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I have an engine with unlimited $\Delta v$. Don't ask how I got it, it's probably one of my earth changing inventions.

Either way: I no longer like Earth and want to get off (I'm headed for a retirement villa on Olympus Mons), but I don't want to lose the nice home comforts, like a sink with a plug hole, or being able to drink from mugs.

So I need to accelerate constantly in order to maintain the illusion of gravity.

You can call me picky if you like, but I don't want all the hassle of strapping things down at the mid way point when the direction of my burn changes and I experience a brief moment of 0g. I just want down to stay down. I know that a flip'n'burn is the fastest route, and that a Hohmann transfer is the most efficient, but frankly I don't care.

So my question is this:

Does a transfer between Earth and Mars exist such that a spacecraft can maintain a relatively constant 'down' from takeoff to landing?

I don't mind variances in the magnitude of the 'gravity' (let's say 0.5g to 1.1 g is acceptable) or the pitch/yaw of the 'gravity' (I've got wide based mugs, 15 degree pitch is fine). I also have a huge stock of tea bags and cuppa soup, so transfer time isn't an issue.

bonus points for proof/disproof that arbitrary transfers of this nature are possible

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You can just do the flip'n'burn but keep burning all the way through the flip to keep the gravity. If the flip is reasonably quick the perturbation to your orbit will be small. Replan your trajectory a bit and you are there. You also don't want to flip so fast that centrifugal force is a big problem, but if your ship isn't too large that is not a problem. – Ross Millikan Feb 2 at 2:37
    
This doesn't feel like Worldbuilding, but rather a fit for Physics or Astronomy. – Frostfyre Feb 2 at 4:23
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"it's probably one of my earth changing inventions" Oh no...you only broke Newton's 3rd, no biggy. – Aron Feb 2 at 7:12
    
@Frostfyre: I placed this in Worldbuilding because the guys in astronomy and physics don't like it when you break conservation laws. Not that that detail turned out to be important, but... – Joe Bloggs Feb 2 at 9:18
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@Aron : When it comes to my earth changing inventions Newton is the least of your worries. – Joe Bloggs Feb 2 at 9:19

Yes

but you have to violate one of your conditions.

Acceleration

To launch from Earth, your acceleration must exceed Earth's gravitational acceleration. So assume an acceleration of 1.1 g (within bounds).

Trajectory

There exists a family of trajectories called Brachistochrone trajectories for vehicles moving at constant acceleration on a trajectory. This is within your constraints.

Space Craft Orientation

Brachistochrone trajectories require a flip at the mid-point so the ship can begin deceleration. The conventional way to think about this is, turn off your engines, rotate the ship 180 degrees, and then restart the engines. This, of course, causes a period of zero-g for a short time during the flight.

In order to remain under constant acceleration, the ship must fly something called a "skew flip" (there's a nice diagram at the link that I can't paste in here), in which you flip the vehicle while remaining under constant acceleration. Since Pitch & Yaw are used to describe the ships orientation to its velocity vector, you violate the pitch/yaw constraint.

As a passenger, you mostly won't feel this because velocity is relative. You will perceive a constant acceleration and, except for possibly a little vertigo, not notice the ship rotation.

The skew flip, violates your minimizing the pitch/yaw - except that the passengers won't really notice this pitch/yaw change. In space, we don't care about our orientation to the velocity vector except in relation to how it causes our velocity vector to change.

More Info

The first place I've seen this term is from Have Spacesuit, Will Travel (and this book appears to be free on Google). The book is a frolicking romp through space but most of the science in it is very real.

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Well, when I said pitch/yaw I really meant what the passenger felt anyway, I didn't even think that it would be defined relative to velocity. +1 for nailing that answer! – Joe Bloggs Feb 1 at 22:48
    
@JoeBloggs These used to be pretty common in classic Science Fiction such as Heinlein IIRC. You could probably find one that has a description of the trip. – Ville Niemi Feb 1 at 23:22
    
I recently read "Have Space Suit, Will Travel" by Heinlein and it does indeed have a description of the trip. – Jim2B Feb 1 at 23:53
    
If you spun around really quickly you would have a noticeable gravity vector change due to the action of the thrusters themselves, and centrifugal and coriolis forces. But as long as you take a couple minutes or longer to do the turn, gravity will stay where you want within limits. The little bit of "sideways" burn you get from that is easily trimmed out over the remainder of an interplanetary trip. – hobbs Feb 2 at 2:11
    
You might want to note that brachistochrone trajectories don't work when there's something else on the path - for example, the Sun. You might want to pick a more arced path if that's the case :) – Luaan Feb 2 at 10:07

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