Returning to Earth from Mars - the Physics Involved

[redliox]

Starting a new thread, this time themed around the return from Mars.  I specify not so much the Trans-Earth-Injection, but more specifically the trajectory post-Mars down to Earth: the minor-yet-critical trajectory maneuvers and either a propulsive capture around Earth or aerocapture.  I thought this portion of the Martian journey worth discussing because there are numerous ways to accomplish it:

1) Really Slow Route - SEP flight
2) Slow Route - Classic Hoffman/Type 2 Trajectory
3) Fast Route -  Type 1 Trajectory

In addition to this there is the means of arriving:
A) Propulsive Capture
B) Aerocapture

...further augmented by additional factors:
C) Lunar Gravity Assists
D) Aerobraking

A handful of assumptions can be made about the arriving Martian spacecraft: most likely it is slightly on the light side, as it likely burned at least 2 km/s to escape High Mars Orbit or as much as ~6.5 km/s directly from the surface.  Naturally, an ion-driven craft would have a different setup (including trajectory) from a chemically-driven one, but the one thing they'd have in common would be the need to arrive at Earth with the minimal amount of delta-v required.

Aerocapture, overall, is likely the most efficient way to arrive...but if there is a means to deliver the crew without a semi-hazardous plasma-plunge it likewise should be considered.  Either residual fuel or a dedicated stage (chemical or ion) could brake the vehicle into a High Earth Orbit...from which the crew could aerobrake at a safer pace than aerocapture while benefiting from the same physics.

In addition, although specific to the speedier routes, there is the possibility of utilizing Earth's huge moon (no offense to poor Phobos and Deimos) prior to the braking maneuver.  Especially if the craft is low on fuel or suffering from a cracked heatshield, Luna's minor assistance at the last minute could prove a lifesaver to a returning mission.

I especially stress discussing the velocity/delta-v required for Earth capture.  Some delta-v charts say this figure can be as low as 400 meters/second.  While that number is smaller than the launch from either Earth or Mars earlier in the journey, hitting that figure would be crucial as it grants access to the Earth-Moon system from a high orbit; a destination like the Deep Space Gateway would be a great reprieve.

Share your thoughts and calculations!

[clongton]

I have always favored ion engines throughout the flight, both ways. What I have envisioned for the return trip is not direct return but rendezvous with a waiting Orion in EML-2. Arriving there should be relatively easy and would eliminate the possibility that their earth-landing capability had been damaged sometime during the mission. That also (1) creates the potential for the Mars spacecraft to be reusable and (2) frees up that spacecraft from carrying the mass of Orion all the way to and back from Mars, allowing better use of that mass for mission equipment and/or supplies.

[redliox]

Okay going to attempt some math beyond my expertise and hope someone can verify it...

Utilizing Hop_David's spreadsheet, in this scenario I'm picturing a departure from Deimos' orbit around Mars for Earth; at Earth we'd be aiming for a capture orbit that is just within Earth's gravity well with a periapsis just above Earth's atmosphere to allow for aerobraking post-capture.  The departure from high Mars orbit is about 1.92 km/s, although this isn't the number this thread is after...rather the EOI burn/capture number.  Presuming I'm reading Hop's chart correctly, the arriving spacecraft needs at least 0.75 km/s to break into High Earth Orbit.

Specifics on the orbit:
Periapsis: 250 KM
Apoapsis: 90,000 KM
Orbital Period: 32.3 Hours/1.35 Days

Numerous options naturally available, although in this case I'm picturing an incoming Martian vehicle with anywhere between 2 to 1 km/s of reserve post Mars departure.  Ideally what's desired is a chemical propulsive capture into the high orbit and then a gradual series of aerobraking leading to either an LEO docking or landing on Earth.  Something safe yet fuel-efficient.

[Oli]

1) Really Slow Route - SEP flight

SEP doesn't have to be slow, especially not when it returns empty after a cargo mission. The most efficient way to do fast Mars transfers is with EP (disregarding fancier stuff such as fusion).

Ideally what's desired is a chemical propulsive capture into the high orbit and then a gradual series of aerobraking leading to either an LEO docking or landing on Earth.  Something safe yet fuel-efficient.

If you do propulsive capture you might as well leave the transfer vehicle in cis-lunar space. Use a smaller vehicle to return the crew.
 

[redliox]

If you do propulsive capture you might as well leave the transfer vehicle in cis-lunar space. Use a smaller vehicle to return the crew.

It's an option, but the point of this thread is to discuss the math behind things.  I want to see how much of a propulsive burn is required purely for Earth capture.  Shifting down to LEO will naturally require a huge amount of delta-v for instance, but an incoming ship, especially a transfer vehicle like you're implying, would not likely be targeting it nominally.  Capture orbit is step one, and verifying how much velocity needs to be bled whether by rocketry or aerocapture is important, moreso since this part of the mission is bringing the crew back to the one planet where help could be obtained.

Can anyone verify if ~0.75 km/s sounds about right for Earth capture?  I've seen charts saying it could even be as low as 0.4.

[Oli]

Can anyone verify if ~0.75 km/s sounds about right for Earth capture?  I've seen charts saying it could even be as low as 0.4.

As always it depends on the opportunity.

Wiki says 0.6km/s.
Here it says 0.48 to 0.55km/s for capture to LDHEO for the opportunities 2033-2041 (page 5).

Minimum energy trajectories of course.

[Welsh Dragon]

Interesting topic! Two remarks:
1) Is there any reason you are not considering direct entry and landing of the crew, rather than capturing into an orbit first? (Guessing you want to reuse the transfer vehicle?)
2) How often would you get an opportunity to make use of lunar gravity assists? How constraining on mission planning would this be?

[redliox]

Two remarks:
1) Is there any reason you are not considering direct entry and landing of the crew, rather than capturing into an orbit first? (Guessing you want to reuse the transfer vehicle?)

As I said before not so much discussing the vehicle but rather the conditions any vehicle may have to deal with.  There are currently 3 main ways we could handle arriving at Earth (or technically most other planets): Electric/Ion Drive, Aerocapture, and Chemical rocketry.  Chemical rocketry is the most straightforward of the bunch although ion drive the most efficent and aerocapture the-best-of-both-if-you-can-stand-the-heat.  If you know about the physics of anyone of these I encourage contributing what you know of the math of their arrival physics.

2) How often would you get an opportunity to make use of lunar gravity assists? How constraining on mission planning would this be?

I wish I knew, although I heard lunar gravity assists go hand-in-hand with the Obereth Effect which requires velocity differences and tends to require routes favorable to chemical impulse or aerocapture.  The only other bit of physics I know of regarding planetary bodies (such as our dear Luna) is that to slow down you must cross in front (so their gravity pulls on you and they absorb your velocity) and approach from behind for vice versa (so their gravity speeds you up and you boost off their velocity).  I am unaware how large an effect the Moon could have, which is another reason I setup this thread to nail down such quandaries.

[envy887]

Two remarks:
1) Is there any reason you are not considering direct entry and landing of the crew, rather than capturing into an orbit first? (Guessing you want to reuse the transfer vehicle?)

As I said before not so much discussing the vehicle but rather the conditions any vehicle may have to deal with.  There are currently 3 main ways we could handle arriving at Earth (or technically most other planets): Electric/Ion Drive, Aerocapture, and Chemical rocketry.  Chemical rocketry is the most straightforward of the bunch although ion drive the most efficent and aerocapture the-best-of-both-if-you-can-stand-the-heat.  If you know about the physics of anyone of these I encourage contributing what you know of the math of their arrival physics.

2) How often would you get an opportunity to make use of lunar gravity assists? How constraining on mission planning would this be?

I wish I knew, although I heard lunar gravity assists go hand-in-hand with the Obereth Effect which requires velocity differences and tends to require routes favorable to chemical impulse or aerocapture.  The only other bit of physics I know of regarding planetary bodies (such as our dear Luna) is that to slow down you must cross in front (so their gravity pulls on you and they absorb your velocity) and approach from behind for vice versa (so their gravity speeds you up and you boost off their velocity).  I am unaware how large an effect the Moon could have, which is another reason I setup this thread to nail down such quandaries.

This paper would probably be useful: https://ntrs.nasa.gov/search.jsp?R=19800062349

Max excess velocity that can be scrubbed with a lunar flyby is 1.9 km/s, or 2.2 km/s with a double flyby.

[redliox]

This paper would probably be useful: https://ntrs.nasa.gov/search.jsp?R=19800062349

Max excess velocity that can be scrubbed with a lunar flyby is 1.9 km/s, or 2.2 km/s with a double flyby.

Useful knowledge.  Much appreciated.  The inbound (or hyperpolic while it's flying through solar system still) velocity of a Martian spacecraft seems to vary between about 3.3 km/s for something Hoffman-esque versus up to 7 km/s for 3-or-4 month transits.  My next question would be how slow would a Martian vehicle need to be traveling to gain the maximum benefit of Luna's assist?