[Lex Computer & Tech Group/LCTG] NASA thrusters

[Ted Kochanski]

John, et al

The basic are simple the Hall Effect is a bit more complicated


Fundamentally the rocket equation [it is rocket science] is that you throw
mass out the back and that makes you accelerate forward [Newton Law of
Action/Reaction and F=ma]

So you start with the mass of your total system [rocket structure +
propellent] M0 and its initial velocity V0  -- -this gives you the initial
momentum of the rocket
After ejecting the increment of propellent out the rear nozzle -- you will
achieve a new mass of the rocket M1= (M0-dM) where dM=M0-M1 is the
reduction in the mass of the rocket] and where [dm is the mass of the
propellant expelled out the nozzle at  velocity Vp
There is also a new velocity of the rocket V1 where dV = V1-V0

Now of course you need to put everything into the same frame of reference
[in Newton's View the Fixed stars] so the velocity of the expelled
propellent is only Vp referenced to the rocket -- to the fixed stars the
velocity of the expelled propellant is V of the rocket relative to the
fixed stars minus the propellent ejection velocity

Conservation of the total momentum of the system
allows you to compute the change in the rocket's momentum after the
expulsion of the small amount of mass dm is then
M0dV=dmdv+dmv
Note the dmdV term is the result of the resultant change in propellant
velocity relative to the fixed stars but since this is multiplied by the
minute change in mass -- the term can essentially be ignored especially for
a rocket whose mass is much more than the propellent [e.g. for an ionic
thruster]

dV=−Vp dm/M0

if you want to see what happens for a continuing "thruster firing" all you
need to do is to Integrate from the initial mass M0 to the final mass Mf of
the rocket to get the overall change in velocity of the rocket ΔV

This results in the famous logarithmic relationship with mass due to the
Russian physicist Konstantin Tsiolkovsky in 1897.
It gives us the change of velocity that the rocket obtains from burning a
mass of fuel that decreases the total rocket mass from  M0 to Mf

ΔV=Vpln(M0/Mf)
This result is called the rocket equation. It was originally derived by the
Soviet physicist Konstantin Tsiolkovsky in 1897. It gives us the change of
velocity that the rocket obtains from burning a mass of fuel that decreases
the total rocket mass from M0 down to Mf. As expected, the relationship
between ΔV and the change of mass of the rocket is nonlinear.

So the key to ionic and fission/fusion thermal drives is that you can
achieve much higher Vp than you can with chemical combustion.  The other
advantage is that you can use much less propellent to achieve the same ΔV

Ted

PS: check out the following for even more information on such matters
https://www.nasa.gov/smallsat-institute/sst-soa/in-space_propulsion/


On Wed, Oct 11, 2023 at 4:28 PM John Rudy via LCTG <lctg at lists.toku.us>
wrote:

> I just read this 3 times and still don’t understand it.  Of course there
> is a sentence in the middle that reminds me of my high school teacher’s
> “the proof will be left to the reader”.
>
> John
>
> ==================================================
>
>
>
> *Sci-fi propulsion is now a reality*
>
> David Oh, chief engineer for operations at NASA's Jet Propulsion
> Laboratory says this will be the first-ever mission to use Hall Effect
> thrusters in interplanetary space. What does that mean? Well basically,
> Hall Effect thrusters use electricity to ionize xenon gas — ionization
> refers to removing or adding one or two electrons from the atoms that make
> up a substance. In this case, the substance is a gas.
>
> Upon ionization, those atoms gain a charge. (Regular old atoms have
> neutral charges because their positive proton count and negative electron
> count are equal. Remove some electrons, for instance, and you lose some
> negativity.) The result? Ions. Then, those charged ions form an electric
> field which can, through a series of complicated steps, propel an object.
> In this case, that's the Psyche spacecraft.
>
> "They come out of the thruster going at 15 kilometers per second, or nine
> miles per second," Oh said. "That's five times faster than the speed of the
> fuel coming out of a regular chemical rocket."
>
>
>
>
>
> John Rudy
>
>
>
> 781-861-0402
>
> 781-718-8334  cell
>
> 13 Hawthorne Lane
>
> Bedford MA
>
> jjrudy1 at comcast.net
>
>
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