What's wrong with using a Lagrange point? The penalty is no more than tens of m/s, and that doesn't count any reduction in gravity losses through lower thrust requirements.
Let's say you have a spacecraft (MAVEN) and for whatever reason you want it to leave the vicinity of Earth on a specific date: December 7, 2013, no matter what.[...]The other requirements are that the trans-Mars burn (or at least the major part of the burn) occur on the day of launch, and that transits through the Van Allen belt should be minimize. This means that long duration parking orbits in LEO or HEO really aren't useful.
What I am looking for is to see if the spacecraft could be launched weeks or months ahead of time into a heliocentric orbit that would later intercept the Earth's orbit while the Earth is there, and use the gravity of the Earth for a swingby on December 7 2013 to go to Mars.
QuoteWhat I am looking for is to see if the spacecraft could be launched weeks or months ahead of time into a heliocentric orbit that would later intercept the Earth's orbit while the Earth is there, and use the gravity of the Earth for a swingby on December 7 2013 to go to Mars.No. It is not possible. In order to intercept the Earth again in such a short time, the aphelion must be small. This lacks the orbital energy required to reach Mars. An unpowered gravity assist will not help.You could use a powered gravity assist, but this will not save you any fuel compared to simply going straight for Mars on the desired date (either from LEO or from Earth's surface).
Maybe that's a good choice if the actual delta v requirements to enter and depart the LaGrange point is that low. And assuming that a return to the vicinity to Earth for a gravitation swingby could be achieved from that location.
I think you are getting close to nailing the problem
- since the requirement is for most of the trans-Mars burn to occur on the day of launch (for various reasons), then the duration of the loop away from the Earth will be a function of the magnitude of that burn. If the burn is Earth C3 + a small delta-v, yep, the aphelion will indeed be small.
So, the Earth swingby must incorporate a fairly significant burn to enable the spacecraft to actually get to Mars. This is not an "extra" burn in the sense of requiring more propellant than a direct injection to Mars on December 7 2012, but it does entail the risk of splitting the trans-Mars injection into two distinct burns, precisely what killed the Nozomi mission.
You could do a swingby from EML1/2 or, as Farquhar figured out, even more efficiently (but less flexibly as Kirk Sorensen pointed out) both an Earth and a moon swingby from SEL1/2.
What would you gain from the lunar swingby?
Quote from: Danderman on 03/07/2011 06:40 pmWhat would you gain from the lunar swingby?I got the impression the idea was to gain efficiency through use of two powered swingbys.
It appears that the Delta-V required to achieve EML1 or EML2 is fairly high for a direct injection (3.8 meters/second) - I am not sure how much of this could be recaptured after an Earth swingby for a Mars trajectory.
Quote from: Danderman on 03/07/2011 07:47 pmIt appears that the Delta-V required to achieve EML1 or EML2 is fairly high for a direct injection (3.8 meters/second) - I am not sure how much of this could be recaptured after an Earth swingby for a Mars trajectory.The injection into a fast transfer trajectory is a little under 3.2km/s while the injection into a slow one is a little over 3.2km/s. The fast trajectory requires a ~0.6km/s insertion burn, while the slow one doesn't require one at all, instead relying on perturbation of the transfer orbit by the Sun. After a 0.6km/s perigee lowering burn for the swingby you should recover the 3.2km/s over LEO orbital velocity at perigee. This suggests the penalty is ~0.6km/s and not the mere tens of m/s I mentioned above. Of course in the case of an MTV that still disregards the large savings of cycling between the edges of gravity wells instead ascending / descending them completely.EDIT: I suspect you could use the ballistic trajectory in reverse too, in which case the penalty should really be mere tens of m/s be zero(?), but at the cost of another 100 days travel time, which may or may not be an advantage for a manned mission. This would be similar to Farquhar's SEL1/2 scheme.
You can't use an unpowered gravitational assist to gain more orbital energy than you could have started with.
Quote from: IsaacKuo on 03/07/2011 05:04 pmYou can't use an unpowered gravitational assist to gain more orbital energy than you could have started with.Actually, it is possible and is done. Here's Wikipedia's explanation. Basically, viewed in the frame of the planet, the spacecraft's energy is conserved, and it arrives and departs at the same speed though different directions. In the sun's frame, however, the spacecraft can gain or lose energy. Energy is still conserved, because in the sun's frame the planet's speed changes a (very tiny) bit too.
Polar orbits are unable to use that extra bump from the earths rotation, and actually have to counter it. So yes you take a payload hit. But the name of the game is logistics, not the optimal launch profile. Antarctica would be darn expensive to operate out of.
Quote from: kevin-rf on 03/18/2011 04:02 pmPolar orbits are unable to use that extra bump from the earths rotation, and actually have to counter it. So yes you take a payload hit. But the name of the game is logistics, not the optimal launch profile. Antarctica would be darn expensive to operate out of. what about Ushuaia? It's got an airport, a deep water port and it's home to electronics manufacturing. They are also developing a deep space radar station around there.