not exactly sure where to ask it so i will ask it here.
I am going to be talking to my physics students about using EML-1 as a hypothetical spot to build a spacestation and then launch a probe to mars. To get the probe to mars do they do a small burn to get it into a large elliptical orbit around earth (apogee of EML1 distance and perigee altitude of about 200km(?) ) and then do a burn at perigee to get the probe into the earth mars transfer orbit?
is 1) this right way to do it..
The answer here is "it depends".
If your probe has a very weak but high-Isp engine (IE Solar Electric Propulsion, like Dawn
), then your probe doesn't want to struggle out of Earth's gravity well. Dawn only fired it's SEP once Delta II had injected it past escape velocity.
This mode would also work spiralling away from EML, after you'd perhaps used a chemical stage to deliver your probe to the Moon, though the Dawn mode (chemical injection past escape, then SEP in interplanetary space) is probably better.
If your probe has a powerful rocket engine, then you get an advantage from the Oberth effect if it perform it's TMI burn as close as possible to the Earth. If it starts in the vicinity of the Moon, a relatively small burn will leave the Moon and put the probe into an elliptical orbit that has it's perigee at LEO. The Oberth benefit at perigee when it does the TMI is bigger than the cost of the departure burn from the Moon.
But, it's worth noting that EML is not a free lunch. Imagine your spacecraft was launched through TLI, but the Moon happened to be in the wrong part of the sky. The s/c would end up in an elliptical orbit around the Earth with it's apogee near the Moon's orbit and it's perigee at LEO. The s/c could perform it's TMI burn at any subsequent perigee and gain the Oberth benefit mentioned above.
In order to go to EML you need to add some velocity to circularise the orbit. Then, you need another burn to reverse that and leave EML again, and further dV to reduce the orbit's perigee down to LEO, and that's just to put you back into essentially the same orbit
you were in just after you'd finished TLI. That's quite a lot of extra dV, and is badly counter-productive if all the manoeuvres are performed by a single stage. Far more efficient if your stage just performs a simple TMI directly from LEO immediately after it's launched, exactly like all current Mars missions have done.
To get any benefit from EML you need a more complicated mission plan - some form of assembly of components:-
A chemical stage that boosts your stage through TLI, docks and gets refueled at EML, before leaving, reducing perigee and performing TMI (via the Lunar flyby).
Or, the probe and it's TMI stage delivered separately to EML, docking together and then performing TMI. This mode would work for either a chemical or SEP TMI stage.
As far as getting to EML, if the element can survive a long transit (months) then it can can get to EML quite efficiently using a ballistic capture trajectory
. For quick transits, EML2 needs less total dV. This may allow crew to quickly transit to a hab or TMI stage that is bigger because it was able to get there via a slow-boat trajectory.
For chemical propulsion, I believe you can get from EML2 into that elliptical orbit that takes advantage of the Oberth effect with less dV than from EML1.