I inserted into a solar system n-body simulation a CSM in orbit of the moon at 50000 feet altitude at an inclination and ascending node to match the moon's orbit around the earth and then a 1000 m/s TEI burn when angled appropriately for Earth return. This was the result:
Fight path departing Lunar Orbit:
https://i.imgur.com/vSprVbG.png

Moon-Earth return flight path: (positions of the Earth and Moon and shadows of those objects as of 10 minutes past the TLE burn):
https://i.imgur.com/tW4aBcq.png

Velocity of the Apollo 11 CSM relative to the center of the Earth:
https://i.imgur.com/GQYsNmT.png

As you can see, most of the velocity gain is at the end of the flight. Peak velocity is just before entry to the atmosphere and is 10712 meters/second (23963 miles/hour). That was my "winging it" TEI burn and CSM orbit position and orientation and would have resulted in a return to Earth, but I didn't particularly care where around Earth it reentered so my flight "plan" will be a bit off from the official one, but completely coincidentally would have reentered Earth's atmosphere south-west of Hawaii: https://i.imgur.com/kr6qKNi.png


On Mon, Jul 20, 2020 at 7:13 AM <xxxxxx@gmail.com> wrote:
Those are more like the G-loads I'd have expected... yet....

"On their way back from a lap around the Moon in 1969, the astronauts’ capsule hit a peak of 24,790mph (39,897km/h) relative to planet Earth."

39,897 km/h -> 39,897 m in 3600 seconds -> 11.0825 m/s

So if this is their top speed relative to earth (that may be the issue as it is a fast moving target), that is not 1000 m/s.

So if both your figures from the linked doc and the BBC's figures are accurate, there has to be something to tie them together... but I can't get there.

Was the Earth receding at 990 m/s?

And the other question I had was whether the figures you quoted included any portion of the velocity of their orbit (I'm guessing some of that is preserved if you break orbit right...)?

======

Aside: Your 6.7 m/s should be m/s^2 (a minor thing).

======

All that said, a 0.25 to 1.0 G acceleration (for some time) would be more what I'd have expected.

If you were using some kind of nuclear turbine or some other sort of engine that ejected reaction mass, I wonder practically what speed you could get moving on the way to mars if you planned to stop there, do some stuff and come back (and not arrive back so fast you crashed into Earth or bounced off)?

I'm guessing with some higher G capabilities, you could do 0.5 gees or more continuously or spike up over 1G for short periods several times a day to build up speed. You could orient the vessels floors perpendicular to the main drive when moving at 1 G or less, you could just walk around (maybe up to 1.25 G or something), but anything higher for an acceleration burn, would be sit in our chair, rotate it so your back is to the floor, and the chair would maybe inflate or have gel that would help cushion you. Then you might be able to do limited 1.5 or 2G or more burns for short periods.

The record, I understand, for Gs was a fellow who tried out the original 'rocket sled' (rocket on rails) at a momentary acceleration of 82.6 Gs. (Yes, I said that...) He passed out, but because of the very short duration and his good general conditioning, he recovered fully.

On Mon, Jul 20, 2020 at 8:43 AM Jeffrey Schwartz <xxxxxx@gmail.com> wrote:
I think this is what you're wanting.
https://www.hq.nasa.gov/alsj/a11/a11fltpln_final_reformat.pdf

Go to page 1-8 (page 30 in the file)
It's got time, duration of burn, and delta-v in feet per second

TransLunarInjection (breaking Earth Orbit and heading for the moon) is
a 5:20 minute burn  (320 seconds) for 10,451 fps.
I call that about 3185 m/s over 320sec , or right about 1g
Note this is the last of the fuel in the last stage of the Saturn
launch vehicle, and they dump it after this.

Lunar Orbit Injection is just shy of 6 minutes (5:58.9 or 358.9sec) for 888m/s
I make that 2.47 m/s^2 , or about  1/4g

TransEarthInjection (breaking lunar orbit) is 2:29.4 (149.4 sec) for
3292.7 fps or about 1000m/s
I make that as 6.7m/s, or about 2/3g
(Note the performance increase from not pushing the LM any more)

There's a lot of really neat stuff in that document...
If I had a bunch of free time, it'd be tempting to rewrite it as an
IISS "Mission Planning Workbook", with fill-in-the-blank sections.

On Mon, Jul 20, 2020 at 1:02 AM <xxxxxx@gmail.com> wrote:
>
>
> So this article https://www.bbc.com/future/article/20150809-how-fast-could-humans-travel-safely-through-space got me thinking....
>
> The Apollo 11 capsule was doing around 40K km/h at top speed coming back. The distance to the moon was 377,349km at that time.
>
> Now, I've seen some discussion of the S shaped curve to enter a retrograde orbit around the moon as well, but it was lacking in some of the information I wanted (I did find out about 600 m/s was the velocity you need to enter said orbit).
>
> So if they left the moon starting with 600 m/s and accelerated half way back, flipped, and decelerated, and they were doing 40K km/h at flip over, if I get my math right, they would have reached 40 K km/hr  minus 600 m/s in half the distance of 377K km.
>
> Close to 250 minutes at the flip.
>
> Now, I don't think they did constant acceleration nor constant deceleration nor did they need to get intercept velocity to zero (the atmo helps here on the return).
>
> Punching in:
> V(0) = 600 m/s (orbital velocity of the moon)
> V(final at th flip) = 40,000,000 m/s
> Time = 250 mins
>
> Acceleration then looks to be 42 m/s^2.
>
> That looks like 4 gees for nearly 5 hours accel then flip and decel at the same, so that's about 10 hours of 4 gees... that seems pretty hard on the astronauts.
>
> Am I off in space with my numbers? The G load would be worse if you accelerated like mad for some minutes and then cut off for the rest of the trip to the mid-point.
>
> I'm trying to figure out what sorts of acceleration you could reasonably sustain during system travel without grav plates if the journey took more than a short window (say 10 minutes or so)...
>
> Would system ships in these settings then boost at a maximum of about 1.25 gees for a long haul? Or would they burst at 2-3Gs or more for up to 15 or 30 minutes, then come down, then have another heavy accel again if needed every (insert period of hours)?
>
> Thoughts?
>
> (I'm also thinking about, for say a trip to mars with a conventional rocket, how much would be coasting and what sort of Gs would be applied to get you moving? I'm assuming you couldn't burn all the way due to fuel weight...)
>
> (Also curious if some form of maglev launch from the moon (lower escape velocity) might get you some of your initial velocity for a trip out to mars ...)
>
> (Also curious - having trouble figuring out (via research) how fast one could 'fly' with a good push off inside a station in zero-G - I'm not sure what sort of velocity a straight jump from a surface using strong leg muscles could produce...)
>
> Tom B
>
>
>
>
>
>
> --
> “The only stable state is the one in which all men are equal before the law.” ― Aristotle
>
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