🚀 go-pugleaf

Hi Forni,

My contribution is down below.

Forni wrote:

> Hi everybody, finally my report is almost finished!
>
> Thanks A LOT to all those nice people who helped me.
>
> This morning I showed my work to my lecturer and il looks like he likes
> it!
> Anyway, I still have to fix few things and I'm asking your help again.
>
> This is the Tsiolkovsky equation with variable gravity inserted:
>
> Vfin = V0 + U ln( Mr+g / Mr ) -g(h)t
>
> is it correct?
>
> Escape velocity from earth is 11.2 km/s
> Which is the most used value in aerospace flight? I mean, that's the
> physical value, but in real flights a little higher value should be
> needed.
>
> What was the orbital velocity of the CSM/LM around the moon?
> How did exactly the LM landed? Which was the techic used?
>
> Did the LM got separated from the CSM and then applied a force in the
> same verse and direction of its orbit so that it could do a ballistic
> arc (relative to the moon) and therefore, land?
> Sort of the inverse example of Newton's cannon ball. The LM was orbiting
> around the moon, at time t it was in a point in orbit like the cannon
> ball at the tip of the mountain, then it applied a force in the same
> direction and verse of it orbit, decelerating its orbital velocity and
> landing with a ballistic arc like the first times when the cannon ball
> can't get to orbit.
> I don't know if I made myself clear :-))))

Yes that's correct.  The LM used its decent engine to drop its orbital
speed, there by
decelerating out of orbit.  The arc of the orbit was determined by the
amount of
fuel to use, and many other factors.  You are most efficient, if you burn to
a stop,
drop straight down, and then burn at the last moment to stop your vertical
velocity just before impact.  But the decent engine can't stop the velocity
on a dime, and I would imagine (guess work on my part), that after a
initial burn to decelerate into a impact arc, that they coasted to get over
the landing
area and into a lower altitude before entering a endgame landing burn.

The endgame burn starts with a mostly horizontal burn component to slow its
horizontal velocity (mostly).  The craft would continue to loose altitude
during this phase of the burn.  As the horizontal velocity dropped the
engine and LM would be slowly swiveled bottom down, so that more and
more of the thrust would be in combating both horizontal and vertical
velocities.  Some horizontal velocity is nice if your not to high up, as you
can
survey landing sites up ahead and let the HV carry you into them.  Finally
when you are over a good size, the last of the HV is killed, and the engine
is used to drop the ship down and land.  Its my belief, listening to the
Apollo 11 landing, that the HV component was finally killed at a height of
only about 100 feet or so, and less then 500 feet it probably was very
small.  Call it only about 20 MPH.

>
> Another possibility, did the lunar module was "shot" (with its engines
> of course) from the CSM in a direction towards the moon with a
> inclination angle that could let it do a quite long ballistic arc too?

No, you must fire the engines into a retro-orbit, decelerating the LM.

Seems to me that I recall that the CSM was posed to go fetch the LM
prior to its endgame burn.  If the LM went into a decelerating orbit, it
would
speed out ahead of the CSM.  The CSM would then be able to catch it
by doing its own retro-burn (only one better), putting it into a lower
faster orbit as well.  This would allow the CSM to overtake the LM, and
rescue it.

>
> Which was the way chosen?

If you fire toward the moon, your HV is unchecked, and you have to
completely remove it at a low altitude.  If you decelerate to get to a
impact orbit, you have already removed part of your HV, and you have
less fuel to burn to get down when you enter the end game burn.

>
> Which were the vertical and horizontal velocity of the lunar module in
> its last minutes of descent?
> I suppose there was a range of vertical and horizontal velocity values
> for the landing of  the lunar module; with higher values, there would
> have been a crash. Do you know these values?

The LM is pretty tall, so I would imagine that the horizontal velocity
would have to be just about zero.  It also had probes that extended
down below the landing legs, so if you have any HV, the probes would
have hit before the legs landed and the craft would have toppled over.

>
>
> That's all! :-)
> Thanks!!!
>
> ciao, Ippolito

Hope that helps,

Larry Taborek