it would be beneficial to perform the TMI burn in LEO to take advantage of the Oberth effect and/or use a gravity assist. The advantages should outweigh the cost of the detour to LEO.

But I am not sure whether this is true.

Should I keep pushing this idea or did I make a mistake?

 

[Urwumpe]

Well, you can calculate it.

Coarsely done:

C3=0 to Mars means 0.6 km/s difference. You always need it.
You need 2.80 to get from lunar surface to C3=0

Thus, in sum: 3.4 km/s if you start from the lunar surface.

You need 2.74 to get from lunar surface to LEO
You gain about 3.1 km/s by staying in lunar transfer orbit
You need 3.22 to get from LEO to C3=0
Again, the 0.6 km/s are needed to get to Mars.

Means: ~3.5 km/s for getting from lunar surface to Mars via LEO.

So, yes, it doesn't sound too bad at first iteration, but likely not worth the increased travel time.

It will look much worse, if you assume, that the spacecraft is assembled in lunar orbit with components from Earth and Moon.

 

[Marijn]

Ok, thanks for doing the calculation. I am not sure how the C3 works. I will read up on it.

It will look much worse, if you assume, that the spacecraft is assembled in lunar orbit with components from Earth and Moon.

Just to be sure, you mean that going back to the earth is not the best way to go to Mars from the moon?

 

[Urwumpe]

Just to be sure, you mean that going back to the earth is not the best way to go to Mars from the moon?

Yes, I think that the coarse advantages look too small to really expect some big improvements there, when calculating accurately.

And then, if you assume that the spacecraft is assembled in DRO instead of lunar surface, with critical parts being made on Earth, the whole economy looks far worse, since you could use WSB transfers to further reduce DV compared to a Oberth maneuver.

Still, it only makes sense with a lunar surface base. transporting all goods from Earth wouldn't work out.

 

[jedidia]

and/or use a gravity assist.

Since the moon is already orbiting the earth, there's really not much to be gained by a gravity assist, I think.

 

[Marijn]

And if earth would have a bigger mass. Like 5 earth masses or so. Would that change the outcome of this question becuase the gravity assist would be more productive?

---------- Post added at 04:27 PM ---------- Previous post was at 04:24 PM ----------

Since the moon is already orbiting the earth, there's really not much to be gained by a gravity assist, I think.

My discussion partner said that a gravity assist would not be possible because you haven't reached escape velocity yet. But I don't think that's true. The effect is perhaps small, but not impossible. Right?

 

[Urwumpe]

My discussion partner said that a gravity assist would not be possible because you haven't reached escape velocity yet. But I don't think that's true. The effect is perhaps small, but not impossible. Right?

No, the effect is zero then. gravity assist works by adding a part of the velocity of the planet to you in solar frame of reference. Relative to the planet, you leave the planet with the same velocity as you entered it.

So, by flying past Earth within Earths frame - which velocity would you like to add? There is none (Frame of reference moves with the planet!). A gravity assist around the moon is possible, but not very powerful.

If you leave Earth for mars, the velocity of Earth is already added to your excess velocity to become your initial velocity vector in the solar frame.

 

[Marijn]

Crap. I got everything wrong.. :blink:

 

[Urwumpe]

This drawing explains it pretty well, maybe a bit of German doesn't distract too much:

 

[Marijn]

This drawing explains it pretty well

Thanks, I'll study it.

 

[BrianJ]

You might find this old thread interesting.....
https://www.orbiter-forum.com/showthread.php?p=64936&postcount=5

Also, you might like to have a look at the Japanese "Nozomi" probe. Although it used an Earth->Moon->WSB->Moon->Earth(powered flyby)->Mars sequence:

http://areology.blogspot.com/2007/08/

Cheers,
BrianJ

 

[jedidia]

Crap. I got everything wrong.. :blink:

Don't worry, it's a very common misconception. A gravity assist provides energy by the gravity of a body pulling you along with its motion. All velocity you gain from simply falling towards a body you lose again when falling away from it (in other words, it doesn't change the sum of your kinetic and potential energy, merely converts one into the other).

It's only the body's motion that passes energy to you. Or takes some away, depending on how you approach it.

 

[Urwumpe]

It's only the body's motion that passes energy to you. Or takes some away, depending on how you approach it.

And you take the energy away from the planet or give energy to the planet. Every gravity assist with Jupiter makes Jupiter approach the sun by a atom diameter or so...

 

[jedidia]

And you take the energy away from the planet or give energy to the planet.

Well, "passing on" and "taking away" are terms that imply change of ownership...

 

[Marijn]

So, basicly, you can't do a gravity-assist using the body you're currently orbiting.. Only bodies which you are not orbiting. Is that a correct statement?

 

[Urwumpe]

Well, "passing on" and "taking away" are terms that imply change of ownership...

Well, practically it is, at least in a civil law kind of way. This small difference between owner and possessor... You can own a car, but you can not possess it...

In this case, energy changes the possession... but it is really doubtful Jupiter ever was the legal owner of it.

 

[jedidia]

Just as well. I would hate humanity getting sued by the planetary collective for energy theft! :rofl:

So, basicly, you can't do a gravity-assist using the body you're currently orbiting.. Only bodies which you are not orbiting. Is that a correct statement?

Yup, pretty much. If that statement were not true, it would mean that we could gravity-assist ourselves out of orbit without using any engines...

 

[Tommy]

Performing the Moon - Earth - Mars trajectory can be more fuel efficient than Moon - Mars direct. The "slingshot" around the earth doesn't provide any gravity assist, but the Oberth effect still applies.

Assuming the force is applied in the same direction as the displacement (distance),as it is in a prograde burn then Power=Force * (Distance/time). This means that increasing Force or Distance increases Power, as does reducing Time.

What this means for us is that the higher your velocity during the burn (thus increasing the distance traveled in a given time period) the shorter the burn can be while still producing the same amount of Power.

In simplest terms, it is more efficient to change the magnitude of your velocity vector when speed is high, and the law of inertia makes it more efficient to change the direction of you velocity vector when your speed is low.

For Maximum efficiency, you would want the Earth Periapsis to be as low as possible (to ensure the highest speed) and as close to the ejection point as possible. Also, the plane of the Moon- Earth transfer(as referenced to Earth) needs to be as close as possible to the ejection plane.

IMFD is not well suited to setting up this plan. I've had some luck by "eyeballing" the moon's position relative to the Earth and leaving the Moon when it is between the Earth and the Sun, Setting up the off-axis transfer in [Course], setting [Slingshot] to "plan", and using manual RCS planar adjustments just inside the Earth's SOI in order to minimize the EIn shown in [Slingshot]. it may be easier to make that MCC by using [Slingshot]'s burn view to reduce the DvI and Dvp.

---------- Post added at 05:49 AM ---------- Previous post was at 05:36 AM ----------

Well, practically it is, at least in a civil law kind of way. This small difference between owner and possessor... You can own a car, but you can not possess it...

Possesion is to have access to, and control of an object. Ownership means having the legal right to possess said object.



You can own and/or possess a car, but possessing a car you don't own is called Grand Theft Auto.

 

[jedidia]

possessing a car you don't own is called Grand Theft Auto.

I thought it was called marriage! :lol:

 

[Urwumpe]

Possesion is to have access to, and control of an object. Ownership means having the legal right to possess said object.

You can own and/or possess a car, but possessing a car you don't own is called Grand Theft Auto.

No, not at all, its way more complex. For example, if you rent a car - you don't own it. You simply possess it. If your rented car is stolen, the new possessor does not legally have it. But you are not the one damaged there - the car was stolen from the legal owner, who permitted you to possess it. :tiphat: